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

Percentage Accurate: 72.6% → 80.6%

Time: 18.1s

Alternatives: 15

Speedup: 0.5×

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

Specification

Math

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

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: 72.6% 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: 80.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;\left(t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\right) + t\_2 \leq \infty:\\ \;\;\;\;\left(t\_1 + \left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right)\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot \left(c - \frac{x \cdot t}{j}\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if ((t_1 - (b * ((z * c) - (t * i)))) + t_2) <= math.inf:
		tmp = (t_1 + ((b * (t * i)) - (b * (z * c)))) + t_2
	else:
		tmp = j * (a * (c - ((x * t) / j)))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (((t_1 - (b * ((z * c) - (t * i)))) + t_2) <= Inf)
		tmp = (t_1 + ((b * (t * i)) - (b * (z * c)))) + t_2;
	else
		tmp = j * (a * (c - ((x * t) / j)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.9%

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

      1. sub-neg 91.9%

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

      2. distribute-rgt-in 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

   4. Applied egg-rr 91.9%

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

   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 a around inf 45.0%

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

      1. +-commutative 45.0%

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

      2. mul-1-neg 45.0%

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

      3. unsub-neg 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in j around inf 31.0%

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

      1. +-commutative 31.0%

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

      2. mul-1-neg 31.0%

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

      3. unsub-neg 31.0%

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

      4. *-commutative 31.0%

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

      5. associate-/l* 37.9%

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

      6. associate-/l* 37.9%

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

   8. Simplified 37.9%

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

   9. Taylor expanded in a around 0 47.2%

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

4. Final simplification 84.4%

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

Alternative 2: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.9%

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

   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 a around inf 45.0%

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

      1. +-commutative 45.0%

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

      2. mul-1-neg 45.0%

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

      3. unsub-neg 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in j around inf 31.0%

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

      1. +-commutative 31.0%

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

      2. mul-1-neg 31.0%

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

      3. unsub-neg 31.0%

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

      4. *-commutative 31.0%

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

      5. associate-/l* 37.9%

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

      6. associate-/l* 37.9%

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

   8. Simplified 37.9%

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

   9. Taylor expanded in a around 0 47.2%

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

4. Final simplification 84.4%

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

Alternative 3: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.1 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;\left(t\_1 + b \cdot \left(t \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -5.1e+94)
     t_2
     (if (<= j 2.7e+82) (- (+ t_1 (* b (* t i))) (* b (* z c))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.1e+94) {
		tmp = t_2;
	} else if (j <= 2.7e+82) {
		tmp = (t_1 + (b * (t * i))) - (b * (z * c));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-5.1d+94)) then
        tmp = t_2
    else if (j <= 2.7d+82) then
        tmp = (t_1 + (b * (t * i))) - (b * (z * c))
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.1e+94) {
		tmp = t_2;
	} else if (j <= 2.7e+82) {
		tmp = (t_1 + (b * (t * i))) - (b * (z * c));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -5.1e+94:
		tmp = t_2
	elif j <= 2.7e+82:
		tmp = (t_1 + (b * (t * i))) - (b * (z * c))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5.1e+94)
		tmp = t_2;
	elseif (j <= 2.7e+82)
		tmp = Float64(Float64(t_1 + Float64(b * Float64(t * i))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -5.1e+94)
		tmp = t_2;
	elseif (j <= 2.7e+82)
		tmp = (t_1 + (b * (t * i))) - (b * (z * c));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.1e+94], t$95$2, If[LessEqual[j, 2.7e+82], N[(N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.1000000000000003e94

   1. Initial program 78.2%

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

      1. sub-neg 78.2%

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

      2. distribute-rgt-in 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

   4. Applied egg-rr 78.2%

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

   5. Taylor expanded in j around inf 78.1%

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

      1. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -5.1000000000000003e94 < j < 2.6999999999999999e82

   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 j around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in i around 0 74.7%

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

   if 2.6999999999999999e82 < j

   1. Initial program 81.0%

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

   3. Taylor expanded in b around 0 81.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.1 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.7e+94)
     t_1
     (if (<= j -1.3e-58)
       (* x (- (* y z) (* t a)))
       (if (<= j 2.6e-128)
         (- (* x (* y z)) (* b (- (* z c) (* t i))))
         (if (<= j 8.5e+86) (* t (- (* b i) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.7e+94) {
		tmp = t_1;
	} else if (j <= -1.3e-58) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.6e-128) {
		tmp = (x * (y * z)) - (b * ((z * c) - (t * i)));
	} else if (j <= 8.5e+86) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2.7d+94)) then
        tmp = t_1
    else if (j <= (-1.3d-58)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 2.6d-128) then
        tmp = (x * (y * z)) - (b * ((z * c) - (t * i)))
    else if (j <= 8.5d+86) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.7e+94) {
		tmp = t_1;
	} else if (j <= -1.3e-58) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.6e-128) {
		tmp = (x * (y * z)) - (b * ((z * c) - (t * i)));
	} else if (j <= 8.5e+86) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.7e+94:
		tmp = t_1
	elif j <= -1.3e-58:
		tmp = x * ((y * z) - (t * a))
	elif j <= 2.6e-128:
		tmp = (x * (y * z)) - (b * ((z * c) - (t * i)))
	elif j <= 8.5e+86:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.7e+94)
		tmp = t_1;
	elseif (j <= -1.3e-58)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 2.6e-128)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	elseif (j <= 8.5e+86)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.7e+94)
		tmp = t_1;
	elseif (j <= -1.3e-58)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 2.6e-128)
		tmp = (x * (y * z)) - (b * ((z * c) - (t * i)));
	elseif (j <= 8.5e+86)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+94], t$95$1, If[LessEqual[j, -1.3e-58], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e-128], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+86], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.7000000000000001e94 or 8.5000000000000005e86 < j

   1. Initial program 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. distribute-rgt-neg-in 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in j around inf 75.8%

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

      1. *-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -2.7000000000000001e94 < j < -1.30000000000000003e-58

   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. sub-neg 81.6%

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

      2. distribute-rgt-in 81.6%

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

      3. distribute-rgt-neg-in 81.6%

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

   4. Applied egg-rr 81.6%

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

   5. Taylor expanded in x around inf 64.2%

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

      1. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   if -1.30000000000000003e-58 < j < 2.59999999999999981e-128

   1. Initial program 72.3%

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

   3. Taylor expanded in j around 0 74.6%

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

      1. *-commutative 74.6%

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

      2. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in a around 0 62.3%

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

   if 2.59999999999999981e-128 < j < 8.5000000000000005e86

   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 t around inf 70.6%

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

      1. distribute-lft-out-- 70.6%

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

      2. *-commutative 70.6%

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

   5. Simplified 70.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+46} \lor \neg \left(b \leq 360000000000\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(i \cdot \left(\frac{z \cdot c}{i} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.4e+46) (not (<= b 360000000000.0)))
   (- (* x (* y z)) (* b (* i (- (/ (* z c) i) t))))
   (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.4e+46) || !(b <= 360000000000.0)) {
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.4d+46)) .or. (.not. (b <= 360000000000.0d0))) then
        tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.4e+46) || !(b <= 360000000000.0)) {
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.4e+46) or not (b <= 360000000000.0):
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.4e+46) || !(b <= 360000000000.0))
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(i * Float64(Float64(Float64(z * c) / i) - t))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.4e+46) || ~((b <= 360000000000.0)))
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.4e+46], N[Not[LessEqual[b, 360000000000.0]], $MachinePrecision]], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(i * N[(N[(N[(z * c), $MachinePrecision] / i), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3999999999999998e46 or 3.6e11 < b

   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. Taylor expanded in j around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. *-commutative 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in a around 0 72.8%

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

   7. Taylor expanded in i around inf 72.8%

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

   if -3.3999999999999998e46 < b < 3.6e11

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 76.3%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+46} \lor \neg \left(b \leq 360000000000\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(i \cdot \left(\frac{z \cdot c}{i} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+83}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.55e+99)
     t_2
     (if (<= j 1.45e+83) (- t_1 (* b (- (* z c) (* t i)))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.55e+99) {
		tmp = t_2;
	} else if (j <= 1.45e+83) {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.55d+99)) then
        tmp = t_2
    else if (j <= 1.45d+83) then
        tmp = t_1 - (b * ((z * c) - (t * i)))
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.55e+99) {
		tmp = t_2;
	} else if (j <= 1.45e+83) {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.55e+99:
		tmp = t_2
	elif j <= 1.45e+83:
		tmp = t_1 - (b * ((z * c) - (t * i)))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.55e+99)
		tmp = t_2;
	elseif (j <= 1.45e+83)
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.55e+99)
		tmp = t_2;
	elseif (j <= 1.45e+83)
		tmp = t_1 - (b * ((z * c) - (t * i)));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.55e+99], t$95$2, If[LessEqual[j, 1.45e+83], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.55e99

   1. Initial program 78.2%

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

      1. sub-neg 78.2%

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

      2. distribute-rgt-in 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

   4. Applied egg-rr 78.2%

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

   5. Taylor expanded in j around inf 78.1%

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

      1. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -1.55e99 < j < 1.45e83

   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 j around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if 1.45e83 < j

   1. Initial program 81.0%

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

   3. Taylor expanded in b around 0 81.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.75 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(i \cdot \left(\frac{z \cdot c}{i} - t\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.75e+96)
     t_1
     (if (<= j 1.15e-229)
       (- (* x (* y z)) (* b (* i (- (/ (* z c) i) t))))
       (if (<= j 8.5e+86) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.75e+96) {
		tmp = t_1;
	} else if (j <= 1.15e-229) {
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)));
	} else if (j <= 8.5e+86) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2.75d+96)) then
        tmp = t_1
    else if (j <= 1.15d-229) then
        tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)))
    else if (j <= 8.5d+86) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.75e+96) {
		tmp = t_1;
	} else if (j <= 1.15e-229) {
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)));
	} else if (j <= 8.5e+86) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.75e+96:
		tmp = t_1
	elif j <= 1.15e-229:
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)))
	elif j <= 8.5e+86:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.75e+96)
		tmp = t_1;
	elseif (j <= 1.15e-229)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(i * Float64(Float64(Float64(z * c) / i) - t))));
	elseif (j <= 8.5e+86)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.75e+96)
		tmp = t_1;
	elseif (j <= 1.15e-229)
		tmp = (x * (y * z)) - (b * (i * (((z * c) / i) - t)));
	elseif (j <= 8.5e+86)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.75e+96], t$95$1, If[LessEqual[j, 1.15e-229], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(i * N[(N[(N[(z * c), $MachinePrecision] / i), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+86], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.7500000000000001e96 or 8.5000000000000005e86 < j

   1. Initial program 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. distribute-rgt-neg-in 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in j around inf 75.8%

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

      1. *-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -2.7500000000000001e96 < j < 1.14999999999999998e-229

   1. Initial program 77.2%

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

   3. Taylor expanded in j around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. *-commutative 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in a around 0 57.0%

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

   7. Taylor expanded in i around inf 59.9%

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

   if 1.14999999999999998e-229 < j < 8.5000000000000005e86

   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 68.0%

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

      1. distribute-lft-out-- 68.0%

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

      2. *-commutative 68.0%

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

   5. Simplified 68.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.75 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(i \cdot \left(\frac{z \cdot c}{i} - t\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.6 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -4.6e+95)
     t_1
     (if (<= j 5e-253)
       (* x (- (* y z) (* t a)))
       (if (<= j 8.2e+86) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -4.6e+95) {
		tmp = t_1;
	} else if (j <= 5e-253) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 8.2e+86) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-4.6d+95)) then
        tmp = t_1
    else if (j <= 5d-253) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 8.2d+86) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -4.6e+95) {
		tmp = t_1;
	} else if (j <= 5e-253) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 8.2e+86) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -4.6e+95:
		tmp = t_1
	elif j <= 5e-253:
		tmp = x * ((y * z) - (t * a))
	elif j <= 8.2e+86:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.6e+95)
		tmp = t_1;
	elseif (j <= 5e-253)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 8.2e+86)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.6e+95)
		tmp = t_1;
	elseif (j <= 5e-253)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 8.2e+86)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.6e+95], t$95$1, If[LessEqual[j, 5e-253], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+86], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.59999999999999994e95 or 8.1999999999999998e86 < j

   1. Initial program 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. distribute-rgt-neg-in 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in j around inf 75.8%

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

      1. *-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -4.59999999999999994e95 < j < 4.99999999999999971e-253

   1. Initial program 78.3%

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

      1. sub-neg 78.3%

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

      2. distribute-rgt-in 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

   4. Applied egg-rr 78.3%

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

   5. Taylor expanded in x around inf 55.1%

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

      1. *-commutative 55.1%

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

   7. Simplified 55.1%

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

   if 4.99999999999999971e-253 < j < 8.1999999999999998e86

   1. Initial program 69.8%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. distribute-lft-out-- 65.8%

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

      2. *-commutative 65.8%

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

   5. Simplified 65.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.95 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.95e+94)
     t_1
     (if (<= j -4.4e-279)
       (* x (- (* y z) (* t a)))
       (if (<= j 7.5e+82) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.95e+94) {
		tmp = t_1;
	} else if (j <= -4.4e-279) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.5e+82) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2.95d+94)) then
        tmp = t_1
    else if (j <= (-4.4d-279)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 7.5d+82) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.95e+94) {
		tmp = t_1;
	} else if (j <= -4.4e-279) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 7.5e+82) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.95e+94:
		tmp = t_1
	elif j <= -4.4e-279:
		tmp = x * ((y * z) - (t * a))
	elif j <= 7.5e+82:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (j <= -2.95e+94)
		tmp = t_1;
	elseif (j <= -4.4e-279)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 7.5e+82)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.95e+94)
		tmp = t_1;
	elseif (j <= -4.4e-279)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 7.5e+82)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.95e+94], t$95$1, If[LessEqual[j, -4.4e-279], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+82], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.94999999999999995e94 or 7.4999999999999999e82 < j

   1. Initial program 79.5%

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

      1. sub-neg 79.5%

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

      2. distribute-rgt-in 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

   4. Applied egg-rr 79.5%

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

   5. Taylor expanded in j around inf 75.2%

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

      1. *-commutative 75.2%

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

   7. Simplified 75.2%

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

   if -2.94999999999999995e94 < j < -4.40000000000000001e-279

   1. Initial program 77.0%

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

      1. sub-neg 77.0%

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

      2. distribute-rgt-in 77.0%

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

      3. distribute-rgt-neg-in 77.0%

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

   4. Applied egg-rr 77.0%

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

   5. Taylor expanded in x around inf 56.8%

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

      1. *-commutative 56.8%

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

   7. Simplified 56.8%

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

   if -4.40000000000000001e-279 < j < 7.4999999999999999e82

   1. Initial program 72.8%

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

   3. Taylor expanded in b around inf 58.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.95 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -3.6e+112)
   (* j (* a c))
   (if (<= j -2e-276)
     (* x (* y z))
     (if (<= j 2.05e+87) (* t (* b i)) (* a (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -3.6e+112) {
		tmp = j * (a * c);
	} else if (j <= -2e-276) {
		tmp = x * (y * z);
	} else if (j <= 2.05e+87) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-3.6d+112)) then
        tmp = j * (a * c)
    else if (j <= (-2d-276)) then
        tmp = x * (y * z)
    else if (j <= 2.05d+87) then
        tmp = t * (b * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -3.6e+112) {
		tmp = j * (a * c);
	} else if (j <= -2e-276) {
		tmp = x * (y * z);
	} else if (j <= 2.05e+87) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -3.6e+112:
		tmp = j * (a * c)
	elif j <= -2e-276:
		tmp = x * (y * z)
	elif j <= 2.05e+87:
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -3.6e+112)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= -2e-276)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 2.05e+87)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -3.6e+112)
		tmp = j * (a * c);
	elseif (j <= -2e-276)
		tmp = x * (y * z);
	elseif (j <= 2.05e+87)
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -3.6e+112], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2e-276], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.05e+87], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.6e112

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. distribute-rgt-in 79.0%

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

      3. distribute-rgt-neg-in 79.0%

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

   4. Applied egg-rr 79.0%

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

   5. Taylor expanded in j around inf 77.5%

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

      1. *-commutative 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in c around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. *-commutative 52.1%

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

      3. associate-*r* 52.1%

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

   10. Simplified 52.1%

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

   if -3.6e112 < j < -2e-276

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 39.7%

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

   4. Taylor expanded in x around inf 33.5%

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

      1. *-commutative 33.5%

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

   6. Simplified 33.5%

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

   if -2e-276 < j < 2.05e87

   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 j around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in i around 0 73.9%

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

   7. Taylor expanded in i around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*r* 33.2%

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

      3. *-commutative 33.2%

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

      4. associate-*r* 37.4%

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

   9. Simplified 37.4%

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

   if 2.05e87 < j

   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 57.5%

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

      1. +-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in c around inf 44.8%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+47} \lor \neg \left(b \leq 200000000000\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1e+47) (not (<= b 200000000000.0)))
   (* 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 <= -1e+47) || !(b <= 200000000000.0)) {
		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 <= (-1d+47)) .or. (.not. (b <= 200000000000.0d0))) 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 <= -1e+47) || !(b <= 200000000000.0)) {
		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 <= -1e+47) or not (b <= 200000000000.0):
		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 <= -1e+47) || !(b <= 200000000000.0))
		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 <= -1e+47) || ~((b <= 200000000000.0)))
		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, -1e+47], N[Not[LessEqual[b, 200000000000.0]], $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 < -1e47 or 2e11 < b

   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. Taylor expanded in b around inf 66.3%

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

   if -1e47 < b < 2e11

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 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%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+47} \lor \neg \left(b \leq 200000000000\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+205}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.55e+205)
   (* b (* t i))
   (if (<= i 1.9e+217) (* a (- (* c j) (* x t))) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.55e+205) {
		tmp = b * (t * i);
	} else if (i <= 1.9e+217) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.55d+205)) then
        tmp = b * (t * i)
    else if (i <= 1.9d+217) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.55e+205) {
		tmp = b * (t * i);
	} else if (i <= 1.9e+217) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.55e+205:
		tmp = b * (t * i)
	elif i <= 1.9e+217:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.55e+205)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 1.9e+217)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.55e+205)
		tmp = b * (t * i);
	elseif (i <= 1.9e+217)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.55e+205], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.9e+217], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.55000000000000009e205

   1. Initial program 66.8%

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

   3. Taylor expanded in j around 0 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in i around inf 59.6%

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

   if -1.55000000000000009e205 < i < 1.90000000000000001e217

   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 a around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

   5. Simplified 45.8%

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

   if 1.90000000000000001e217 < i

   1. Initial program 69.1%

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

   3. Taylor expanded in j around 0 59.2%

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

      1. *-commutative 59.2%

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

      2. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in i around 0 59.2%

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

   7. Taylor expanded in i around inf 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-*r* 59.3%

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

      3. *-commutative 59.3%

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

      4. associate-*r* 69.3%

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

   9. Simplified 69.3%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+205}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{-59} \lor \neg \left(j \leq 3.5 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -9.5e-59) (not (<= j 3.5e+87))) (* a (* c j)) (* t (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9.5e-59) || !(j <= 3.5e+87)) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-9.5d-59)) .or. (.not. (j <= 3.5d+87))) then
        tmp = a * (c * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9.5e-59) || !(j <= 3.5e+87)) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -9.5e-59) or not (j <= 3.5e+87):
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -9.5e-59) || !(j <= 3.5e+87))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -9.5e-59) || ~((j <= 3.5e+87)))
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -9.5e-59], N[Not[LessEqual[j, 3.5e+87]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9.4999999999999994e-59 or 3.49999999999999986e87 < j

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in c around inf 38.8%

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

   if -9.4999999999999994e-59 < j < 3.49999999999999986e87

   1. Initial program 73.4%

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

   3. Taylor expanded in j around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in i around 0 73.8%

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

   7. Taylor expanded in i around inf 31.3%

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

      1. *-commutative 31.3%

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

      2. associate-*r* 30.7%

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

      3. *-commutative 30.7%

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

      4. associate-*r* 32.6%

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

   9. Simplified 32.6%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{-59} \lor \neg \left(j \leq 3.5 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{-37} \lor \neg \left(j \leq 3.4 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.5e-37) (not (<= j 3.4e+87))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.5e-37) || !(j <= 3.4e+87)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.5d-37)) .or. (.not. (j <= 3.4d+87))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.5e-37) || !(j <= 3.4e+87)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.5e-37) or not (j <= 3.4e+87):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.5e-37) || !(j <= 3.4e+87))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.5e-37) || ~((j <= 3.4e+87)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.5e-37], N[Not[LessEqual[j, 3.4e+87]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.4999999999999999e-37 or 3.4000000000000002e87 < j

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in c around inf 40.3%

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

   if -2.4999999999999999e-37 < j < 3.4000000000000002e87

   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 j around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in i around inf 30.6%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{-37} \lor \neg \left(j \leq 3.4 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.2% 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 76.4%

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

3. Taylor expanded in a around inf 41.8%

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

   1. +-commutative 41.8%

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

   2. mul-1-neg 41.8%

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

   3. unsub-neg 41.8%

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

5. Simplified 41.8%

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

6. Taylor expanded in c around inf 22.5%

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

Developer Target 1: 59.1% 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 2024137 
(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)))))