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

Percentage Accurate: 72.5% → 82.3%

Time: 20.6s

Alternatives: 21

Speedup: 0.5×

• 58.1% 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: 72.5% accurate, 1.0× speedup

Math

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

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: 82.3% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (fma j t_2 t_1)
     (* a (* j (- c (* t (/ x 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 * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = a * (j * (c - (t * (x / j))));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $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 90.8%

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

      1. +-commutative 90.8%

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

      2. fma-define 90.8%

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

      3. *-commutative 90.8%

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

      4. *-commutative 90.8%

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

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. 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 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in j around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

      3. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 83.7%

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

Alternative 2: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (j * (c - (t * (x / 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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / 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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (j * (c - (t * (x / 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[(t * i), $MachinePrecision] - N[(z * c), $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[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $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 90.8%

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

   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 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in j around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

      3. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 83.7%

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

Alternative 3: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3700000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -2.35 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -4.2e+134)
     t_1
     (if (<= c -3700000000.0)
       (* j (- (* a c) (* y i)))
       (if (<= c -2.35e-209)
         (* x (- (* y z) (* t a)))
         (if (<= c 1.1e-150)
           (* y (- (* x z) (* i j)))
           (if (<= c 5e+28) (* 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.2e+134) {
		tmp = t_1;
	} else if (c <= -3700000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= -2.35e-209) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.1e-150) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 5e+28) {
		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 = c * ((a * j) - (z * b))
    if (c <= (-4.2d+134)) then
        tmp = t_1
    else if (c <= (-3700000000.0d0)) then
        tmp = j * ((a * c) - (y * i))
    else if (c <= (-2.35d-209)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 1.1d-150) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 5d+28) 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.2e+134) {
		tmp = t_1;
	} else if (c <= -3700000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= -2.35e-209) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.1e-150) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 5e+28) {
		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 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -4.2e+134:
		tmp = t_1
	elif c <= -3700000000.0:
		tmp = j * ((a * c) - (y * i))
	elif c <= -2.35e-209:
		tmp = x * ((y * z) - (t * a))
	elif c <= 1.1e-150:
		tmp = y * ((x * z) - (i * j))
	elif c <= 5e+28:
		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(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.2e+134)
		tmp = t_1;
	elseif (c <= -3700000000.0)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (c <= -2.35e-209)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 1.1e-150)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 5e+28)
		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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.2e+134)
		tmp = t_1;
	elseif (c <= -3700000000.0)
		tmp = j * ((a * c) - (y * i));
	elseif (c <= -2.35e-209)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 1.1e-150)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 5e+28)
		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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+134], t$95$1, If[LessEqual[c, -3700000000.0], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.35e-209], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e-150], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e+28], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.2000000000000002e134 or 4.99999999999999957e28 < c

   1. Initial program 51.3%

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

   3. Taylor expanded in c around inf 69.5%

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

   if -4.2000000000000002e134 < c < -3.7e9

   1. Initial program 57.3%

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

      1. *-commutative 57.3%

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

      2. prod-diff 52.7%

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

      3. *-commutative 52.7%

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

      4. fma-neg 52.7%

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

      5. *-commutative 52.7%

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

      6. prod-diff 52.7%

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

      7. *-commutative 52.7%

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

      8. fma-neg 52.7%

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

      9. associate-+l+ 52.7%

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

      10. *-commutative 52.7%

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

      11. fma-neg 52.7%

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

      12. distribute-rgt-neg-in 52.7%

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

      13. *-commutative 52.7%

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

      14. *-commutative 52.7%

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

   4. Applied egg-rr 52.7%

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

      1. distribute-rgt-neg-out 52.7%

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

      2. fma-neg 52.7%

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

      3. *-commutative 52.7%

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

      4. count-2 52.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(c \cdot z - t \cdot i\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Simplified 52.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(c \cdot z - t \cdot i\right) + 2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   7. Taylor expanded in j around inf 57.7%

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

      1. *-commutative 57.7%

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

   9. Simplified 57.7%

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

   if -3.7e9 < c < -2.35e-209

   1. Initial program 82.6%

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

   3. Taylor expanded in x around inf 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   if -2.35e-209 < c < 1.1e-150

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if 1.1e-150 < c < 4.99999999999999957e28

   1. Initial program 89.4%

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

   3. Taylor expanded in b around inf 54.0%

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

      1. *-commutative 54.0%

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

   5. Simplified 54.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3700000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -2.35 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z c))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.6e-15)
     t_2
     (if (<= j -1.42e-179)
       (* t (- (* b i) (* x a)))
       (if (<= j 1.35e-15) (- (* x (- (* y z) (* t a))) t_1) (- t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * c);
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.6e-15) {
		tmp = t_2;
	} else if (j <= -1.42e-179) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 1.35e-15) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (z * c)
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-2.6d-15)) then
        tmp = t_2
    else if (j <= (-1.42d-179)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 1.35d-15) then
        tmp = (x * ((y * z) - (t * a))) - t_1
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * c);
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.6e-15) {
		tmp = t_2;
	} else if (j <= -1.42e-179) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 1.35e-15) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * c)
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.6e-15:
		tmp = t_2
	elif j <= -1.42e-179:
		tmp = t * ((b * i) - (x * a))
	elif j <= 1.35e-15:
		tmp = (x * ((y * z) - (t * a))) - t_1
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * c))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.6e-15)
		tmp = t_2;
	elseif (j <= -1.42e-179)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 1.35e-15)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1);
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * c);
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.6e-15)
		tmp = t_2;
	elseif (j <= -1.42e-179)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 1.35e-15)
		tmp = (x * ((y * z) - (t * a))) - t_1;
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e-15], t$95$2, If[LessEqual[j, -1.42e-179], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e-15], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.60000000000000004e-15

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. prod-diff 66.9%

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

      3. *-commutative 66.9%

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

      4. fma-neg 66.9%

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

      5. *-commutative 66.9%

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

      6. prod-diff 66.9%

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

      7. *-commutative 66.9%

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

      8. fma-neg 66.9%

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

      9. associate-+l+ 66.9%

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

      10. *-commutative 66.9%

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

      11. fma-neg 66.9%

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

      12. distribute-rgt-neg-in 66.9%

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

      13. *-commutative 66.9%

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

      14. *-commutative 66.9%

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

   4. Applied egg-rr 66.9%

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

      1. distribute-rgt-neg-out 66.9%

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

      2. fma-neg 66.9%

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

      3. *-commutative 66.9%

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

      4. count-2 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(c \cdot z - t \cdot i\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Simplified 66.9%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(c \cdot z - t \cdot i\right) + 2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   7. Taylor expanded in j around inf 65.0%

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

      1. *-commutative 65.0%

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

   9. Simplified 65.0%

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

   if -2.60000000000000004e-15 < j < -1.42e-179

   1. Initial program 76.3%

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

      1. add-cube-cbrt 75.9%

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

      2. pow3 75.9%

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

      3. fma-neg 75.9%

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

      4. *-commutative 75.9%

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

      5. distribute-rgt-neg-in 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in t around -inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. *-commutative 58.7%

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

      4. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -1.42e-179 < j < 1.35000000000000005e-15

   1. Initial program 71.4%

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

   3. Taylor expanded in j around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in c around inf 68.0%

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

   if 1.35000000000000005e-15 < j

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0 74.1%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

   6. Simplified 65.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{-15}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - t\_1\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* y i) (* a c)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= j -1.75e-40)
     (- (* b (* t i)) t_1)
     (if (<= j 3.3e-5) (+ (* x (- (* y z) (* t a))) t_2) (- t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((y * i) - (a * c));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -1.75e-40) {
		tmp = (b * (t * i)) - t_1;
	} else if (j <= 3.3e-5) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((y * i) - (a * c))
    t_2 = b * ((t * i) - (z * c))
    if (j <= (-1.75d-40)) then
        tmp = (b * (t * i)) - t_1
    else if (j <= 3.3d-5) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else
        tmp = t_2 - 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 * ((y * i) - (a * c));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -1.75e-40) {
		tmp = (b * (t * i)) - t_1;
	} else if (j <= 3.3e-5) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((y * i) - (a * c))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -1.75e-40:
		tmp = (b * (t * i)) - t_1
	elif j <= 3.3e-5:
		tmp = (x * ((y * z) - (t * a))) + t_2
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(y * i) - Float64(a * c)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -1.75e-40)
		tmp = Float64(Float64(b * Float64(t * i)) - t_1);
	elseif (j <= 3.3e-5)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((y * i) - (a * c));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -1.75e-40)
		tmp = (b * (t * i)) - t_1;
	elseif (j <= 3.3e-5)
		tmp = (x * ((y * z) - (t * a))) + t_2;
	else
		tmp = t_2 - 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[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e-40], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 3.3e-5], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.7500000000000001e-40

   1. Initial program 74.3%

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

   3. Taylor expanded in x around 0 70.9%

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

   4. Taylor expanded in z around 0 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-*r* 72.3%

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

      3. neg-mul-1 72.3%

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

      4. *-commutative 72.3%

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

   6. Simplified 72.3%

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

   if -1.7500000000000001e-40 < j < 3.3000000000000003e-5

   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 j around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   if 3.3000000000000003e-5 < j

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0 74.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{if}\;j \leq -8.8 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - t\_1\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* y i) (* a c)))))
   (if (<= j -8.8e-156)
     (- (* b (* t i)) t_1)
     (if (<= j 2.05e-25)
       (- (* x (- (* y z) (* t a))) (* b (* z c)))
       (- (* 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 * ((y * i) - (a * c));
	double tmp;
	if (j <= -8.8e-156) {
		tmp = (b * (t * i)) - t_1;
	} else if (j <= 2.05e-25) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else {
		tmp = (b * ((t * i) - (z * c))) - 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 * ((y * i) - (a * c))
    if (j <= (-8.8d-156)) then
        tmp = (b * (t * i)) - t_1
    else if (j <= 2.05d-25) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else
        tmp = (b * ((t * i) - (z * c))) - 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 * ((y * i) - (a * c));
	double tmp;
	if (j <= -8.8e-156) {
		tmp = (b * (t * i)) - t_1;
	} else if (j <= 2.05e-25) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else {
		tmp = (b * ((t * i) - (z * c))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((y * i) - (a * c))
	tmp = 0
	if j <= -8.8e-156:
		tmp = (b * (t * i)) - t_1
	elif j <= 2.05e-25:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	else:
		tmp = (b * ((t * i) - (z * c))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(y * i) - Float64(a * c)))
	tmp = 0.0
	if (j <= -8.8e-156)
		tmp = Float64(Float64(b * Float64(t * i)) - t_1);
	elseif (j <= 2.05e-25)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((y * i) - (a * c));
	tmp = 0.0;
	if (j <= -8.8e-156)
		tmp = (b * (t * i)) - t_1;
	elseif (j <= 2.05e-25)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	else
		tmp = (b * ((t * i) - (z * c))) - 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[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.8e-156], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 2.05e-25], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.7999999999999996e-156

   1. Initial program 74.9%

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

   3. Taylor expanded in x around 0 66.4%

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

   4. Taylor expanded in z around 0 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*r* 66.6%

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

      3. neg-mul-1 66.6%

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

      4. *-commutative 66.6%

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

   6. Simplified 66.6%

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

   if -8.7999999999999996e-156 < j < 2.04999999999999994e-25

   1. Initial program 71.0%

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

   3. Taylor expanded in j around 0 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in c around inf 68.6%

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

   if 2.04999999999999994e-25 < j

   1. Initial program 70.3%

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

   3. Taylor expanded in x around 0 73.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.8 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+123}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-148}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.05e+123)
   (* z (* b (- c)))
   (if (<= c -3.3e-211)
     (* a (* t (- x)))
     (if (<= c 3.5e-148)
       (* (* i j) (- y))
       (if (<= c 1.15e+29) (* b (* t i)) (* j (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.05e+123) {
		tmp = z * (b * -c);
	} else if (c <= -3.3e-211) {
		tmp = a * (t * -x);
	} else if (c <= 3.5e-148) {
		tmp = (i * j) * -y;
	} else if (c <= 1.15e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.05d+123)) then
        tmp = z * (b * -c)
    else if (c <= (-3.3d-211)) then
        tmp = a * (t * -x)
    else if (c <= 3.5d-148) then
        tmp = (i * j) * -y
    else if (c <= 1.15d+29) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.05e+123) {
		tmp = z * (b * -c);
	} else if (c <= -3.3e-211) {
		tmp = a * (t * -x);
	} else if (c <= 3.5e-148) {
		tmp = (i * j) * -y;
	} else if (c <= 1.15e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.05e+123:
		tmp = z * (b * -c)
	elif c <= -3.3e-211:
		tmp = a * (t * -x)
	elif c <= 3.5e-148:
		tmp = (i * j) * -y
	elif c <= 1.15e+29:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.05e+123)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (c <= -3.3e-211)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= 3.5e-148)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 1.15e+29)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.05e+123)
		tmp = z * (b * -c);
	elseif (c <= -3.3e-211)
		tmp = a * (t * -x);
	elseif (c <= 3.5e-148)
		tmp = (i * j) * -y;
	elseif (c <= 1.15e+29)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.05e+123], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.3e-211], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e-148], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 1.15e+29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.04999999999999997e123

   1. Initial program 49.2%

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

   3. Taylor expanded in x around 0 57.3%

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

   4. Taylor expanded in z around inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

      3. *-commutative 41.7%

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

   6. Simplified 41.7%

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

   7. Taylor expanded in b around 0 41.7%

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

      1. neg-mul-1 41.7%

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

      2. associate-*r* 50.4%

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

      3. distribute-rgt-neg-in 50.4%

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

   9. Simplified 50.4%

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

   if -1.04999999999999997e123 < c < -3.3000000000000002e-211

   1. Initial program 74.7%

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

   3. Taylor expanded in a around inf 38.7%

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

      1. +-commutative 38.7%

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

      2. mul-1-neg 38.7%

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

      3. unsub-neg 38.7%

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

   5. Simplified 38.7%

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

   6. Taylor expanded in c around 0 30.1%

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

      1. mul-1-neg 30.1%

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

      2. distribute-lft-neg-out 30.1%

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

      3. *-commutative 30.1%

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

   8. Simplified 30.1%

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

   if -3.3000000000000002e-211 < c < 3.5e-148

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around 0 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-lft-neg-out 40.1%

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

      3. *-commutative 40.1%

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

   8. Simplified 40.1%

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

   if 3.5e-148 < c < 1.1500000000000001e29

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 72.1%

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

   4. Taylor expanded in t around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if 1.1500000000000001e29 < c

   1. Initial program 54.5%

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

   3. Taylor expanded in a around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in c around inf 40.3%

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

      1. associate-*r* 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+123}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-148}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.8 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-151}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.52 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -9.8e+138)
   (* b (* z (- c)))
   (if (<= c -3e-211)
     (* a (* t (- x)))
     (if (<= c 2e-151)
       (* (* i j) (- y))
       (if (<= c 1.52e+29) (* b (* t i)) (* j (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.8e+138) {
		tmp = b * (z * -c);
	} else if (c <= -3e-211) {
		tmp = a * (t * -x);
	} else if (c <= 2e-151) {
		tmp = (i * j) * -y;
	} else if (c <= 1.52e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-9.8d+138)) then
        tmp = b * (z * -c)
    else if (c <= (-3d-211)) then
        tmp = a * (t * -x)
    else if (c <= 2d-151) then
        tmp = (i * j) * -y
    else if (c <= 1.52d+29) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.8e+138) {
		tmp = b * (z * -c);
	} else if (c <= -3e-211) {
		tmp = a * (t * -x);
	} else if (c <= 2e-151) {
		tmp = (i * j) * -y;
	} else if (c <= 1.52e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -9.8e+138:
		tmp = b * (z * -c)
	elif c <= -3e-211:
		tmp = a * (t * -x)
	elif c <= 2e-151:
		tmp = (i * j) * -y
	elif c <= 1.52e+29:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -9.8e+138)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -3e-211)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= 2e-151)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 1.52e+29)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -9.8e+138)
		tmp = b * (z * -c);
	elseif (c <= -3e-211)
		tmp = a * (t * -x);
	elseif (c <= 2e-151)
		tmp = (i * j) * -y;
	elseif (c <= 1.52e+29)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -9.8e+138], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e-211], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-151], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 1.52e+29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -9.79999999999999966e138

   1. Initial program 45.9%

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

   3. Taylor expanded in x around 0 55.0%

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

   4. Taylor expanded in z around inf 46.3%

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

      1. associate-*r* 46.3%

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

      2. neg-mul-1 46.3%

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

      3. *-commutative 46.3%

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

   6. Simplified 46.3%

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

   if -9.79999999999999966e138 < c < -3.00000000000000005e-211

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf 39.4%

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

      1. +-commutative 39.4%

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

      2. mul-1-neg 39.4%

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

      3. unsub-neg 39.4%

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

   5. Simplified 39.4%

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

   6. Taylor expanded in c around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. distribute-lft-neg-out 30.0%

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

      3. *-commutative 30.0%

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

   8. Simplified 30.0%

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

   if -3.00000000000000005e-211 < c < 1.9999999999999999e-151

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in z around 0 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-lft-neg-out 40.1%

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

      3. *-commutative 40.1%

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

   8. Simplified 40.1%

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

   if 1.9999999999999999e-151 < c < 1.52e29

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 72.1%

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

   4. Taylor expanded in t around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if 1.52e29 < c

   1. Initial program 54.5%

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

   3. Taylor expanded in a around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in c around inf 40.3%

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

      1. associate-*r* 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.8 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-151}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.52 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{-156} \lor \neg \left(j \leq 2.05 \cdot 10^{-25}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -8e-156) (not (<= j 2.05e-25)))
   (- (* b (* t i)) (* j (- (* y i) (* a c))))
   (- (* x (- (* y z) (* t a))) (* b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -8e-156) || !(j <= 2.05e-25)) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-8d-156)) .or. (.not. (j <= 2.05d-25))) then
        tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
    else
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -8e-156) || !(j <= 2.05e-25)) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -8e-156) or not (j <= 2.05e-25):
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -8e-156) || !(j <= 2.05e-25))
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -8e-156) || ~((j <= 2.05e-25)))
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	else
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -8e-156], N[Not[LessEqual[j, 2.05e-25]], $MachinePrecision]], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -8.00000000000000032e-156 or 2.04999999999999994e-25 < j

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 69.2%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*r* 68.8%

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

      3. neg-mul-1 68.8%

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

      4. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   if -8.00000000000000032e-156 < j < 2.04999999999999994e-25

   1. Initial program 71.0%

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

   3. Taylor expanded in j around 0 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in c around inf 68.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{-156} \lor \neg \left(j \leq 2.05 \cdot 10^{-25}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+123} \lor \neg \left(t \leq 2.3 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.25e+123) (not (<= t 2.3e+65)))
   (* t (- (* b i) (* x a)))
   (- (* j (- (* a c) (* y i))) (* b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.25e+123) || !(t <= 2.3e+65)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.25d+123)) .or. (.not. (t <= 2.3d+65))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.25e+123) || !(t <= 2.3e+65)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.25e+123) or not (t <= 2.3e+65):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.25e+123) || !(t <= 2.3e+65))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.25e+123) || ~((t <= 2.3e+65)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.25e+123], N[Not[LessEqual[t, 2.3e+65]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999994e123 or 2.3e65 < t

   1. Initial program 65.8%

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

      1. add-cube-cbrt 65.6%

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

      2. pow3 65.6%

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

      3. fma-neg 66.6%

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

      4. *-commutative 66.6%

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

      5. distribute-rgt-neg-in 66.6%

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

   4. Applied egg-rr 66.6%

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

   5. Taylor expanded in t around -inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. *-commutative 70.0%

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

      4. *-commutative 70.0%

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

   7. Simplified 70.0%

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

   if -1.24999999999999994e123 < t < 2.3e65

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 62.5%

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

   4. Taylor expanded in t around 0 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   6. Simplified 56.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+123} \lor \neg \left(t \leq 2.3 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.25 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 550:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.25e-14)
     t_1
     (if (<= j -3.4e-290)
       (* t (- (* b i) (* x a)))
       (if (<= j 550.0) (* z (- (* x y) (* b 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 <= -2.25e-14) {
		tmp = t_1;
	} else if (j <= -3.4e-290) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 550.0) {
		tmp = z * ((x * y) - (b * 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 <= (-2.25d-14)) then
        tmp = t_1
    else if (j <= (-3.4d-290)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 550.0d0) then
        tmp = z * ((x * y) - (b * 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 <= -2.25e-14) {
		tmp = t_1;
	} else if (j <= -3.4e-290) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 550.0) {
		tmp = z * ((x * y) - (b * 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 <= -2.25e-14:
		tmp = t_1
	elif j <= -3.4e-290:
		tmp = t * ((b * i) - (x * a))
	elif j <= 550.0:
		tmp = z * ((x * y) - (b * 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 <= -2.25e-14)
		tmp = t_1;
	elseif (j <= -3.4e-290)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 550.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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 <= -2.25e-14)
		tmp = t_1;
	elseif (j <= -3.4e-290)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 550.0)
		tmp = z * ((x * y) - (b * 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, -2.25e-14], t$95$1, If[LessEqual[j, -3.4e-290], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 550.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.2499999999999999e-14 or 550 < j

   1. Initial program 71.4%

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

      1. *-commutative 71.4%

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

      2. prod-diff 66.5%

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

      3. *-commutative 66.5%

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

      4. fma-neg 66.5%

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

      5. *-commutative 66.5%

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

      6. prod-diff 66.5%

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

      7. *-commutative 66.5%

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

      8. fma-neg 66.5%

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

      9. associate-+l+ 66.5%

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

      10. *-commutative 66.5%

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

      11. fma-neg 66.5%

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

      12. distribute-rgt-neg-in 66.5%

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

      13. *-commutative 66.5%

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

      14. *-commutative 66.5%

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

   4. Applied egg-rr 66.5%

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

      1. distribute-rgt-neg-out 66.5%

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

      2. fma-neg 66.5%

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

      3. *-commutative 66.5%

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

      4. count-2 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(c \cdot z - t \cdot i\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Simplified 66.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(c \cdot z - t \cdot i\right) + 2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   7. Taylor expanded in j around inf 65.5%

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

      1. *-commutative 65.5%

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

   9. Simplified 65.5%

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

   if -2.2499999999999999e-14 < j < -3.39999999999999984e-290

   1. Initial program 67.3%

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

      1. add-cube-cbrt 67.1%

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

      2. pow3 67.0%

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

      3. fma-neg 67.0%

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

      4. *-commutative 67.0%

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

      5. distribute-rgt-neg-in 67.0%

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

   4. Applied egg-rr 67.0%

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

   5. Taylor expanded in t around -inf 59.2%

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

      1. associate-*r* 59.2%

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

      2. neg-mul-1 59.2%

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

      3. *-commutative 59.2%

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

      4. *-commutative 59.2%

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

   7. Simplified 59.2%

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

   if -3.39999999999999984e-290 < j < 550

   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. Taylor expanded in z around inf 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.25 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 550:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8.1 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 245:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -0.05)
     t_1
     (if (<= j -8.1e-290)
       (* x (- (* y z) (* t a)))
       (if (<= j 245.0) (* z (- (* x y) (* b 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 <= -0.05) {
		tmp = t_1;
	} else if (j <= -8.1e-290) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 245.0) {
		tmp = z * ((x * y) - (b * 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 <= (-0.05d0)) then
        tmp = t_1
    else if (j <= (-8.1d-290)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 245.0d0) then
        tmp = z * ((x * y) - (b * 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 <= -0.05) {
		tmp = t_1;
	} else if (j <= -8.1e-290) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 245.0) {
		tmp = z * ((x * y) - (b * 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 <= -0.05:
		tmp = t_1
	elif j <= -8.1e-290:
		tmp = x * ((y * z) - (t * a))
	elif j <= 245.0:
		tmp = z * ((x * y) - (b * 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 <= -0.05)
		tmp = t_1;
	elseif (j <= -8.1e-290)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 245.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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 <= -0.05)
		tmp = t_1;
	elseif (j <= -8.1e-290)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 245.0)
		tmp = z * ((x * y) - (b * 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, -0.05], t$95$1, If[LessEqual[j, -8.1e-290], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 245.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -0.050000000000000003 or 245 < j

   1. Initial program 71.4%

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

      1. *-commutative 71.4%

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

      2. prod-diff 66.5%

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

      3. *-commutative 66.5%

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

      4. fma-neg 66.5%

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

      5. *-commutative 66.5%

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

      6. prod-diff 66.5%

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

      7. *-commutative 66.5%

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

      8. fma-neg 66.5%

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

      9. associate-+l+ 66.5%

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

      10. *-commutative 66.5%

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

      11. fma-neg 66.5%

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

      12. distribute-rgt-neg-in 66.5%

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

      13. *-commutative 66.5%

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

      14. *-commutative 66.5%

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

   4. Applied egg-rr 66.5%

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

      1. distribute-rgt-neg-out 66.5%

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

      2. fma-neg 66.5%

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

      3. *-commutative 66.5%

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

      4. count-2 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(c \cdot z - t \cdot i\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Simplified 66.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(c \cdot z - t \cdot i\right) + 2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   7. Taylor expanded in j around inf 65.5%

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

      1. *-commutative 65.5%

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

   9. Simplified 65.5%

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

   if -0.050000000000000003 < j < -8.10000000000000053e-290

   1. Initial program 67.3%

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

   3. Taylor expanded in x around inf 50.9%

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

      1. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   if -8.10000000000000053e-290 < j < 245

   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. Taylor expanded in z around inf 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.05:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.1 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 245:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+53}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1e-58)
     t_1
     (if (<= a 2.25e-242)
       (* y (* x z))
       (if (<= a 1.4e+53) (* (* i j) (- y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1e-58) {
		tmp = t_1;
	} else if (a <= 2.25e-242) {
		tmp = y * (x * z);
	} else if (a <= 1.4e+53) {
		tmp = (i * j) * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1d-58)) then
        tmp = t_1
    else if (a <= 2.25d-242) then
        tmp = y * (x * z)
    else if (a <= 1.4d+53) then
        tmp = (i * j) * -y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1e-58) {
		tmp = t_1;
	} else if (a <= 2.25e-242) {
		tmp = y * (x * z);
	} else if (a <= 1.4e+53) {
		tmp = (i * j) * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1e-58:
		tmp = t_1
	elif a <= 2.25e-242:
		tmp = y * (x * z)
	elif a <= 1.4e+53:
		tmp = (i * j) * -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1e-58)
		tmp = t_1;
	elseif (a <= 2.25e-242)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.4e+53)
		tmp = Float64(Float64(i * j) * Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1e-58)
		tmp = t_1;
	elseif (a <= 2.25e-242)
		tmp = y * (x * z);
	elseif (a <= 1.4e+53)
		tmp = (i * j) * -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-58], t$95$1, If[LessEqual[a, 2.25e-242], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+53], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e-58 or 1.4e53 < a

   1. Initial program 67.6%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

   if -1e-58 < a < 2.2499999999999999e-242

   1. Initial program 74.7%

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

   3. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around inf 41.9%

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

   if 2.2499999999999999e-242 < a < 1.4e53

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in z around 0 34.4%

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

      1. mul-1-neg 34.4%

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

      2. distribute-lft-neg-out 34.4%

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

      3. *-commutative 34.4%

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

   8. Simplified 34.4%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+53}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.1:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -6.1)
   (* a (* c j))
   (if (<= c 1.22e-160)
     (* y (* x z))
     (if (<= c 2.05e+29) (* b (* t i)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -6.1) {
		tmp = a * (c * j);
	} else if (c <= 1.22e-160) {
		tmp = y * (x * z);
	} else if (c <= 2.05e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-6.1d0)) then
        tmp = a * (c * j)
    else if (c <= 1.22d-160) then
        tmp = y * (x * z)
    else if (c <= 2.05d+29) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -6.1) {
		tmp = a * (c * j);
	} else if (c <= 1.22e-160) {
		tmp = y * (x * z);
	} else if (c <= 2.05e+29) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -6.1:
		tmp = a * (c * j)
	elif c <= 1.22e-160:
		tmp = y * (x * z)
	elif c <= 2.05e+29:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -6.1)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= 1.22e-160)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 2.05e+29)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -6.1)
		tmp = a * (c * j);
	elseif (c <= 1.22e-160)
		tmp = y * (x * z);
	elseif (c <= 2.05e+29)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -6.1], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.22e-160], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.05e+29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.0999999999999996

   1. Initial program 53.1%

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

   3. Taylor expanded in a around inf 38.3%

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

      1. +-commutative 38.3%

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

      2. mul-1-neg 38.3%

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

      3. unsub-neg 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in c around inf 31.0%

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

   if -6.0999999999999996 < c < 1.22000000000000003e-160

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in z around inf 34.5%

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

   if 1.22000000000000003e-160 < c < 2.0500000000000002e29

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 71.0%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. *-commutative 49.0%

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

   6. Simplified 49.0%

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

   if 2.0500000000000002e29 < c

   1. Initial program 54.5%

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

   3. Taylor expanded in a around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in c around inf 40.3%

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

      1. associate-*r* 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.1:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -61:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{-161}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -61.0)
     t_1
     (if (<= c 3.45e-161)
       (* y (* x z))
       (if (<= c 1.5e+30) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -61.0) {
		tmp = t_1;
	} else if (c <= 3.45e-161) {
		tmp = y * (x * z);
	} else if (c <= 1.5e+30) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (c <= (-61.0d0)) then
        tmp = t_1
    else if (c <= 3.45d-161) then
        tmp = y * (x * z)
    else if (c <= 1.5d+30) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -61.0) {
		tmp = t_1;
	} else if (c <= 3.45e-161) {
		tmp = y * (x * z);
	} else if (c <= 1.5e+30) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -61.0:
		tmp = t_1
	elif c <= 3.45e-161:
		tmp = y * (x * z)
	elif c <= 1.5e+30:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -61.0)
		tmp = t_1;
	elseif (c <= 3.45e-161)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 1.5e+30)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (c <= -61.0)
		tmp = t_1;
	elseif (c <= 3.45e-161)
		tmp = y * (x * z);
	elseif (c <= 1.5e+30)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -61.0], t$95$1, If[LessEqual[c, 3.45e-161], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+30], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -61 or 1.49999999999999989e30 < c

   1. Initial program 53.8%

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

   3. Taylor expanded in a around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in c around inf 35.6%

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

   if -61 < c < 3.45000000000000001e-161

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in z around inf 34.5%

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

   if 3.45000000000000001e-161 < c < 1.49999999999999989e30

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 71.0%

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

   4. Taylor expanded in t around inf 49.0%

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

      1. *-commutative 49.0%

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

   6. Simplified 49.0%

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

Alternative 16: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -0.000115 \lor \neg \left(j \leq 3.5 \cdot 10^{-5}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -0.000115) (not (<= j 3.5e-5)))
   (* j (- (* a c) (* y i)))
   (* x (- (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -0.000115) || !(j <= 3.5e-5)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-0.000115d0)) .or. (.not. (j <= 3.5d-5))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -0.000115) || !(j <= 3.5e-5)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -0.000115) or not (j <= 3.5e-5):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -0.000115) || !(j <= 3.5e-5))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -0.000115) || ~((j <= 3.5e-5)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -0.000115], N[Not[LessEqual[j, 3.5e-5]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.15e-4 or 3.4999999999999997e-5 < j

   1. Initial program 71.9%

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

      1. *-commutative 71.9%

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

      2. prod-diff 67.0%

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

      3. *-commutative 67.0%

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

      4. fma-neg 67.0%

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

      5. *-commutative 67.0%

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

      6. prod-diff 67.0%

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

      7. *-commutative 67.0%

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

      8. fma-neg 67.0%

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

      9. associate-+l+ 67.0%

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

      10. *-commutative 67.0%

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

      11. fma-neg 67.0%

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

      12. distribute-rgt-neg-in 67.0%

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

      13. *-commutative 67.0%

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

      14. *-commutative 67.0%

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

   4. Applied egg-rr 67.0%

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

      1. distribute-rgt-neg-out 67.0%

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

      2. fma-neg 67.0%

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

      3. *-commutative 67.0%

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

      4. count-2 67.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(c \cdot z - t \cdot i\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Simplified 67.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(c \cdot z - t \cdot i\right) + 2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   7. Taylor expanded in j around inf 64.5%

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

      1. *-commutative 64.5%

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

   9. Simplified 64.5%

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

   if -1.15e-4 < j < 3.4999999999999997e-5

   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 x around inf 48.6%

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

      1. *-commutative 48.6%

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

   5. Simplified 48.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.000115 \lor \neg \left(j \leq 3.5 \cdot 10^{-5}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-25} \lor \neg \left(j \leq 370\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.7e-25) (not (<= j 370.0)))
   (* j (- (* a c) (* y i)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.7e-25) || !(j <= 370.0)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.7d-25)) .or. (.not. (j <= 370.0d0))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.7e-25) || !(j <= 370.0)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.7e-25) or not (j <= 370.0):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.7e-25) || !(j <= 370.0))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.7e-25) || ~((j <= 370.0)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.7e-25], N[Not[LessEqual[j, 370.0]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.70000000000000001e-25 or 370 < j

   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. Step-by-step derivation

      1. *-commutative 72.1%

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

      2. prod-diff 66.5%

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

      3. *-commutative 66.5%

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

      4. fma-neg 66.5%

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

      5. *-commutative 66.5%

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

      6. prod-diff 66.5%

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

      7. *-commutative 66.5%

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

      8. fma-neg 66.5%

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

      9. associate-+l+ 66.5%

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

      10. *-commutative 66.5%

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

      11. fma-neg 66.5%

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

      12. distribute-rgt-neg-in 66.5%

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

      13. *-commutative 66.5%

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

      14. *-commutative 66.5%

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

   4. Applied egg-rr 66.5%

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

      1. distribute-rgt-neg-out 66.5%

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

      2. fma-neg 66.5%

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

      3. *-commutative 66.5%

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

      4. count-2 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(c \cdot z - t \cdot i\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Simplified 66.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(c \cdot z - t \cdot i\right) + 2 \cdot \mathsf{fma}\left(-i, t, t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   7. Taylor expanded in j around inf 64.7%

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

      1. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if -1.70000000000000001e-25 < j < 370

   1. Initial program 72.5%

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

   3. Taylor expanded in b around inf 43.5%

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

      1. *-commutative 43.5%

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

   5. Simplified 43.5%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-25} \lor \neg \left(j \leq 370\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+169} \lor \neg \left(a \leq 2.3 \cdot 10^{+121}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6e+169) (not (<= a 2.3e+121)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6e+169) || !(a <= 2.3e+121)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-6d+169)) .or. (.not. (a <= 2.3d+121))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6e+169) || !(a <= 2.3e+121)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -6e+169) or not (a <= 2.3e+121):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6e+169) || !(a <= 2.3e+121))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -6e+169) || ~((a <= 2.3e+121)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6e+169], N[Not[LessEqual[a, 2.3e+121]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.9999999999999999e169 or 2.2999999999999999e121 < a

   1. Initial program 62.3%

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

   3. Taylor expanded in a around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

   5. Simplified 74.2%

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

   if -5.9999999999999999e169 < a < 2.2999999999999999e121

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf 41.8%

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

      1. *-commutative 41.8%

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

   5. Simplified 41.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+169} \lor \neg \left(a \leq 2.3 \cdot 10^{+121}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{+118} \lor \neg \left(i \leq 1.35 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -7e+118) (not (<= i 1.35e-20))) (* 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 ((i <= -7e+118) || !(i <= 1.35e-20)) {
		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 ((i <= (-7d+118)) .or. (.not. (i <= 1.35d-20))) 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 ((i <= -7e+118) || !(i <= 1.35e-20)) {
		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 (i <= -7e+118) or not (i <= 1.35e-20):
		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 ((i <= -7e+118) || !(i <= 1.35e-20))
		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 ((i <= -7e+118) || ~((i <= 1.35e-20)))
		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[Or[LessEqual[i, -7e+118], N[Not[LessEqual[i, 1.35e-20]], $MachinePrecision]], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.00000000000000033e118 or 1.35e-20 < i

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0 68.9%

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

   4. Taylor expanded in t around inf 36.4%

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

      1. *-commutative 36.4%

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

   6. Simplified 36.4%

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

   7. Taylor expanded in b around 0 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-*l* 38.1%

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

      3. *-commutative 38.1%

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

      4. associate-*l* 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 -7.00000000000000033e118 < i < 1.35e-20

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 47.8%

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

      1. +-commutative 47.8%

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

      2. mul-1-neg 47.8%

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

      3. unsub-neg 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in c around inf 29.4%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{+118} \lor \neg \left(i \leq 1.35 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+118} \lor \neg \left(i \leq 2.9 \cdot 10^{-22}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -3.8e+118) (not (<= i 2.9e-22))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -3.8e+118) || !(i <= 2.9e-22)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-3.8d+118)) .or. (.not. (i <= 2.9d-22))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -3.8e+118) || !(i <= 2.9e-22)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -3.8e+118) or not (i <= 2.9e-22):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -3.8e+118) || !(i <= 2.9e-22))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -3.8e+118) || ~((i <= 2.9e-22)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -3.8e+118], N[Not[LessEqual[i, 2.9e-22]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.80000000000000016e118 or 2.9000000000000002e-22 < i

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0 68.9%

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

   4. Taylor expanded in t around inf 36.4%

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

      1. *-commutative 36.4%

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

   6. Simplified 36.4%

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

   if -3.80000000000000016e118 < i < 2.9000000000000002e-22

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 47.8%

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

      1. +-commutative 47.8%

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

      2. mul-1-neg 47.8%

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

      3. unsub-neg 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in c around inf 29.4%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.8 \cdot 10^{+118} \lor \neg \left(i \leq 2.9 \cdot 10^{-22}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.5% 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 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 a around inf 39.5%

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

   1. +-commutative 39.5%

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

   2. mul-1-neg 39.5%

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

   3. unsub-neg 39.5%

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

5. Simplified 39.5%

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

6. Taylor expanded in c around inf 22.3%

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

Developer Target 1: 58.5% 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 2024138 
(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)))))