Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 82.7%

Time: 16.9s

Alternatives: 21

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$1 + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * N[(b - N[(j * N[(y / a), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. fma-define 90.3%

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

      3. *-commutative 90.3%

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

      4. *-commutative 90.3%

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

      5. cancel-sign-sub-inv 90.3%

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

      6. cancel-sign-sub 90.3%

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

      7. sub-neg 90.3%

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

      8. sub-neg 90.3%

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

      9. *-commutative 90.3%

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

      10. fma-neg 90.3%

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

      11. *-commutative 90.3%

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

      12. distribute-rgt-neg-out 90.3%

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

      13. remove-double-neg 90.3%

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

      14. *-commutative 90.3%

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

      15. *-commutative 90.3%

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

   3. Simplified 90.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 37.8%

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

      1. distribute-lft-out-- 37.8%

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

      2. *-commutative 37.8%

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

      3. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 54.4%

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

   8. Simplified 54.4%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(a \cdot \left(j \cdot \frac{y}{a} - b\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

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

Alternative 2: 82.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(a * N[(b - N[(j * N[(y / a), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 90.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 37.8%

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

      1. distribute-lft-out-- 37.8%

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

      2. *-commutative 37.8%

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

      3. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 54.4%

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

   8. Simplified 54.4%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(a \cdot \left(j \cdot \frac{y}{a} - b\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.5%

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

Alternative 3: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := \left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;t\_1 + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+218}:\\ \;\;\;\;t\_1 + \left(z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* (* a b) (- i (* c (/ z a))))))
   (if (<= b -5.8e+47)
     t_2
     (if (<= b 8.2e-14)
       (+ t_1 (- (* x (- (* y z) (* t a))) (* c (* z b))))
       (if (<= b 7.5e+218)
         (+ t_1 (- (* z (* x y)) (* b (- (* z c) (* a i)))))
         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 * ((t * c) - (y * i));
	double t_2 = (a * b) * (i - (c * (z / a)));
	double tmp;
	if (b <= -5.8e+47) {
		tmp = t_2;
	} else if (b <= 8.2e-14) {
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	} else if (b <= 7.5e+218) {
		tmp = t_1 + ((z * (x * y)) - (b * ((z * c) - (a * i))));
	} 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 * ((t * c) - (y * i))
    t_2 = (a * b) * (i - (c * (z / a)))
    if (b <= (-5.8d+47)) then
        tmp = t_2
    else if (b <= 8.2d-14) then
        tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)))
    else if (b <= 7.5d+218) then
        tmp = t_1 + ((z * (x * y)) - (b * ((z * c) - (a * i))))
    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 * ((t * c) - (y * i));
	double t_2 = (a * b) * (i - (c * (z / a)));
	double tmp;
	if (b <= -5.8e+47) {
		tmp = t_2;
	} else if (b <= 8.2e-14) {
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	} else if (b <= 7.5e+218) {
		tmp = t_1 + ((z * (x * y)) - (b * ((z * c) - (a * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = (a * b) * (i - (c * (z / a)))
	tmp = 0
	if b <= -5.8e+47:
		tmp = t_2
	elif b <= 8.2e-14:
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)))
	elif b <= 7.5e+218:
		tmp = t_1 + ((z * (x * y)) - (b * ((z * c) - (a * i))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(Float64(a * b) * Float64(i - Float64(c * Float64(z / a))))
	tmp = 0.0
	if (b <= -5.8e+47)
		tmp = t_2;
	elseif (b <= 8.2e-14)
		tmp = Float64(t_1 + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b))));
	elseif (b <= 7.5e+218)
		tmp = Float64(t_1 + Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(a * i)))));
	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 * ((t * c) - (y * i));
	t_2 = (a * b) * (i - (c * (z / a)));
	tmp = 0.0;
	if (b <= -5.8e+47)
		tmp = t_2;
	elseif (b <= 8.2e-14)
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	elseif (b <= 7.5e+218)
		tmp = t_1 + ((z * (x * y)) - (b * ((z * c) - (a * i))));
	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[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * N[(i - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+47], t$95$2, If[LessEqual[b, 8.2e-14], N[(t$95$1 + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+218], N[(t$95$1 + N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.79999999999999961e47 or 7.4999999999999993e218 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 74.3%

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

   4. Taylor expanded in a around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-/l* 69.3%

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

      3. associate-*r/ 73.9%

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

      4. distribute-rgt-neg-in 73.9%

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

      5. associate-*r/ 69.3%

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

      6. mul-1-neg 69.3%

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

      7. distribute-lft-in 74.4%

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

      8. remove-double-neg 74.4%

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

      9. neg-mul-1 74.4%

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

      10. sub-neg 74.4%

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

      11. associate-*r* 72.9%

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

      12. sub-neg 72.9%

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

      13. neg-mul-1 72.9%

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

      14. remove-double-neg 72.9%

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

      15. +-commutative 72.9%

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

      16. mul-1-neg 72.9%

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

      17. associate-*r/ 80.6%

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

   6. Simplified 80.6%

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

   if -5.79999999999999961e47 < b < 8.2000000000000004e-14

   1. Initial program 76.0%

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

   3. Taylor expanded in c around inf 85.0%

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

      1. +-commutative 85.0%

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

      2. mul-1-neg 85.0%

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

      3. unsub-neg 85.0%

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

      4. associate-/l* 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 85.0%

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

   if 8.2000000000000004e-14 < b < 7.4999999999999993e218

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 79.9%

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

      1. *-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*l* 78.0%

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

      4. *-commutative 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+218}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+48} \lor \neg \left(b \leq 1.4 \cdot 10^{+211}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -7.8e+48) (not (<= b 1.4e+211)))
   (* (* a b) (- i (* c (/ z a))))
   (+ (* j (- (* t c) (* y i))) (- (* x (- (* y z) (* t a))) (* c (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -7.8e+48) || !(b <= 1.4e+211)) {
		tmp = (a * b) * (i - (c * (z / a)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-7.8d+48)) .or. (.not. (b <= 1.4d+211))) then
        tmp = (a * b) * (i - (c * (z / a)))
    else
        tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -7.8e+48) || !(b <= 1.4e+211)) {
		tmp = (a * b) * (i - (c * (z / a)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -7.8e+48) or not (b <= 1.4e+211):
		tmp = (a * b) * (i - (c * (z / a)))
	else:
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -7.8e+48) || !(b <= 1.4e+211))
		tmp = Float64(Float64(a * b) * Float64(i - Float64(c * Float64(z / a))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -7.8e+48) || ~((b <= 1.4e+211)))
		tmp = (a * b) * (i - (c * (z / a)));
	else
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -7.8e+48], N[Not[LessEqual[b, 1.4e+211]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] * N[(i - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.8000000000000002e48 or 1.4e211 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in b around inf 74.7%

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

   4. Taylor expanded in a around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-/l* 68.4%

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

      3. associate-*r/ 72.9%

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

      4. distribute-rgt-neg-in 72.9%

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

      5. associate-*r/ 68.4%

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

      6. mul-1-neg 68.4%

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

      7. distribute-lft-in 73.4%

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

      8. remove-double-neg 73.4%

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

      9. neg-mul-1 73.4%

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

      10. sub-neg 73.4%

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

      11. associate-*r* 73.4%

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

      12. sub-neg 73.4%

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

      13. neg-mul-1 73.4%

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

      14. remove-double-neg 73.4%

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

      15. +-commutative 73.4%

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

      16. mul-1-neg 73.4%

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

      17. associate-*r/ 79.5%

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

   6. Simplified 79.5%

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

   if -7.8000000000000002e48 < b < 1.4e211

   1. Initial program 77.4%

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

   3. Taylor expanded in c around inf 83.0%

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

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. unsub-neg 83.0%

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

      4. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around inf 80.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+48} \lor \neg \left(b \leq 1.4 \cdot 10^{+211}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;b \leq 112000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.9e+43)
   (* (* a b) (- i (* c (/ z a))))
   (if (<= b 112000000000.0)
     (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
     (* b (- (* a i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.9e+43) {
		tmp = (a * b) * (i - (c * (z / a)));
	} else if (b <= 112000000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.9d+43)) then
        tmp = (a * b) * (i - (c * (z / a)))
    else if (b <= 112000000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.9e+43) {
		tmp = (a * b) * (i - (c * (z / a)));
	} else if (b <= 112000000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.9e+43:
		tmp = (a * b) * (i - (c * (z / a)))
	elif b <= 112000000000.0:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.9e+43)
		tmp = Float64(Float64(a * b) * Float64(i - Float64(c * Float64(z / a))));
	elseif (b <= 112000000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.9e+43)
		tmp = (a * b) * (i - (c * (z / a)));
	elseif (b <= 112000000000.0)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.9e+43], N[(N[(a * b), $MachinePrecision] * N[(i - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 112000000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.9000000000000002e43

   1. Initial program 70.9%

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

   3. Taylor expanded in b around inf 67.2%

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

   4. Taylor expanded in a around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. associate-/l* 64.9%

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

      3. associate-*r/ 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. associate-*r/ 64.9%

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

      6. mul-1-neg 64.9%

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

      7. distribute-lft-in 67.4%

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

      8. remove-double-neg 67.4%

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

      9. neg-mul-1 67.4%

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

      10. sub-neg 67.4%

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

      11. associate-*r* 65.3%

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

      12. sub-neg 65.3%

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

      13. neg-mul-1 65.3%

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

      14. remove-double-neg 65.3%

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

      15. +-commutative 65.3%

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

      16. mul-1-neg 65.3%

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

      17. associate-*r/ 73.7%

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

   6. Simplified 73.7%

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

   if -2.9000000000000002e43 < b < 1.12e11

   1. Initial program 74.9%

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

   3. Taylor expanded in b around 0 79.5%

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

   if 1.12e11 < b

   1. Initial program 81.0%

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

   3. Taylor expanded in b around inf 68.5%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(i - c \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;b \leq 112000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-40}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))))
   (if (<= z -1.9e+179)
     (* x (* y z))
     (if (<= z -5.8e+82)
       t_1
       (if (<= z 2e-235)
         (* a (* x (- t)))
         (if (<= z 2.8e-40) (* i (* a b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * -c;
	double tmp;
	if (z <= -1.9e+179) {
		tmp = x * (y * z);
	} else if (z <= -5.8e+82) {
		tmp = t_1;
	} else if (z <= 2e-235) {
		tmp = a * (x * -t);
	} else if (z <= 2.8e-40) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * b) * -c
    if (z <= (-1.9d+179)) then
        tmp = x * (y * z)
    else if (z <= (-5.8d+82)) then
        tmp = t_1
    else if (z <= 2d-235) then
        tmp = a * (x * -t)
    else if (z <= 2.8d-40) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * -c;
	double tmp;
	if (z <= -1.9e+179) {
		tmp = x * (y * z);
	} else if (z <= -5.8e+82) {
		tmp = t_1;
	} else if (z <= 2e-235) {
		tmp = a * (x * -t);
	} else if (z <= 2.8e-40) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	tmp = 0
	if z <= -1.9e+179:
		tmp = x * (y * z)
	elif z <= -5.8e+82:
		tmp = t_1
	elif z <= 2e-235:
		tmp = a * (x * -t)
	elif z <= 2.8e-40:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (z <= -1.9e+179)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -5.8e+82)
		tmp = t_1;
	elseif (z <= 2e-235)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (z <= 2.8e-40)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * b) * -c;
	tmp = 0.0;
	if (z <= -1.9e+179)
		tmp = x * (y * z);
	elseif (z <= -5.8e+82)
		tmp = t_1;
	elseif (z <= 2e-235)
		tmp = a * (x * -t);
	elseif (z <= 2.8e-40)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[z, -1.9e+179], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e+82], t$95$1, If[LessEqual[z, 2e-235], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-40], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e179

   1. Initial program 64.7%

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

   3. Taylor expanded in z around inf 71.8%

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

   4. Taylor expanded in x around inf 62.1%

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

      1. *-commutative 62.1%

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

   6. Simplified 62.1%

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

   if -1.9e179 < z < -5.8000000000000003e82 or 2.8e-40 < z

   1. Initial program 69.3%

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

   3. Taylor expanded in c around inf 69.5%

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

      1. +-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

      4. associate-/l* 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around inf 70.5%

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

   7. Taylor expanded in b around inf 32.7%

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

      1. associate-*r* 36.7%

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

      2. *-commutative 36.7%

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

      3. associate-*r* 39.0%

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

      4. neg-mul-1 39.0%

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

      5. distribute-rgt-neg-in 39.0%

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

   9. Simplified 39.0%

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

   if -5.8000000000000003e82 < z < 1.9999999999999999e-235

   1. Initial program 80.5%

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

   3. Taylor expanded in c around inf 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around inf 73.1%

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

   7. Taylor expanded in a around inf 37.8%

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

      1. associate-*r* 37.8%

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

      2. neg-mul-1 37.8%

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

   9. Simplified 37.8%

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

   if 1.9999999999999999e-235 < z < 2.8e-40

   1. Initial program 86.3%

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

   3. Taylor expanded in b around inf 42.0%

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

   4. Taylor expanded in a around inf 39.2%

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

      1. associate-*r* 41.6%

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

   6. Simplified 41.6%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-40}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))))
   (if (<= z -1.9e+179)
     (* x (* y z))
     (if (<= z -4.5e+80)
       t_1
       (if (<= z 4.9e-237)
         (* x (* t (- a)))
         (if (<= z 2.6e-38) (* i (* a b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * -c;
	double tmp;
	if (z <= -1.9e+179) {
		tmp = x * (y * z);
	} else if (z <= -4.5e+80) {
		tmp = t_1;
	} else if (z <= 4.9e-237) {
		tmp = x * (t * -a);
	} else if (z <= 2.6e-38) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * b) * -c
    if (z <= (-1.9d+179)) then
        tmp = x * (y * z)
    else if (z <= (-4.5d+80)) then
        tmp = t_1
    else if (z <= 4.9d-237) then
        tmp = x * (t * -a)
    else if (z <= 2.6d-38) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * -c;
	double tmp;
	if (z <= -1.9e+179) {
		tmp = x * (y * z);
	} else if (z <= -4.5e+80) {
		tmp = t_1;
	} else if (z <= 4.9e-237) {
		tmp = x * (t * -a);
	} else if (z <= 2.6e-38) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	tmp = 0
	if z <= -1.9e+179:
		tmp = x * (y * z)
	elif z <= -4.5e+80:
		tmp = t_1
	elif z <= 4.9e-237:
		tmp = x * (t * -a)
	elif z <= 2.6e-38:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (z <= -1.9e+179)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -4.5e+80)
		tmp = t_1;
	elseif (z <= 4.9e-237)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (z <= 2.6e-38)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * b) * -c;
	tmp = 0.0;
	if (z <= -1.9e+179)
		tmp = x * (y * z);
	elseif (z <= -4.5e+80)
		tmp = t_1;
	elseif (z <= 4.9e-237)
		tmp = x * (t * -a);
	elseif (z <= 2.6e-38)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[z, -1.9e+179], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e+80], t$95$1, If[LessEqual[z, 4.9e-237], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-38], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e179

   1. Initial program 64.7%

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

   3. Taylor expanded in z around inf 71.8%

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

   4. Taylor expanded in x around inf 62.1%

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

      1. *-commutative 62.1%

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

   6. Simplified 62.1%

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

   if -1.9e179 < z < -4.50000000000000007e80 or 2.60000000000000011e-38 < z

   1. Initial program 69.3%

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

   3. Taylor expanded in c around inf 69.5%

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

      1. +-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

      4. associate-/l* 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around inf 70.5%

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

   7. Taylor expanded in b around inf 32.7%

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

      1. associate-*r* 36.7%

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

      2. *-commutative 36.7%

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

      3. associate-*r* 39.0%

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

      4. neg-mul-1 39.0%

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

      5. distribute-rgt-neg-in 39.0%

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

   9. Simplified 39.0%

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

   if -4.50000000000000007e80 < z < 4.9000000000000001e-237

   1. Initial program 80.5%

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

   3. Taylor expanded in c around inf 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around inf 73.1%

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

   7. Taylor expanded in x around inf 41.9%

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

      1. *-commutative 41.9%

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

      2. *-commutative 41.9%

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

   9. Simplified 41.9%

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

   10. Taylor expanded in z around 0 37.8%

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

       1. mul-1-neg 37.8%

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

       2. *-commutative 37.8%

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

       3. distribute-rgt-neg-in 37.8%

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

   12. Simplified 37.8%

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

   if 4.9000000000000001e-237 < z < 2.60000000000000011e-38

   1. Initial program 86.3%

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

   3. Taylor expanded in b around inf 42.0%

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

   4. Taylor expanded in a around inf 39.2%

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

      1. associate-*r* 41.6%

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

   6. Simplified 41.6%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9.2e+29)
   (* i (* j (- y)))
   (if (<= j -7.6e-19)
     (* x (* y z))
     (if (<= j 5.4e-118)
       (* x (* t (- a)))
       (if (<= j 1.3e+87) (* b (* a i)) (* c (* t j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.2e+29) {
		tmp = i * (j * -y);
	} else if (j <= -7.6e-19) {
		tmp = x * (y * z);
	} else if (j <= 5.4e-118) {
		tmp = x * (t * -a);
	} else if (j <= 1.3e+87) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-9.2d+29)) then
        tmp = i * (j * -y)
    else if (j <= (-7.6d-19)) then
        tmp = x * (y * z)
    else if (j <= 5.4d-118) then
        tmp = x * (t * -a)
    else if (j <= 1.3d+87) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.2e+29) {
		tmp = i * (j * -y);
	} else if (j <= -7.6e-19) {
		tmp = x * (y * z);
	} else if (j <= 5.4e-118) {
		tmp = x * (t * -a);
	} else if (j <= 1.3e+87) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -9.2e+29:
		tmp = i * (j * -y)
	elif j <= -7.6e-19:
		tmp = x * (y * z)
	elif j <= 5.4e-118:
		tmp = x * (t * -a)
	elif j <= 1.3e+87:
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9.2e+29)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (j <= -7.6e-19)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 5.4e-118)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 1.3e+87)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -9.2e+29)
		tmp = i * (j * -y);
	elseif (j <= -7.6e-19)
		tmp = x * (y * z);
	elseif (j <= 5.4e-118)
		tmp = x * (t * -a);
	elseif (j <= 1.3e+87)
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9.2e+29], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.6e-19], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e-118], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e+87], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -9.2000000000000004e29

   1. Initial program 83.4%

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

   3. Taylor expanded in b around 0 79.7%

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

   4. Taylor expanded in i around inf 48.4%

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

      1. associate-*r* 48.4%

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

      2. neg-mul-1 48.4%

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

      3. *-commutative 48.4%

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

   6. Simplified 48.4%

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

   if -9.2000000000000004e29 < j < -7.6e-19

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf 68.4%

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

   4. Taylor expanded in x around inf 78.7%

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

      1. *-commutative 78.7%

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

   6. Simplified 78.7%

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

   if -7.6e-19 < j < 5.39999999999999988e-118

   1. Initial program 73.1%

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

   3. Taylor expanded in c around inf 75.1%

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

      1. +-commutative 75.1%

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

      2. mul-1-neg 75.1%

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

      3. unsub-neg 75.1%

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

      4. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around inf 67.8%

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

   7. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

   9. Simplified 54.9%

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

   10. Taylor expanded in z around 0 35.1%

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

       1. mul-1-neg 35.1%

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

       2. *-commutative 35.1%

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

       3. distribute-rgt-neg-in 35.1%

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

   12. Simplified 35.1%

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

   if 5.39999999999999988e-118 < j < 1.29999999999999999e87

   1. Initial program 75.6%

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

   3. Taylor expanded in b around inf 61.6%

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

   4. Taylor expanded in a around inf 45.1%

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

   if 1.29999999999999999e87 < j

   1. Initial program 70.1%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around inf 44.3%

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

      1. *-commutative 44.3%

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

   6. Simplified 44.3%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.22e+95)
     t_1
     (if (<= j -1.35e-263)
       (* x (- (* y z) (* t a)))
       (if (<= j 8.2e+86) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.22e+95) {
		tmp = t_1;
	} else if (j <= -1.35e-263) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 8.2e+86) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.22d+95)) then
        tmp = t_1
    else if (j <= (-1.35d-263)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 8.2d+86) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.22e+95) {
		tmp = t_1;
	} else if (j <= -1.35e-263) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 8.2e+86) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.22e+95:
		tmp = t_1
	elif j <= -1.35e-263:
		tmp = x * ((y * z) - (t * a))
	elif j <= 8.2e+86:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.22e+95)
		tmp = t_1;
	elseif (j <= -1.35e-263)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 8.2e+86)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.22e+95)
		tmp = t_1;
	elseif (j <= -1.35e-263)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 8.2e+86)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.22e+95], t$95$1, If[LessEqual[j, -1.35e-263], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+86], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.22000000000000007e95 or 8.1999999999999998e86 < j

   1. Initial program 76.8%

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

   3. Taylor expanded in b around 0 79.5%

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

   4. Taylor expanded in j around inf 77.2%

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

   if -1.22000000000000007e95 < j < -1.35000000000000002e-263

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0 68.0%

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

   4. Taylor expanded in j around 0 62.8%

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

   if -1.35000000000000002e-263 < j < 8.1999999999999998e86

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf 58.7%

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

      1. distribute-lft-out-- 58.7%

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

      2. *-commutative 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.1 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -4.1e+95)
     t_1
     (if (<= j -7.2e-287)
       (* x (- (* y z) (* t a)))
       (if (<= j 8.2e+86) (* b (- (* a 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 * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.1e+95) {
		tmp = t_1;
	} else if (j <= -7.2e-287) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 8.2e+86) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-4.1d+95)) then
        tmp = t_1
    else if (j <= (-7.2d-287)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 8.2d+86) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.1e+95) {
		tmp = t_1;
	} else if (j <= -7.2e-287) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 8.2e+86) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -4.1e+95:
		tmp = t_1
	elif j <= -7.2e-287:
		tmp = x * ((y * z) - (t * a))
	elif j <= 8.2e+86:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.1e+95)
		tmp = t_1;
	elseif (j <= -7.2e-287)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 8.2e+86)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.1e+95)
		tmp = t_1;
	elseif (j <= -7.2e-287)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 8.2e+86)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.1e+95], t$95$1, If[LessEqual[j, -7.2e-287], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+86], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.09999999999999986e95 or 8.1999999999999998e86 < j

   1. Initial program 76.8%

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

   3. Taylor expanded in b around 0 79.5%

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

   4. Taylor expanded in j around inf 77.2%

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

   if -4.09999999999999986e95 < j < -7.2000000000000003e-287

   1. Initial program 77.4%

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

   3. Taylor expanded in b around 0 66.8%

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

   4. Taylor expanded in j around 0 62.0%

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

   if -7.2000000000000003e-287 < j < 8.1999999999999998e86

   1. Initial program 73.5%

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

   3. Taylor expanded in b around inf 58.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 110000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -8e+18)
     t_1
     (if (<= b 3.5e-211)
       (* j (- (* t c) (* y i)))
       (if (<= b 110000000000.0) (* t (- (* c j) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8e+18) {
		tmp = t_1;
	} else if (b <= 3.5e-211) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 110000000000.0) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-8d+18)) then
        tmp = t_1
    else if (b <= 3.5d-211) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 110000000000.0d0) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8e+18) {
		tmp = t_1;
	} else if (b <= 3.5e-211) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 110000000000.0) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -8e+18:
		tmp = t_1
	elif b <= 3.5e-211:
		tmp = j * ((t * c) - (y * i))
	elif b <= 110000000000.0:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8e+18)
		tmp = t_1;
	elseif (b <= 3.5e-211)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 110000000000.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -8e+18)
		tmp = t_1;
	elseif (b <= 3.5e-211)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 110000000000.0)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+18], t$95$1, If[LessEqual[b, 3.5e-211], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 110000000000.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8e18 or 1.1e11 < b

   1. Initial program 77.2%

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

   3. Taylor expanded in b around inf 67.4%

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

   if -8e18 < b < 3.5e-211

   1. Initial program 75.6%

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

   3. Taylor expanded in b around 0 79.2%

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

   4. Taylor expanded in j around inf 47.7%

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

   if 3.5e-211 < b < 1.1e11

   1. Initial program 72.7%

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

   3. Taylor expanded in t around inf 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

   5. Simplified 68.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 110000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.45e+97)
   (* j (* y (- i)))
   (if (<= j -6e-264)
     (* x (* y z))
     (if (<= j 8.2e+86) (* b (* a i)) (* c (* t j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.45e+97) {
		tmp = j * (y * -i);
	} else if (j <= -6e-264) {
		tmp = x * (y * z);
	} else if (j <= 8.2e+86) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.45d+97)) then
        tmp = j * (y * -i)
    else if (j <= (-6d-264)) then
        tmp = x * (y * z)
    else if (j <= 8.2d+86) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.45e+97) {
		tmp = j * (y * -i);
	} else if (j <= -6e-264) {
		tmp = x * (y * z);
	} else if (j <= 8.2e+86) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.45e+97:
		tmp = j * (y * -i)
	elif j <= -6e-264:
		tmp = x * (y * z)
	elif j <= 8.2e+86:
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.45e+97)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (j <= -6e-264)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 8.2e+86)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.45e+97)
		tmp = j * (y * -i);
	elseif (j <= -6e-264)
		tmp = x * (y * z);
	elseif (j <= 8.2e+86)
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.45e+97], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-264], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+86], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.44999999999999994e97

   1. Initial program 82.5%

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

   3. Taylor expanded in c around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in z around inf 80.4%

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

   7. Taylor expanded in i around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. *-commutative 53.6%

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

      3. *-commutative 53.6%

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

      4. distribute-rgt-neg-in 53.6%

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

      5. *-commutative 53.6%

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

      6. associate-*l* 46.8%

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

   9. Simplified 46.8%

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

   if -1.44999999999999994e97 < j < -6.0000000000000001e-264

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf 43.7%

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

   4. Taylor expanded in x around inf 34.6%

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

      1. *-commutative 34.6%

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

   6. Simplified 34.6%

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

   if -6.0000000000000001e-264 < j < 8.1999999999999998e86

   1. Initial program 72.0%

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

   3. Taylor expanded in b around inf 56.5%

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

   4. Taylor expanded in a around inf 37.6%

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

   if 8.1999999999999998e86 < j

   1. Initial program 70.1%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around inf 44.3%

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

      1. *-commutative 44.3%

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

   6. Simplified 44.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -8.5e+29)
   (* t (* c j))
   (if (<= j -4.7e-265)
     (* x (* y z))
     (if (<= j 8.8e+86) (* b (* a i)) (* c (* t j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8.5e+29) {
		tmp = t * (c * j);
	} else if (j <= -4.7e-265) {
		tmp = x * (y * z);
	} else if (j <= 8.8e+86) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-8.5d+29)) then
        tmp = t * (c * j)
    else if (j <= (-4.7d-265)) then
        tmp = x * (y * z)
    else if (j <= 8.8d+86) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8.5e+29) {
		tmp = t * (c * j);
	} else if (j <= -4.7e-265) {
		tmp = x * (y * z);
	} else if (j <= 8.8e+86) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -8.5e+29:
		tmp = t * (c * j)
	elif j <= -4.7e-265:
		tmp = x * (y * z)
	elif j <= 8.8e+86:
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -8.5e+29)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= -4.7e-265)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 8.8e+86)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -8.5e+29)
		tmp = t * (c * j);
	elseif (j <= -4.7e-265)
		tmp = x * (y * z);
	elseif (j <= 8.8e+86)
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -8.5e+29], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.7e-265], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.8e+86], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.5000000000000006e29

   1. Initial program 83.4%

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

   3. Taylor expanded in b around 0 79.7%

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

   4. Taylor expanded in c around inf 37.9%

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

      1. associate-*r* 39.6%

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

   6. Simplified 39.6%

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

   if -8.5000000000000006e29 < j < -4.69999999999999986e-265

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 44.3%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. *-commutative 37.0%

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

   6. Simplified 37.0%

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

   if -4.69999999999999986e-265 < j < 8.80000000000000013e86

   1. Initial program 72.0%

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

   3. Taylor expanded in b around inf 56.5%

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

   4. Taylor expanded in a around inf 37.6%

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

   if 8.80000000000000013e86 < j

   1. Initial program 70.1%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around inf 44.3%

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

      1. *-commutative 44.3%

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

   6. Simplified 44.3%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -8 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.86 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -8e+29)
     t_1
     (if (<= j -1.86e-264)
       (* x (* y z))
       (if (<= j 8.8e+86) (* b (* a 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 = c * (t * j);
	double tmp;
	if (j <= -8e+29) {
		tmp = t_1;
	} else if (j <= -1.86e-264) {
		tmp = x * (y * z);
	} else if (j <= 8.8e+86) {
		tmp = b * (a * 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 = c * (t * j)
    if (j <= (-8d+29)) then
        tmp = t_1
    else if (j <= (-1.86d-264)) then
        tmp = x * (y * z)
    else if (j <= 8.8d+86) then
        tmp = b * (a * 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 = c * (t * j);
	double tmp;
	if (j <= -8e+29) {
		tmp = t_1;
	} else if (j <= -1.86e-264) {
		tmp = x * (y * z);
	} else if (j <= 8.8e+86) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -8e+29:
		tmp = t_1
	elif j <= -1.86e-264:
		tmp = x * (y * z)
	elif j <= 8.8e+86:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -8e+29)
		tmp = t_1;
	elseif (j <= -1.86e-264)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 8.8e+86)
		tmp = Float64(b * Float64(a * 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 = c * (t * j);
	tmp = 0.0;
	if (j <= -8e+29)
		tmp = t_1;
	elseif (j <= -1.86e-264)
		tmp = x * (y * z);
	elseif (j <= 8.8e+86)
		tmp = b * (a * 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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8e+29], t$95$1, If[LessEqual[j, -1.86e-264], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.8e+86], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.99999999999999931e29 or 8.80000000000000013e86 < j

   1. Initial program 77.7%

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

   3. Taylor expanded in b around 0 78.1%

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

   4. Taylor expanded in c around inf 40.6%

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

      1. *-commutative 40.6%

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

   6. Simplified 40.6%

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

   if -7.99999999999999931e29 < j < -1.86e-264

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 44.3%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. *-commutative 37.0%

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

   6. Simplified 37.0%

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

   if -1.86e-264 < j < 8.80000000000000013e86

   1. Initial program 72.0%

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

   3. Taylor expanded in b around inf 56.5%

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

   4. Taylor expanded in a around inf 37.6%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.86 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+14} \lor \neg \left(j \leq 1.1 \cdot 10^{+87}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -7e+14) (not (<= j 1.1e+87)))
   (* j (- (* t c) (* y i)))
   (* b (- (* a 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 <= -7e+14) || !(j <= 1.1e+87)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * 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 <= (-7d+14)) .or. (.not. (j <= 1.1d+87))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = b * ((a * 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 <= -7e+14) || !(j <= 1.1e+87)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -7e+14) or not (j <= 1.1e+87):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -7e+14) || !(j <= 1.1e+87))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(Float64(a * 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 <= -7e+14) || ~((j <= 1.1e+87)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -7e+14], N[Not[LessEqual[j, 1.1e+87]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -7e14 or 1.1e87 < j

   1. Initial program 76.9%

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

   3. Taylor expanded in b around 0 78.4%

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

   4. Taylor expanded in j around inf 73.1%

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

   if -7e14 < j < 1.1e87

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 47.5%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+14} \lor \neg \left(j \leq 1.1 \cdot 10^{+87}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -88 \lor \neg \left(i \leq 1.25 \cdot 10^{-44}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -88.0) (not (<= i 1.25e-44)))
   (* i (- (* a b) (* y j)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -88.0) || !(i <= 1.25e-44)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-88.0d0)) .or. (.not. (i <= 1.25d-44))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -88.0) || !(i <= 1.25e-44)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -88.0) or not (i <= 1.25e-44):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -88.0) || !(i <= 1.25e-44))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -88.0) || ~((i <= 1.25e-44)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -88.0], N[Not[LessEqual[i, 1.25e-44]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -88 or 1.2500000000000001e-44 < i

   1. Initial program 69.8%

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

   3. Taylor expanded in i around inf 60.2%

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

      1. distribute-lft-out-- 60.2%

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

      2. *-commutative 60.2%

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

      3. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in i around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. *-commutative 60.2%

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

      3. *-commutative 60.2%

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

      4. fma-neg 61.8%

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

      5. distribute-lft-neg-in 61.8%

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

      6. distribute-rgt-neg-out 61.8%

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

      7. neg-sub0 61.8%

         \[\leadsto i \cdot \color{blue}{\left(0 - \mathsf{fma}\left(y, j, \left(-b\right) \cdot a\right)\right)} \]

      8. distribute-lft-neg-in 61.8%

         \[\leadsto i \cdot \left(0 - \mathsf{fma}\left(y, j, \color{blue}{-b \cdot a}\right)\right) \]

      9. fma-neg 60.2%

         \[\leadsto i \cdot \left(0 - \color{blue}{\left(y \cdot j - b \cdot a\right)}\right) \]

      10. associate--r- 60.2%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - y \cdot j\right) + b \cdot a\right)} \]

      11. neg-sub0 60.2%

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

      12. *-commutative 60.2%

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

      13. mul-1-neg 60.2%

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

      14. *-commutative 60.2%

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

      15. +-commutative 60.2%

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

      16. *-commutative 60.2%

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

      17. mul-1-neg 60.2%

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

      18. *-commutative 60.2%

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

      19. unsub-neg 60.2%

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

      20. *-commutative 60.2%

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

   8. Simplified 60.2%

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

   if -88 < i < 1.2500000000000001e-44

   1. Initial program 81.8%

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

   3. Taylor expanded in c around inf 48.4%

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

      1. *-commutative 48.4%

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

   5. Simplified 48.4%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -88 \lor \neg \left(i \leq 1.25 \cdot 10^{-44}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -260 \lor \neg \left(i \leq 2.7 \cdot 10^{+23}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -260.0) (not (<= i 2.7e+23)))
   (* b (- (* a i) (* z c)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -260.0) || !(i <= 2.7e+23)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-260.0d0)) .or. (.not. (i <= 2.7d+23))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -260.0) || !(i <= 2.7e+23)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -260.0) or not (i <= 2.7e+23):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -260.0) || !(i <= 2.7e+23))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -260.0) || ~((i <= 2.7e+23)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -260.0], N[Not[LessEqual[i, 2.7e+23]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -260 or 2.6999999999999999e23 < i

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 53.2%

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

   if -260 < i < 2.6999999999999999e23

   1. Initial program 82.8%

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

   3. Taylor expanded in c around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -260 \lor \neg \left(i \leq 2.7 \cdot 10^{+23}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9.8e+54)
   (* i (* j (- y)))
   (if (<= j 1.5e+87) (* b (- (* a i) (* z c))) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.8e+54) {
		tmp = i * (j * -y);
	} else if (j <= 1.5e+87) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-9.8d+54)) then
        tmp = i * (j * -y)
    else if (j <= 1.5d+87) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.8e+54) {
		tmp = i * (j * -y);
	} else if (j <= 1.5e+87) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -9.8e+54:
		tmp = i * (j * -y)
	elif j <= 1.5e+87:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9.8e+54)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (j <= 1.5e+87)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -9.8e+54)
		tmp = i * (j * -y);
	elseif (j <= 1.5e+87)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9.8e+54], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+87], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.80000000000000002e54

   1. Initial program 83.3%

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

   3. Taylor expanded in b around 0 83.3%

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

   4. Taylor expanded in i around inf 53.5%

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

      1. associate-*r* 53.5%

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

      2. neg-mul-1 53.5%

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

      3. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   if -9.80000000000000002e54 < j < 1.4999999999999999e87

   1. Initial program 75.1%

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

   3. Taylor expanded in b around inf 46.7%

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

   if 1.4999999999999999e87 < j

   1. Initial program 70.1%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around inf 44.3%

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

      1. *-commutative 44.3%

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

   6. Simplified 44.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2400 \lor \neg \left(i \leq 2.9 \cdot 10^{+20}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2400.0) (not (<= i 2.9e+20))) (* b (* a i)) (* c (* t 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 <= -2400.0) || !(i <= 2.9e+20)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * 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 <= (-2400.0d0)) .or. (.not. (i <= 2.9d+20))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * 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 <= -2400.0) || !(i <= 2.9e+20)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2400.0) or not (i <= 2.9e+20):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2400.0) || !(i <= 2.9e+20))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2400.0) || ~((i <= 2.9e+20)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2400.0], N[Not[LessEqual[i, 2.9e+20]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2400 or 2.9e20 < i

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 53.2%

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

   4. Taylor expanded in a around inf 44.5%

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

   if -2400 < i < 2.9e20

   1. Initial program 82.8%

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

   3. Taylor expanded in b around 0 71.4%

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

   4. Taylor expanded in c around inf 26.5%

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

      1. *-commutative 26.5%

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

   6. Simplified 26.5%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2400 \lor \neg \left(i \leq 2.9 \cdot 10^{+20}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.8%

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

3. Taylor expanded in b around inf 37.9%

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

4. Taylor expanded in a around inf 23.7%

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

Alternative 21: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.8%

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

3. Taylor expanded in b around inf 37.9%

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

4. Taylor expanded in a around inf 22.9%

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

Developer Target 1: 68.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

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