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

Percentage Accurate: 73.9% → 83.4%

Time: 18.4s

Alternatives: 17

Speedup: 0.5×

• 57.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. distribute-lft-out-- 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in a around inf 62.2%

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

      1. +-commutative 62.2%

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

      2. neg-mul-1 62.2%

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

      3. unsub-neg 62.2%

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

      4. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

4. Final simplification 86.9%

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

Alternative 2: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.95 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(a \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.95e+208)
   (* t (* a (- (* b (/ i a)) x)))
   (if (<= i -1.65e+31)
     (+ (* y (- (* x z) (* i j))) (* b (* t i)))
     (if (<= i 2.3e+67)
       (+ (* x (- (* y z) (* t a))) (* a (* c j)))
       (* i (- (* t b) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.95e+208) {
		tmp = t * (a * ((b * (i / a)) - x));
	} else if (i <= -1.65e+31) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if (i <= 2.3e+67) {
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.95d+208)) then
        tmp = t * (a * ((b * (i / a)) - x))
    else if (i <= (-1.65d+31)) then
        tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
    else if (i <= 2.3d+67) then
        tmp = (x * ((y * z) - (t * a))) + (a * (c * j))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.95e+208) {
		tmp = t * (a * ((b * (i / a)) - x));
	} else if (i <= -1.65e+31) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if (i <= 2.3e+67) {
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.95e+208:
		tmp = t * (a * ((b * (i / a)) - x))
	elif i <= -1.65e+31:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	elif i <= 2.3e+67:
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.95e+208)
		tmp = Float64(t * Float64(a * Float64(Float64(b * Float64(i / a)) - x)));
	elseif (i <= -1.65e+31)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)));
	elseif (i <= 2.3e+67)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(a * Float64(c * j)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.95e+208)
		tmp = t * (a * ((b * (i / a)) - x));
	elseif (i <= -1.65e+31)
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	elseif (i <= 2.3e+67)
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.95e+208], N[(t * N[(a * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.65e+31], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e+67], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.95e208

   1. Initial program 39.6%

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

   3. Taylor expanded in t around inf 78.5%

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

      1. distribute-lft-out-- 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in a around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. neg-mul-1 82.7%

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

      3. unsub-neg 82.7%

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

      4. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -1.95e208 < i < -1.64999999999999996e31

   1. Initial program 80.0%

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

      1. add-cube-cbrt 79.8%

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

      2. pow3 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 79.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. mul-1-neg 77.0%

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

      4. unsub-neg 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in c around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 74.2%

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

      4. mul-1-neg 74.2%

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

      5. associate-*r* 71.3%

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

      6. distribute-lft-neg-in 71.3%

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

      7. distribute-rgt-neg-in 71.3%

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

      8. distribute-rgt-in 71.3%

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

      9. distribute-rgt-neg-in 71.3%

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

      10. unsub-neg 71.3%

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

      11. +-commutative 71.3%

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

      12. *-commutative 71.3%

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

      13. associate-*r* 71.3%

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

      14. mul-1-neg 71.3%

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

      15. associate-*r* 71.2%

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

      16. distribute-lft-neg-in 71.2%

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

      17. mul-1-neg 71.2%

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

      18. distribute-rgt-in 71.2%

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

      19. mul-1-neg 71.2%

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

   10. Simplified 71.2%

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

   11. Taylor expanded in a around 0 71.4%

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

   if -1.64999999999999996e31 < i < 2.2999999999999999e67

   1. Initial program 81.6%

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

      1. add-cube-cbrt 81.5%

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

      2. pow3 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. *-commutative 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in c around inf 63.4%

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

   if 2.2999999999999999e67 < i

   1. Initial program 60.3%

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

   3. Taylor expanded in a around 0 68.0%

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

   4. Taylor expanded in i around -inf 77.6%

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

      1. associate-*r* 77.6%

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

      2. neg-mul-1 77.6%

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

      3. *-commutative 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.95 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(a \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -4.5e+67)
     t_2
     (if (<= b -1.95e-25)
       t_1
       (if (<= b -7.5e-280)
         (* x (- (* y z) (* t a)))
         (if (<= b 4.4e+43) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.5e+67) {
		tmp = t_2;
	} else if (b <= -1.95e-25) {
		tmp = t_1;
	} else if (b <= -7.5e-280) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 4.4e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-4.5d+67)) then
        tmp = t_2
    else if (b <= (-1.95d-25)) then
        tmp = t_1
    else if (b <= (-7.5d-280)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 4.4d+43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.5e+67) {
		tmp = t_2;
	} else if (b <= -1.95e-25) {
		tmp = t_1;
	} else if (b <= -7.5e-280) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 4.4e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.5e+67:
		tmp = t_2
	elif b <= -1.95e-25:
		tmp = t_1
	elif b <= -7.5e-280:
		tmp = x * ((y * z) - (t * a))
	elif b <= 4.4e+43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.5e+67)
		tmp = t_2;
	elseif (b <= -1.95e-25)
		tmp = t_1;
	elseif (b <= -7.5e-280)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 4.4e+43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.5e+67)
		tmp = t_2;
	elseif (b <= -1.95e-25)
		tmp = t_1;
	elseif (b <= -7.5e-280)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 4.4e+43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+67], t$95$2, If[LessEqual[b, -1.95e-25], t$95$1, If[LessEqual[b, -7.5e-280], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+43], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4999999999999998e67 or 4.40000000000000001e43 < b

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -4.4999999999999998e67 < b < -1.95e-25 or -7.4999999999999999e-280 < b < 4.40000000000000001e43

   1. Initial program 68.2%

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

      1. add-cube-cbrt 68.1%

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

      2. pow3 68.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 68.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 68.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around 0 68.3%

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

      1. +-commutative 68.3%

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

      2. *-commutative 68.3%

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

      3. mul-1-neg 68.3%

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

      4. unsub-neg 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in j around inf 63.0%

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

      1. sub-neg 63.0%

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

      2. *-commutative 63.0%

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

      3. sub-neg 63.0%

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

   10. Simplified 63.0%

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

   if -1.95e-25 < b < -7.4999999999999999e-280

   1. Initial program 76.0%

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

      1. add-cube-cbrt 76.0%

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

      2. pow3 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. *-commutative 76.0%

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

      3. mul-1-neg 76.0%

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

      4. unsub-neg 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in c around 0 64.3%

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

      1. +-commutative 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-*r* 62.8%

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

      4. mul-1-neg 62.8%

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

      5. associate-*r* 67.4%

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

      6. distribute-lft-neg-in 67.4%

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

      7. distribute-rgt-neg-in 67.4%

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

      8. distribute-rgt-in 67.4%

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

      9. distribute-rgt-neg-in 67.4%

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

      10. unsub-neg 67.4%

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

      11. +-commutative 67.4%

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

      12. *-commutative 67.4%

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

      13. associate-*r* 65.8%

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

      14. mul-1-neg 65.8%

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

      15. associate-*r* 69.0%

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

      16. distribute-lft-neg-in 69.0%

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

      17. mul-1-neg 69.0%

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

      18. distribute-rgt-in 70.6%

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

      19. mul-1-neg 70.6%

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

   10. Simplified 70.6%

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

   11. Taylor expanded in x around inf 60.7%

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

       1. *-commutative 60.7%

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

   13. Simplified 60.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3e+81)
   (* t (- (* b i) (* x a)))
   (if (<= b 2.3e+16)
     (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
     (+ (* b (- (* t i) (* z c))) (* 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 <= -3e+81) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 2.3e+16) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = (b * ((t * i) - (z * c))) + (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 <= (-3d+81)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 2.3d+16) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else
        tmp = (b * ((t * i) - (z * c))) + (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 <= -3e+81) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 2.3e+16) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3e+81:
		tmp = t * ((b * i) - (x * a))
	elif b <= 2.3e+16:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	else:
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3e+81)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 2.3e+16)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + 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 <= -3e+81)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 2.3e+16)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	else
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3e+81], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+16], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999997e81

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. distribute-lft-out-- 69.6%

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

   5. Simplified 69.6%

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

   if -2.99999999999999997e81 < b < 2.3e16

   1. Initial program 73.2%

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

   3. Taylor expanded in b around 0 74.6%

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

   if 2.3e16 < b

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0 83.4%

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

   5. Simplified 83.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 170000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.2e+81)
   (* t (- (* b i) (* x a)))
   (if (<= b 170000000000.0)
     (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
     (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.2e+81) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 170000000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4.2d+81)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 170000000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.2e+81) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 170000000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.2e+81:
		tmp = t * ((b * i) - (x * a))
	elif b <= 170000000000.0:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.2e+81)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 170000000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.2e+81)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 170000000000.0)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.2e+81], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 170000000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1999999999999997e81

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. distribute-lft-out-- 69.6%

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

   5. Simplified 69.6%

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

   if -4.1999999999999997e81 < b < 1.7e11

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0 76.0%

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

   if 1.7e11 < b

   1. Initial program 73.0%

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

   3. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 170000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-286}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+135}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))))
   (if (<= x -1.5e+78)
     t_1
     (if (<= x -1.75e-286)
       (* a (* c j))
       (if (<= x 7.4e-113)
         (* i (* t b))
         (if (<= x 5.4e+135) (* i (* j (- y))) 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 * (x * -a);
	double tmp;
	if (x <= -1.5e+78) {
		tmp = t_1;
	} else if (x <= -1.75e-286) {
		tmp = a * (c * j);
	} else if (x <= 7.4e-113) {
		tmp = i * (t * b);
	} else if (x <= 5.4e+135) {
		tmp = i * (j * -y);
	} 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 * (x * -a)
    if (x <= (-1.5d+78)) then
        tmp = t_1
    else if (x <= (-1.75d-286)) then
        tmp = a * (c * j)
    else if (x <= 7.4d-113) then
        tmp = i * (t * b)
    else if (x <= 5.4d+135) then
        tmp = i * (j * -y)
    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 * (x * -a);
	double tmp;
	if (x <= -1.5e+78) {
		tmp = t_1;
	} else if (x <= -1.75e-286) {
		tmp = a * (c * j);
	} else if (x <= 7.4e-113) {
		tmp = i * (t * b);
	} else if (x <= 5.4e+135) {
		tmp = i * (j * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	tmp = 0
	if x <= -1.5e+78:
		tmp = t_1
	elif x <= -1.75e-286:
		tmp = a * (c * j)
	elif x <= 7.4e-113:
		tmp = i * (t * b)
	elif x <= 5.4e+135:
		tmp = i * (j * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (x <= -1.5e+78)
		tmp = t_1;
	elseif (x <= -1.75e-286)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= 7.4e-113)
		tmp = Float64(i * Float64(t * b));
	elseif (x <= 5.4e+135)
		tmp = Float64(i * Float64(j * Float64(-y)));
	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 * (x * -a);
	tmp = 0.0;
	if (x <= -1.5e+78)
		tmp = t_1;
	elseif (x <= -1.75e-286)
		tmp = a * (c * j);
	elseif (x <= 7.4e-113)
		tmp = i * (t * b);
	elseif (x <= 5.4e+135)
		tmp = i * (j * -y);
	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[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+78], t$95$1, If[LessEqual[x, -1.75e-286], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-113], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e+135], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.49999999999999991e78 or 5.3999999999999997e135 < x

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf 65.9%

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

      1. distribute-lft-out-- 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in a around inf 56.9%

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

      1. associate-*r* 56.9%

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

      2. neg-mul-1 56.9%

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

   8. Simplified 56.9%

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

   if -1.49999999999999991e78 < x < -1.74999999999999994e-286

   1. Initial program 72.1%

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

   3. Taylor expanded in a around inf 42.5%

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

      1. +-commutative 42.5%

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

      2. mul-1-neg 42.5%

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

      3. unsub-neg 42.5%

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

   5. Simplified 42.5%

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

   6. Taylor expanded in c around inf 34.2%

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

   if -1.74999999999999994e-286 < x < 7.3999999999999996e-113

   1. Initial program 70.8%

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

   3. Taylor expanded in t around inf 50.5%

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

      1. distribute-lft-out-- 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in a around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. neg-mul-1 50.6%

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

      3. unsub-neg 50.6%

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

      4. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in a around 0 47.0%

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

       1. *-commutative 47.0%

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

   11. Simplified 47.0%

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

   12. Taylor expanded in b around 0 47.0%

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

       1. associate-*r* 47.1%

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

       2. *-commutative 47.1%

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

       3. associate-*r* 51.2%

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

   14. Simplified 51.2%

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

   if 7.3999999999999996e-113 < x < 5.3999999999999997e135

   1. Initial program 74.6%

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

   3. Taylor expanded in y around inf 51.6%

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

      1. +-commutative 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%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in z around 0 36.7%

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

      1. mul-1-neg 36.7%

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

      2. *-commutative 36.7%

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

      3. distribute-rgt-neg-in 36.7%

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

      4. *-commutative 36.7%

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

      5. mul-1-neg 36.7%

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

      6. associate-*r* 36.7%

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

      7. neg-mul-1 36.7%

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

   8. Simplified 36.7%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-286}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+135}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))) (t_2 (* i (* j (- y)))))
   (if (<= y -2.3e+88)
     t_2
     (if (<= y 1.3e-233)
       t_1
       (if (<= y 7e-32) (* i (* t b)) (if (<= y 2e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double t_2 = i * (j * -y);
	double tmp;
	if (y <= -2.3e+88) {
		tmp = t_2;
	} else if (y <= 1.3e-233) {
		tmp = t_1;
	} else if (y <= 7e-32) {
		tmp = i * (t * b);
	} else if (y <= 2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * -x)
    t_2 = i * (j * -y)
    if (y <= (-2.3d+88)) then
        tmp = t_2
    else if (y <= 1.3d-233) then
        tmp = t_1
    else if (y <= 7d-32) then
        tmp = i * (t * b)
    else if (y <= 2d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double t_2 = i * (j * -y);
	double tmp;
	if (y <= -2.3e+88) {
		tmp = t_2;
	} else if (y <= 1.3e-233) {
		tmp = t_1;
	} else if (y <= 7e-32) {
		tmp = i * (t * b);
	} else if (y <= 2e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	t_2 = i * (j * -y)
	tmp = 0
	if y <= -2.3e+88:
		tmp = t_2
	elif y <= 1.3e-233:
		tmp = t_1
	elif y <= 7e-32:
		tmp = i * (t * b)
	elif y <= 2e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	t_2 = Float64(i * Float64(j * Float64(-y)))
	tmp = 0.0
	if (y <= -2.3e+88)
		tmp = t_2;
	elseif (y <= 1.3e-233)
		tmp = t_1;
	elseif (y <= 7e-32)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 2e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	t_2 = i * (j * -y);
	tmp = 0.0;
	if (y <= -2.3e+88)
		tmp = t_2;
	elseif (y <= 1.3e-233)
		tmp = t_1;
	elseif (y <= 7e-32)
		tmp = i * (t * b);
	elseif (y <= 2e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+88], t$95$2, If[LessEqual[y, 1.3e-233], t$95$1, If[LessEqual[y, 7e-32], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000002e88 or 2.00000000000000001e41 < y

   1. Initial program 59.6%

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

   3. Taylor expanded in y around inf 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in z around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. *-commutative 43.1%

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

      3. distribute-rgt-neg-in 43.1%

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

      4. *-commutative 43.1%

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

      5. mul-1-neg 43.1%

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

      6. associate-*r* 43.1%

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

      7. neg-mul-1 43.1%

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

   8. Simplified 43.1%

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

   if -2.3000000000000002e88 < y < 1.2999999999999999e-233 or 6.9999999999999997e-32 < y < 2.00000000000000001e41

   1. Initial program 82.1%

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

   3. Taylor expanded in a around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in c around 0 41.0%

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

      1. neg-mul-1 41.0%

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

      2. distribute-rgt-neg-in 41.0%

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

   8. Simplified 41.0%

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

   if 1.2999999999999999e-233 < y < 6.9999999999999997e-32

   1. Initial program 86.2%

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

   3. Taylor expanded in t around inf 63.0%

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

      1. distribute-lft-out-- 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in a around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. neg-mul-1 57.0%

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

      3. unsub-neg 57.0%

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

      4. associate-/l* 56.9%

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

   8. Simplified 56.9%

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

   9. Taylor expanded in a around 0 57.3%

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

       1. *-commutative 57.3%

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

   11. Simplified 57.3%

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

   12. Taylor expanded in b around 0 57.3%

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

       1. associate-*r* 52.2%

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

       2. *-commutative 52.2%

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

       3. associate-*r* 59.8%

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

   14. Simplified 59.8%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+288}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-286}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= x -2.15e+288)
     (* z (* x y))
     (if (<= x -8.5e+77)
       t_1
       (if (<= x -1.9e-286)
         (* a (* c j))
         (if (<= x 1.75e-112) (* i (* t 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 = a * (t * -x);
	double tmp;
	if (x <= -2.15e+288) {
		tmp = z * (x * y);
	} else if (x <= -8.5e+77) {
		tmp = t_1;
	} else if (x <= -1.9e-286) {
		tmp = a * (c * j);
	} else if (x <= 1.75e-112) {
		tmp = i * (t * 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 = a * (t * -x)
    if (x <= (-2.15d+288)) then
        tmp = z * (x * y)
    else if (x <= (-8.5d+77)) then
        tmp = t_1
    else if (x <= (-1.9d-286)) then
        tmp = a * (c * j)
    else if (x <= 1.75d-112) then
        tmp = i * (t * 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 = a * (t * -x);
	double tmp;
	if (x <= -2.15e+288) {
		tmp = z * (x * y);
	} else if (x <= -8.5e+77) {
		tmp = t_1;
	} else if (x <= -1.9e-286) {
		tmp = a * (c * j);
	} else if (x <= 1.75e-112) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if x <= -2.15e+288:
		tmp = z * (x * y)
	elif x <= -8.5e+77:
		tmp = t_1
	elif x <= -1.9e-286:
		tmp = a * (c * j)
	elif x <= 1.75e-112:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (x <= -2.15e+288)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= -8.5e+77)
		tmp = t_1;
	elseif (x <= -1.9e-286)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= 1.75e-112)
		tmp = Float64(i * Float64(t * 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 = a * (t * -x);
	tmp = 0.0;
	if (x <= -2.15e+288)
		tmp = z * (x * y);
	elseif (x <= -8.5e+77)
		tmp = t_1;
	elseif (x <= -1.9e-286)
		tmp = a * (c * j);
	elseif (x <= 1.75e-112)
		tmp = i * (t * 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[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+288], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e+77], t$95$1, If[LessEqual[x, -1.9e-286], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-112], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1500000000000001e288

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -2.1500000000000001e288 < x < -8.50000000000000018e77 or 1.74999999999999997e-112 < x

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in c around 0 41.9%

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

      1. neg-mul-1 41.9%

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

      2. distribute-rgt-neg-in 41.9%

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

   8. Simplified 41.9%

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

   if -8.50000000000000018e77 < x < -1.9000000000000001e-286

   1. Initial program 72.1%

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

   3. Taylor expanded in a around inf 42.5%

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

      1. +-commutative 42.5%

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

      2. mul-1-neg 42.5%

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

      3. unsub-neg 42.5%

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

   5. Simplified 42.5%

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

   6. Taylor expanded in c around inf 34.2%

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

   if -1.9000000000000001e-286 < x < 1.74999999999999997e-112

   1. Initial program 70.8%

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

   3. Taylor expanded in t around inf 50.5%

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

      1. distribute-lft-out-- 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in a around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. neg-mul-1 50.6%

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

      3. unsub-neg 50.6%

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

      4. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in a around 0 47.0%

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

       1. *-commutative 47.0%

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

   11. Simplified 47.0%

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

   12. Taylor expanded in b around 0 47.0%

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

       1. associate-*r* 47.1%

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

       2. *-commutative 47.1%

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

       3. associate-*r* 51.2%

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

   14. Simplified 51.2%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+288}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-286}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+82} \lor \neg \left(i \leq 1.4 \cdot 10^{+68}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.4e+82) (not (<= i 1.4e+68)))
   (* i (- (* t b) (* y j)))
   (+ (* x (- (* y z) (* t a))) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.4e+82) || !(i <= 1.4e+68)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.4d+82)) .or. (.not. (i <= 1.4d+68))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) + (a * (c * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.4e+82) || !(i <= 1.4e+68)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.4e+82) or not (i <= 1.4e+68):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.4e+82) || !(i <= 1.4e+68))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(a * Float64(c * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.4e+82) || ~((i <= 1.4e+68)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.4e+82], N[Not[LessEqual[i, 1.4e+68]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.4e82 or 1.4e68 < i

   1. Initial program 61.2%

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

   3. Taylor expanded in a around 0 67.0%

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

   4. Taylor expanded in i around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

      3. *-commutative 72.4%

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

   6. Simplified 72.4%

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

   if -1.4e82 < i < 1.4e68

   1. Initial program 81.6%

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

      1. add-cube-cbrt 81.5%

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

      2. pow3 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in x around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in c around inf 63.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+82} \lor \neg \left(i \leq 1.4 \cdot 10^{+68}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-8} \lor \neg \left(t \leq 7.8 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.7e-8) (not (<= t 7.8e-29)))
   (* t (- (* b i) (* x a)))
   (- (* x (* y z)) (* j (- (* y i) (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -2.7e-8) || !(t <= 7.8e-29)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-2.7d-8)) .or. (.not. (t <= 7.8d-29))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -2.7e-8) || !(t <= 7.8e-29)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -2.7e-8) or not (t <= 7.8e-29):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.7e-8) || !(t <= 7.8e-29))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -2.7e-8) || ~((t <= 7.8e-29)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.7e-8], N[Not[LessEqual[t, 7.8e-29]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000002e-8 or 7.7999999999999995e-29 < t

   1. Initial program 63.7%

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

   3. Taylor expanded in t around inf 66.2%

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

      1. distribute-lft-out-- 66.2%

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

   5. Simplified 66.2%

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

   if -2.70000000000000002e-8 < t < 7.7999999999999995e-29

   1. Initial program 86.2%

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

      1. add-cube-cbrt 86.0%

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

      2. pow3 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 86.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around inf 62.9%

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

      1. *-commutative 62.9%

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

   7. Simplified 62.9%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-8} \lor \neg \left(t \leq 7.8 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.25e-99)
     t_1
     (if (<= i -2e-284)
       (* x (- (* y z) (* t a)))
       (if (<= i 4e+68) (* a (- (* c j) (* 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e-99) {
		tmp = t_1;
	} else if (i <= -2e-284) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 4e+68) {
		tmp = a * ((c * j) - (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 = i * ((t * b) - (y * j))
    if (i <= (-1.25d-99)) then
        tmp = t_1
    else if (i <= (-2d-284)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 4d+68) then
        tmp = a * ((c * j) - (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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e-99) {
		tmp = t_1;
	} else if (i <= -2e-284) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 4e+68) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.25e-99:
		tmp = t_1
	elif i <= -2e-284:
		tmp = x * ((y * z) - (t * a))
	elif i <= 4e+68:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.25e-99)
		tmp = t_1;
	elseif (i <= -2e-284)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 4e+68)
		tmp = Float64(a * Float64(Float64(c * j) - 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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.25e-99)
		tmp = t_1;
	elseif (i <= -2e-284)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 4e+68)
		tmp = a * ((c * j) - (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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e-99], t$95$1, If[LessEqual[i, -2e-284], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+68], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.24999999999999992e-99 or 3.99999999999999981e68 < i

   1. Initial program 68.5%

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

   3. Taylor expanded in a around 0 64.6%

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

   4. Taylor expanded in i around -inf 66.4%

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

      1. associate-*r* 66.4%

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

      2. neg-mul-1 66.4%

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

      3. *-commutative 66.4%

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

   6. Simplified 66.4%

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

   if -1.24999999999999992e-99 < i < -2.00000000000000007e-284

   1. Initial program 79.8%

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

      1. add-cube-cbrt 79.8%

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

      2. pow3 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 79.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. *-commutative 74.1%

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

      3. mul-1-neg 74.1%

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

      4. unsub-neg 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in c around 0 60.4%

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

      1. +-commutative 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*r* 56.7%

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

      4. mul-1-neg 56.7%

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

      5. associate-*r* 59.5%

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

      6. distribute-lft-neg-in 59.5%

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

      7. distribute-rgt-neg-in 59.5%

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

      8. distribute-rgt-in 59.5%

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

      9. distribute-rgt-neg-in 59.5%

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

      10. unsub-neg 59.5%

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

      11. +-commutative 59.5%

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

      12. *-commutative 59.5%

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

      13. associate-*r* 65.1%

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

      14. mul-1-neg 65.1%

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

      15. associate-*r* 65.1%

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

      16. distribute-lft-neg-in 65.1%

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

      17. mul-1-neg 65.1%

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

      18. distribute-rgt-in 65.1%

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

      19. mul-1-neg 65.1%

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

   10. Simplified 65.1%

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

   11. Taylor expanded in x around inf 63.4%

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

       1. *-commutative 63.4%

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

   13. Simplified 63.4%

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

   if -2.00000000000000007e-284 < i < 3.99999999999999981e68

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

   5. Simplified 65.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 10^{+44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -1e+80)
     t_1
     (if (<= b -1.15e-279)
       (* a (- (* c j) (* x t)))
       (if (<= b 1e+44) (* j (- (* a c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1e+80) {
		tmp = t_1;
	} else if (b <= -1.15e-279) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1e+44) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-1d+80)) then
        tmp = t_1
    else if (b <= (-1.15d-279)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 1d+44) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1e+80) {
		tmp = t_1;
	} else if (b <= -1.15e-279) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1e+44) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1e+80:
		tmp = t_1
	elif b <= -1.15e-279:
		tmp = a * ((c * j) - (x * t))
	elif b <= 1e+44:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1e+80)
		tmp = t_1;
	elseif (b <= -1.15e-279)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 1e+44)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1e+80)
		tmp = t_1;
	elseif (b <= -1.15e-279)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 1e+44)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+80], t$95$1, If[LessEqual[b, -1.15e-279], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+44], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1e80 or 1.0000000000000001e44 < b

   1. Initial program 75.1%

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

   3. Taylor expanded in b around inf 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   if -1e80 < b < -1.14999999999999998e-279

   1. Initial program 76.6%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   if -1.14999999999999998e-279 < b < 1.0000000000000001e44

   1. Initial program 66.2%

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

      1. add-cube-cbrt 66.2%

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

      2. pow3 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. *-commutative 66.4%

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

      3. mul-1-neg 66.4%

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

      4. unsub-neg 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in j around inf 62.0%

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

      1. sub-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. sub-neg 62.0%

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

   10. Simplified 62.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 10^{+44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+79} \lor \neg \left(b \leq 13600000000000\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.5e+79) (not (<= b 13600000000000.0)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.5e+79) || !(b <= 13600000000000.0)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.5d+79)) .or. (.not. (b <= 13600000000000.0d0))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.5e+79) || !(b <= 13600000000000.0)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.5e+79) or not (b <= 13600000000000.0):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.5e+79) || !(b <= 13600000000000.0))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.5e+79) || ~((b <= 13600000000000.0)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.5e+79], N[Not[LessEqual[b, 13600000000000.0]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5e79 or 1.36e13 < b

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -2.5e79 < b < 1.36e13

   1. Initial program 74.5%

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

   3. Taylor expanded in a around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

   5. Simplified 51.2%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+79} \lor \neg \left(b \leq 13600000000000\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.05 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1e+115)
   (* t (* b i))
   (if (<= i 3.05e+81) (* a (- (* c j) (* x t))) (* y (* i (- j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1e+115) {
		tmp = t * (b * i);
	} else if (i <= 3.05e+81) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1d+115)) then
        tmp = t * (b * i)
    else if (i <= 3.05d+81) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1e+115) {
		tmp = t * (b * i);
	} else if (i <= 3.05e+81) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1e+115:
		tmp = t * (b * i)
	elif i <= 3.05e+81:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1e+115)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 3.05e+81)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1e+115)
		tmp = t * (b * i);
	elseif (i <= 3.05e+81)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1e+115], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.05e+81], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1e115

   1. Initial program 59.7%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. distribute-lft-out-- 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around 0 58.0%

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

   if -1e115 < i < 3.05000000000000019e81

   1. Initial program 79.7%

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

   3. Taylor expanded in a around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 53.0%

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

   if 3.05000000000000019e81 < i

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

      4. *-commutative 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in z around 0 49.0%

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

      1. neg-mul-1 49.0%

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

      2. distribute-rgt-neg-in 49.0%

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

   8. Simplified 49.0%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.05 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4800000 \lor \neg \left(c \leq 3.95 \cdot 10^{+133}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4800000.0) (not (<= c 3.95e+133)))
   (* a (* c j))
   (* i (* t 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 ((c <= -4800000.0) || !(c <= 3.95e+133)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * 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 ((c <= (-4800000.0d0)) .or. (.not. (c <= 3.95d+133))) then
        tmp = a * (c * j)
    else
        tmp = i * (t * 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 ((c <= -4800000.0) || !(c <= 3.95e+133)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -4800000.0) or not (c <= 3.95e+133):
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -4800000.0) || !(c <= 3.95e+133))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -4800000.0) || ~((c <= 3.95e+133)))
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -4800000.0], N[Not[LessEqual[c, 3.95e+133]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.8e6 or 3.94999999999999986e133 < c

   1. Initial program 64.3%

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

   3. Taylor expanded in a around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in c around inf 40.0%

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

   if -4.8e6 < c < 3.94999999999999986e133

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. neg-mul-1 56.6%

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

      3. unsub-neg 56.6%

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

      4. associate-/l* 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in a around 0 35.1%

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

       1. *-commutative 35.1%

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

   11. Simplified 35.1%

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

   12. Taylor expanded in b around 0 35.1%

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

       1. associate-*r* 34.5%

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

       2. *-commutative 34.5%

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

       3. associate-*r* 35.6%

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

   14. Simplified 35.6%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4800000 \lor \neg \left(c \leq 3.95 \cdot 10^{+133}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8200000000 \lor \neg \left(c \leq 2.4 \cdot 10^{+133}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8200000000.0) (not (<= c 2.4e+133)))
   (* a (* c j))
   (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8200000000.0) || !(c <= 2.4e+133)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-8200000000.0d0)) .or. (.not. (c <= 2.4d+133))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8200000000.0) || !(c <= 2.4e+133)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -8200000000.0) or not (c <= 2.4e+133):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -8200000000.0) || !(c <= 2.4e+133))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -8200000000.0) || ~((c <= 2.4e+133)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -8200000000.0], N[Not[LessEqual[c, 2.4e+133]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.2e9 or 2.3999999999999999e133 < c

   1. Initial program 64.9%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in c around inf 40.6%

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

   if -8.2e9 < c < 2.3999999999999999e133

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 57.6%

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

      1. distribute-lft-out-- 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in a around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. neg-mul-1 55.9%

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

      3. unsub-neg 55.9%

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

      4. associate-/l* 56.5%

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

   8. Simplified 56.5%

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

   9. Taylor expanded in a around 0 34.9%

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

       1. *-commutative 34.9%

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

   11. Simplified 34.9%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8200000000 \lor \neg \left(c \leq 2.4 \cdot 10^{+133}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.6% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.2%

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

3. Taylor expanded in a around inf 42.0%

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

   1. +-commutative 42.0%

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

   2. mul-1-neg 42.0%

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

   3. unsub-neg 42.0%

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

5. Simplified 42.0%

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

6. Taylor expanded in c around inf 20.3%

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

Developer Target 1: 60.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

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

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