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

Percentage Accurate: 72.8% → 81.6%

Time: 21.0s

Alternatives: 21

Speedup: 0.7×

• 57.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 19.6%

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

      1. associate--l+ 19.6%

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

      2. cancel-sign-sub-inv 19.6%

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

      3. metadata-eval 19.6%

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

      4. *-lft-identity 19.6%

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

      5. +-commutative 19.6%

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

      6. associate-+r+ 19.6%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in j around -inf 38.8%

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

      1. associate-*r* 38.8%

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

      2. mul-1-neg 38.8%

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

      3. +-commutative 38.8%

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

      4. mul-1-neg 38.8%

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

      5. *-commutative 38.8%

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

      6. unsub-neg 38.8%

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

      7. mul-1-neg 38.8%

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

      8. associate-/l* 42.7%

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

      9. distribute-rgt-neg-in 42.7%

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

      10. *-commutative 42.7%

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

      11. *-commutative 42.7%

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

      12. *-commutative 42.7%

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

   8. Simplified 42.7%

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

   9. Taylor expanded in t around inf 52.4%

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

       1. mul-1-neg 52.4%

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

       2. distribute-rgt-neg-in 52.4%

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

       3. distribute-rgt-neg-out 52.4%

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

       4. div-sub 56.2%

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

   11. Simplified 56.2%

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

4. Final simplification 85.1%

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

Alternative 2: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 + t \cdot \left(b \cdot i\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := t\_3 - a \cdot \left(x \cdot t\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-12}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* t (* b i))))
        (t_3 (* z (- (* x y) (* b c))))
        (t_4 (- t_3 (* a (* x t)))))
   (if (<= z -3.2e+52)
     t_3
     (if (<= z -9.8e+17)
       t_1
       (if (<= z -2.25e-12)
         t_4
         (if (<= z 1.5e-29)
           t_2
           (if (<= z 1e+30)
             (* b (- (* t i) (* z c)))
             (if (<= z 7.1e+53) t_2 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (t * (b * i));
	double t_3 = z * ((x * y) - (b * c));
	double t_4 = t_3 - (a * (x * t));
	double tmp;
	if (z <= -3.2e+52) {
		tmp = t_3;
	} else if (z <= -9.8e+17) {
		tmp = t_1;
	} else if (z <= -2.25e-12) {
		tmp = t_4;
	} else if (z <= 1.5e-29) {
		tmp = t_2;
	} else if (z <= 1e+30) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 7.1e+53) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (t * (b * i))
    t_3 = z * ((x * y) - (b * c))
    t_4 = t_3 - (a * (x * t))
    if (z <= (-3.2d+52)) then
        tmp = t_3
    else if (z <= (-9.8d+17)) then
        tmp = t_1
    else if (z <= (-2.25d-12)) then
        tmp = t_4
    else if (z <= 1.5d-29) then
        tmp = t_2
    else if (z <= 1d+30) then
        tmp = b * ((t * i) - (z * c))
    else if (z <= 7.1d+53) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (t * (b * i));
	double t_3 = z * ((x * y) - (b * c));
	double t_4 = t_3 - (a * (x * t));
	double tmp;
	if (z <= -3.2e+52) {
		tmp = t_3;
	} else if (z <= -9.8e+17) {
		tmp = t_1;
	} else if (z <= -2.25e-12) {
		tmp = t_4;
	} else if (z <= 1.5e-29) {
		tmp = t_2;
	} else if (z <= 1e+30) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 7.1e+53) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (t * (b * i))
	t_3 = z * ((x * y) - (b * c))
	t_4 = t_3 - (a * (x * t))
	tmp = 0
	if z <= -3.2e+52:
		tmp = t_3
	elif z <= -9.8e+17:
		tmp = t_1
	elif z <= -2.25e-12:
		tmp = t_4
	elif z <= 1.5e-29:
		tmp = t_2
	elif z <= 1e+30:
		tmp = b * ((t * i) - (z * c))
	elif z <= 7.1e+53:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(t * Float64(b * i)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_4 = Float64(t_3 - Float64(a * Float64(x * t)))
	tmp = 0.0
	if (z <= -3.2e+52)
		tmp = t_3;
	elseif (z <= -9.8e+17)
		tmp = t_1;
	elseif (z <= -2.25e-12)
		tmp = t_4;
	elseif (z <= 1.5e-29)
		tmp = t_2;
	elseif (z <= 1e+30)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (z <= 7.1e+53)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + (t * (b * i));
	t_3 = z * ((x * y) - (b * c));
	t_4 = t_3 - (a * (x * t));
	tmp = 0.0;
	if (z <= -3.2e+52)
		tmp = t_3;
	elseif (z <= -9.8e+17)
		tmp = t_1;
	elseif (z <= -2.25e-12)
		tmp = t_4;
	elseif (z <= 1.5e-29)
		tmp = t_2;
	elseif (z <= 1e+30)
		tmp = b * ((t * i) - (z * c));
	elseif (z <= 7.1e+53)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+52], t$95$3, If[LessEqual[z, -9.8e+17], t$95$1, If[LessEqual[z, -2.25e-12], t$95$4, If[LessEqual[z, 1.5e-29], t$95$2, If[LessEqual[z, 1e+30], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.1e+53], t$95$2, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2e52

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -3.2e52 < z < -9.8e17

   1. Initial program 60.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -9.8e17 < z < -2.2499999999999999e-12 or 7.09999999999999974e53 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in y around 0 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-commutative 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

   8. Simplified 68.8%

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

   9. Taylor expanded in j around 0 67.3%

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

       1. +-commutative 67.3%

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

       2. mul-1-neg 67.3%

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

       3. associate-*r* 70.6%

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

       4. distribute-lft-neg-in 70.6%

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

       5. mul-1-neg 70.6%

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

       6. associate-*r* 74.2%

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

       7. distribute-rgt-in 77.7%

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

       8. mul-1-neg 77.7%

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

       9. unsub-neg 77.7%

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

       10. +-commutative 77.7%

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

       11. mul-1-neg 77.7%

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

       12. unsub-neg 77.7%

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

       13. *-commutative 77.7%

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

       14. *-commutative 77.7%

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

   11. Simplified 77.7%

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

   if -2.2499999999999999e-12 < z < 1.5000000000000001e-29 or 1e30 < z < 7.09999999999999974e53

   1. Initial program 82.4%

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

   3. Taylor expanded in z around 0 74.0%

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

      1. associate--l+ 74.0%

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

      2. cancel-sign-sub-inv 74.0%

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

      3. metadata-eval 74.0%

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

      4. *-lft-identity 74.0%

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

      5. +-commutative 74.0%

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

      6. associate-+r+ 74.0%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in i around inf 64.6%

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

   if 1.5000000000000001e-29 < z < 1e30

   1. Initial program 66.5%

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

   3. Taylor expanded in b around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. *-commutative 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + t \cdot \frac{b \cdot i - x \cdot a}{j}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j))))
          (* b (* z c))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -7.8e+59)
     t_2
     (if (<= z -5.5e-155)
       t_1
       (if (<= z 9.8e-158)
         (* j (+ (- (* a c) (* y i)) (* t (/ (- (* b i) (* x a)) j))))
         (if (<= z 1.25e+54) t_1 (- t_2 (* a (* x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) - (b * (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -7.8e+59) {
		tmp = t_2;
	} else if (z <= -5.5e-155) {
		tmp = t_1;
	} else if (z <= 9.8e-158) {
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)));
	} else if (z <= 1.25e+54) {
		tmp = t_1;
	} else {
		tmp = t_2 - (a * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) - (b * (z * c))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-7.8d+59)) then
        tmp = t_2
    else if (z <= (-5.5d-155)) then
        tmp = t_1
    else if (z <= 9.8d-158) then
        tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)))
    else if (z <= 1.25d+54) then
        tmp = t_1
    else
        tmp = t_2 - (a * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) - (b * (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -7.8e+59) {
		tmp = t_2;
	} else if (z <= -5.5e-155) {
		tmp = t_1;
	} else if (z <= 9.8e-158) {
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)));
	} else if (z <= 1.25e+54) {
		tmp = t_1;
	} else {
		tmp = t_2 - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) - (b * (z * c))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -7.8e+59:
		tmp = t_2
	elif z <= -5.5e-155:
		tmp = t_1
	elif z <= 9.8e-158:
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)))
	elif z <= 1.25e+54:
		tmp = t_1
	else:
		tmp = t_2 - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) - Float64(b * Float64(z * c)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -7.8e+59)
		tmp = t_2;
	elseif (z <= -5.5e-155)
		tmp = t_1;
	elseif (z <= 9.8e-158)
		tmp = Float64(j * Float64(Float64(Float64(a * c) - Float64(y * i)) + Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / j))));
	elseif (z <= 1.25e+54)
		tmp = t_1;
	else
		tmp = Float64(t_2 - Float64(a * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) - (b * (z * c));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -7.8e+59)
		tmp = t_2;
	elseif (z <= -5.5e-155)
		tmp = t_1;
	elseif (z <= 9.8e-158)
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)));
	elseif (z <= 1.25e+54)
		tmp = t_1;
	else
		tmp = t_2 - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+59], t$95$2, If[LessEqual[z, -5.5e-155], t$95$1, If[LessEqual[z, 9.8e-158], N[(j * N[(N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+54], t$95$1, N[(t$95$2 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.80000000000000043e59

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -7.80000000000000043e59 < z < -5.50000000000000018e-155 or 9.79999999999999986e-158 < z < 1.25000000000000001e54

   1. Initial program 79.0%

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

   3. Taylor expanded in y around 0 83.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in t around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. *-commutative 82.3%

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

      3. distribute-rgt-neg-in 82.3%

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

   8. Simplified 82.3%

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

   if -5.50000000000000018e-155 < z < 9.79999999999999986e-158

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 79.6%

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

      1. associate--l+ 79.6%

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

      2. cancel-sign-sub-inv 79.6%

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

      3. metadata-eval 79.6%

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

      4. *-lft-identity 79.6%

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

      5. +-commutative 79.6%

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

      6. associate-+r+ 79.6%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in j around -inf 83.0%

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

      1. associate-*r* 83.0%

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

      2. mul-1-neg 83.0%

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

      3. +-commutative 83.0%

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

      4. mul-1-neg 83.0%

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

      5. *-commutative 83.0%

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

      6. unsub-neg 83.0%

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

      7. mul-1-neg 83.0%

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

      8. associate-/l* 83.1%

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

      9. distribute-rgt-neg-in 83.1%

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

      10. *-commutative 83.1%

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

      11. *-commutative 83.1%

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

      12. *-commutative 83.1%

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

   8. Simplified 83.1%

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

   if 1.25000000000000001e54 < z

   1. Initial program 63.0%

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

   3. Taylor expanded in y around 0 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. mul-1-neg 64.9%

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

      2. *-commutative 64.9%

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

      3. distribute-rgt-neg-in 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in j around 0 63.3%

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

       1. +-commutative 63.3%

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

       2. mul-1-neg 63.3%

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

       3. associate-*r* 67.2%

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

       4. distribute-lft-neg-in 67.2%

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

       5. mul-1-neg 67.2%

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

       6. associate-*r* 71.5%

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

       7. distribute-rgt-in 75.6%

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

       8. mul-1-neg 75.6%

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

       9. unsub-neg 75.6%

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

       10. +-commutative 75.6%

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

       11. mul-1-neg 75.6%

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

       12. unsub-neg 75.6%

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

       13. *-commutative 75.6%

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

       14. *-commutative 75.6%

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

   11. Simplified 75.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-155}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + t \cdot \frac{b \cdot i - x \cdot a}{j}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t\_2 - a \cdot \left(x \cdot t\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+155}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (- t_2 (* a (* x t)))))
   (if (<= z -1.75e+37)
     t_2
     (if (<= z -6.6e+15)
       t_1
       (if (<= z -8.5e-12)
         t_3
         (if (<= z 7.6e-35)
           (+ (* t (- (* b i) (* x a))) t_1)
           (if (<= z 3e+155) (+ t_1 (* b (- (* t i) (* z c)))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t_2 - (a * (x * t));
	double tmp;
	if (z <= -1.75e+37) {
		tmp = t_2;
	} else if (z <= -6.6e+15) {
		tmp = t_1;
	} else if (z <= -8.5e-12) {
		tmp = t_3;
	} else if (z <= 7.6e-35) {
		tmp = (t * ((b * i) - (x * a))) + t_1;
	} else if (z <= 3e+155) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t_2 - (a * (x * t))
    if (z <= (-1.75d+37)) then
        tmp = t_2
    else if (z <= (-6.6d+15)) then
        tmp = t_1
    else if (z <= (-8.5d-12)) then
        tmp = t_3
    else if (z <= 7.6d-35) then
        tmp = (t * ((b * i) - (x * a))) + t_1
    else if (z <= 3d+155) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t_2 - (a * (x * t));
	double tmp;
	if (z <= -1.75e+37) {
		tmp = t_2;
	} else if (z <= -6.6e+15) {
		tmp = t_1;
	} else if (z <= -8.5e-12) {
		tmp = t_3;
	} else if (z <= 7.6e-35) {
		tmp = (t * ((b * i) - (x * a))) + t_1;
	} else if (z <= 3e+155) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t_2 - (a * (x * t))
	tmp = 0
	if z <= -1.75e+37:
		tmp = t_2
	elif z <= -6.6e+15:
		tmp = t_1
	elif z <= -8.5e-12:
		tmp = t_3
	elif z <= 7.6e-35:
		tmp = (t * ((b * i) - (x * a))) + t_1
	elif z <= 3e+155:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t_2 - Float64(a * Float64(x * t)))
	tmp = 0.0
	if (z <= -1.75e+37)
		tmp = t_2;
	elseif (z <= -6.6e+15)
		tmp = t_1;
	elseif (z <= -8.5e-12)
		tmp = t_3;
	elseif (z <= 7.6e-35)
		tmp = Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + t_1);
	elseif (z <= 3e+155)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t_2 - (a * (x * t));
	tmp = 0.0;
	if (z <= -1.75e+37)
		tmp = t_2;
	elseif (z <= -6.6e+15)
		tmp = t_1;
	elseif (z <= -8.5e-12)
		tmp = t_3;
	elseif (z <= 7.6e-35)
		tmp = (t * ((b * i) - (x * a))) + t_1;
	elseif (z <= 3e+155)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+37], t$95$2, If[LessEqual[z, -6.6e+15], t$95$1, If[LessEqual[z, -8.5e-12], t$95$3, If[LessEqual[z, 7.6e-35], N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 3e+155], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.75e37

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -1.75e37 < z < -6.6e15

   1. Initial program 60.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -6.6e15 < z < -8.4999999999999997e-12 or 3.0000000000000001e155 < z

   1. Initial program 60.7%

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

   3. Taylor expanded in y around 0 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in t around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. *-commutative 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in j around 0 63.3%

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

       1. +-commutative 63.3%

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

       2. mul-1-neg 63.3%

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

       3. associate-*r* 67.9%

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

       4. distribute-lft-neg-in 67.9%

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

       5. mul-1-neg 67.9%

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

       6. associate-*r* 75.5%

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

       7. distribute-rgt-in 80.5%

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

       8. mul-1-neg 80.5%

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

       9. unsub-neg 80.5%

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

       10. +-commutative 80.5%

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

       11. mul-1-neg 80.5%

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

       12. unsub-neg 80.5%

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

       13. *-commutative 80.5%

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

       14. *-commutative 80.5%

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

   11. Simplified 80.5%

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

   if -8.4999999999999997e-12 < z < 7.6000000000000002e-35

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 72.7%

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

      1. associate--l+ 72.7%

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

      2. cancel-sign-sub-inv 72.7%

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

      3. metadata-eval 72.7%

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

      4. *-lft-identity 72.7%

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

      5. +-commutative 72.7%

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

      6. associate-+r+ 72.7%

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

   5. Simplified 76.0%

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

   if 7.6000000000000002e-35 < z < 3.0000000000000001e155

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 76.5%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-140}:\\ \;\;\;\;t\_1 + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.6e+90)
     t_2
     (if (<= t -1.9e-140)
       (+ t_1 (* t (* b i)))
       (if (<= t -4.7e-275)
         (* y (- (* x z) (* i j)))
         (if (<= t -9.5e-293)
           t_1
           (if (<= t 1.45e-143)
             (* z (- (* x y) (* b c)))
             (if (<= t 8.5e+38) (* j (* y (- (/ (* a c) y) 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 * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.6e+90) {
		tmp = t_2;
	} else if (t <= -1.9e-140) {
		tmp = t_1 + (t * (b * i));
	} else if (t <= -4.7e-275) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -9.5e-293) {
		tmp = t_1;
	} else if (t <= 1.45e-143) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 8.5e+38) {
		tmp = j * (y * (((a * c) / y) - 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 * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.6d+90)) then
        tmp = t_2
    else if (t <= (-1.9d-140)) then
        tmp = t_1 + (t * (b * i))
    else if (t <= (-4.7d-275)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= (-9.5d-293)) then
        tmp = t_1
    else if (t <= 1.45d-143) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 8.5d+38) then
        tmp = j * (y * (((a * c) / y) - 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 * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.6e+90) {
		tmp = t_2;
	} else if (t <= -1.9e-140) {
		tmp = t_1 + (t * (b * i));
	} else if (t <= -4.7e-275) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -9.5e-293) {
		tmp = t_1;
	} else if (t <= 1.45e-143) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 8.5e+38) {
		tmp = j * (y * (((a * c) / y) - i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.6e+90:
		tmp = t_2
	elif t <= -1.9e-140:
		tmp = t_1 + (t * (b * i))
	elif t <= -4.7e-275:
		tmp = y * ((x * z) - (i * j))
	elif t <= -9.5e-293:
		tmp = t_1
	elif t <= 1.45e-143:
		tmp = z * ((x * y) - (b * c))
	elif t <= 8.5e+38:
		tmp = j * (y * (((a * c) / y) - 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(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.6e+90)
		tmp = t_2;
	elseif (t <= -1.9e-140)
		tmp = Float64(t_1 + Float64(t * Float64(b * i)));
	elseif (t <= -4.7e-275)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= -9.5e-293)
		tmp = t_1;
	elseif (t <= 1.45e-143)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 8.5e+38)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - 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 * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.6e+90)
		tmp = t_2;
	elseif (t <= -1.9e-140)
		tmp = t_1 + (t * (b * i));
	elseif (t <= -4.7e-275)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= -9.5e-293)
		tmp = t_1;
	elseif (t <= 1.45e-143)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 8.5e+38)
		tmp = j * (y * (((a * c) / y) - 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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+90], t$95$2, If[LessEqual[t, -1.9e-140], N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-275], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e-293], t$95$1, If[LessEqual[t, 1.45e-143], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+38], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.59999999999999999e90 or 8.4999999999999997e38 < t

   1. Initial program 63.7%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. neg-mul-1 69.1%

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

      3. cancel-sign-sub 69.1%

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

      4. +-commutative 69.1%

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

      5. mul-1-neg 69.1%

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

      6. unsub-neg 69.1%

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

      7. *-commutative 69.1%

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

      8. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -1.59999999999999999e90 < t < -1.89999999999999999e-140

   1. Initial program 82.6%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate--l+ 62.9%

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

      2. cancel-sign-sub-inv 62.9%

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

      3. metadata-eval 62.9%

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

      4. *-lft-identity 62.9%

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

      5. +-commutative 62.9%

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

      6. associate-+r+ 62.9%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in i around inf 56.1%

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

   if -1.89999999999999999e-140 < t < -4.6999999999999998e-275

   1. Initial program 62.7%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -4.6999999999999998e-275 < t < -9.50000000000000049e-293

   1. Initial program 100.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -9.50000000000000049e-293 < t < 1.45e-143

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 1.45e-143 < t < 8.4999999999999997e38

   1. Initial program 84.5%

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

   3. Taylor expanded in j around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around inf 62.7%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -3.9e+92)
     t_1
     (if (<= t -4.4e-140)
       (* c (- (* a j) (* z b)))
       (if (<= t -1.75e-220)
         (* y (- (* x z) (* i j)))
         (if (<= t -1.25e-293)
           (* j (- (* a c) (* y i)))
           (if (<= t 8.2e-144)
             (* z (- (* x y) (* b c)))
             (if (<= t 6.2e+41) (* j (* y (- (/ (* a c) y) i))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -3.9e+92) {
		tmp = t_1;
	} else if (t <= -4.4e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -1.75e-220) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -1.25e-293) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 8.2e-144) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6.2e+41) {
		tmp = j * (y * (((a * c) / y) - i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-3.9d+92)) then
        tmp = t_1
    else if (t <= (-4.4d-140)) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= (-1.75d-220)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= (-1.25d-293)) then
        tmp = j * ((a * c) - (y * i))
    else if (t <= 8.2d-144) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 6.2d+41) then
        tmp = j * (y * (((a * c) / y) - i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -3.9e+92) {
		tmp = t_1;
	} else if (t <= -4.4e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -1.75e-220) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -1.25e-293) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 8.2e-144) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6.2e+41) {
		tmp = j * (y * (((a * c) / y) - i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -3.9e+92:
		tmp = t_1
	elif t <= -4.4e-140:
		tmp = c * ((a * j) - (z * b))
	elif t <= -1.75e-220:
		tmp = y * ((x * z) - (i * j))
	elif t <= -1.25e-293:
		tmp = j * ((a * c) - (y * i))
	elif t <= 8.2e-144:
		tmp = z * ((x * y) - (b * c))
	elif t <= 6.2e+41:
		tmp = j * (y * (((a * c) / y) - i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.9e+92)
		tmp = t_1;
	elseif (t <= -4.4e-140)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= -1.75e-220)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= -1.25e-293)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (t <= 8.2e-144)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 6.2e+41)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -3.9e+92)
		tmp = t_1;
	elseif (t <= -4.4e-140)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= -1.75e-220)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= -1.25e-293)
		tmp = j * ((a * c) - (y * i));
	elseif (t <= 8.2e-144)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 6.2e+41)
		tmp = j * (y * (((a * c) / y) - i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+92], t$95$1, If[LessEqual[t, -4.4e-140], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-220], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-293], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-144], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+41], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.90000000000000011e92 or 6.2e41 < t

   1. Initial program 63.7%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. associate-*r* 69.2%

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

      2. neg-mul-1 69.2%

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

      3. cancel-sign-sub 69.2%

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

      4. +-commutative 69.2%

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

      5. mul-1-neg 69.2%

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

      6. unsub-neg 69.2%

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

      7. *-commutative 69.2%

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

      8. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -3.90000000000000011e92 < t < -4.3999999999999998e-140

   1. Initial program 81.7%

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

   3. Taylor expanded in c around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   if -4.3999999999999998e-140 < t < -1.74999999999999994e-220

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -1.74999999999999994e-220 < t < -1.2500000000000001e-293

   1. Initial program 73.6%

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

   3. Taylor expanded in j around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -1.2500000000000001e-293 < t < 8.2e-144

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 8.2e-144 < t < 6.2e41

   1. Initial program 84.5%

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

   3. Taylor expanded in j around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around inf 62.7%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+92}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t\_2 - a \cdot \left(x \cdot t\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;t\_1 + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (- t_2 (* a (* x t)))))
   (if (<= z -2.25e+49)
     t_2
     (if (<= z -3.6e+15)
       t_1
       (if (<= z -2.2e-12)
         t_3
         (if (<= z 2.5e-30)
           (+ t_1 (* t (* b i)))
           (if (<= z 1.4e+96)
             (- (* b (- (* t i) (* z c))) (* i (* y j)))
             t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t_2 - (a * (x * t));
	double tmp;
	if (z <= -2.25e+49) {
		tmp = t_2;
	} else if (z <= -3.6e+15) {
		tmp = t_1;
	} else if (z <= -2.2e-12) {
		tmp = t_3;
	} else if (z <= 2.5e-30) {
		tmp = t_1 + (t * (b * i));
	} else if (z <= 1.4e+96) {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t_2 - (a * (x * t))
    if (z <= (-2.25d+49)) then
        tmp = t_2
    else if (z <= (-3.6d+15)) then
        tmp = t_1
    else if (z <= (-2.2d-12)) then
        tmp = t_3
    else if (z <= 2.5d-30) then
        tmp = t_1 + (t * (b * i))
    else if (z <= 1.4d+96) then
        tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t_2 - (a * (x * t));
	double tmp;
	if (z <= -2.25e+49) {
		tmp = t_2;
	} else if (z <= -3.6e+15) {
		tmp = t_1;
	} else if (z <= -2.2e-12) {
		tmp = t_3;
	} else if (z <= 2.5e-30) {
		tmp = t_1 + (t * (b * i));
	} else if (z <= 1.4e+96) {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t_2 - (a * (x * t))
	tmp = 0
	if z <= -2.25e+49:
		tmp = t_2
	elif z <= -3.6e+15:
		tmp = t_1
	elif z <= -2.2e-12:
		tmp = t_3
	elif z <= 2.5e-30:
		tmp = t_1 + (t * (b * i))
	elif z <= 1.4e+96:
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t_2 - Float64(a * Float64(x * t)))
	tmp = 0.0
	if (z <= -2.25e+49)
		tmp = t_2;
	elseif (z <= -3.6e+15)
		tmp = t_1;
	elseif (z <= -2.2e-12)
		tmp = t_3;
	elseif (z <= 2.5e-30)
		tmp = Float64(t_1 + Float64(t * Float64(b * i)));
	elseif (z <= 1.4e+96)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t_2 - (a * (x * t));
	tmp = 0.0;
	if (z <= -2.25e+49)
		tmp = t_2;
	elseif (z <= -3.6e+15)
		tmp = t_1;
	elseif (z <= -2.2e-12)
		tmp = t_3;
	elseif (z <= 2.5e-30)
		tmp = t_1 + (t * (b * i));
	elseif (z <= 1.4e+96)
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+49], t$95$2, If[LessEqual[z, -3.6e+15], t$95$1, If[LessEqual[z, -2.2e-12], t$95$3, If[LessEqual[z, 2.5e-30], N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+96], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.24999999999999991e49

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -2.24999999999999991e49 < z < -3.6e15

   1. Initial program 60.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.6e15 < z < -2.19999999999999992e-12 or 1.4e96 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in y around 0 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. *-commutative 69.1%

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

      3. distribute-rgt-neg-in 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in j around 0 67.4%

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

       1. +-commutative 67.4%

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

       2. mul-1-neg 67.4%

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

       3. associate-*r* 71.0%

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

       4. distribute-lft-neg-in 71.0%

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

       5. mul-1-neg 71.0%

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

       6. associate-*r* 75.0%

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

       7. distribute-rgt-in 79.0%

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

       8. mul-1-neg 79.0%

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

       9. unsub-neg 79.0%

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

       10. +-commutative 79.0%

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

       11. mul-1-neg 79.0%

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

       12. unsub-neg 79.0%

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

       13. *-commutative 79.0%

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

       14. *-commutative 79.0%

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

   11. Simplified 79.0%

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

   if -2.19999999999999992e-12 < z < 2.49999999999999986e-30

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 72.7%

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

      1. associate--l+ 72.7%

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

      2. cancel-sign-sub-inv 72.7%

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

      3. metadata-eval 72.7%

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

      4. *-lft-identity 72.7%

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

      5. +-commutative 72.7%

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

      6. associate-+r+ 72.7%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in i around inf 62.9%

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

   if 2.49999999999999986e-30 < z < 1.4e96

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 74.4%

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

   4. Taylor expanded in a around 0 66.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-12} \lor \neg \left(z \leq 1.6 \cdot 10^{+54}\right):\\ \;\;\;\;t\_2 - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -5.6e+56)
     t_2
     (if (<= z -1.55e+18)
       t_1
       (if (or (<= z -7e-12) (not (<= z 1.6e+54)))
         (- t_2 (* a (* x t)))
         (+ (* t (- (* b i) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.6e+56) {
		tmp = t_2;
	} else if (z <= -1.55e+18) {
		tmp = t_1;
	} else if ((z <= -7e-12) || !(z <= 1.6e+54)) {
		tmp = t_2 - (a * (x * t));
	} else {
		tmp = (t * ((b * i) - (x * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-5.6d+56)) then
        tmp = t_2
    else if (z <= (-1.55d+18)) then
        tmp = t_1
    else if ((z <= (-7d-12)) .or. (.not. (z <= 1.6d+54))) then
        tmp = t_2 - (a * (x * t))
    else
        tmp = (t * ((b * i) - (x * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.6e+56) {
		tmp = t_2;
	} else if (z <= -1.55e+18) {
		tmp = t_1;
	} else if ((z <= -7e-12) || !(z <= 1.6e+54)) {
		tmp = t_2 - (a * (x * t));
	} else {
		tmp = (t * ((b * i) - (x * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -5.6e+56:
		tmp = t_2
	elif z <= -1.55e+18:
		tmp = t_1
	elif (z <= -7e-12) or not (z <= 1.6e+54):
		tmp = t_2 - (a * (x * t))
	else:
		tmp = (t * ((b * i) - (x * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -5.6e+56)
		tmp = t_2;
	elseif (z <= -1.55e+18)
		tmp = t_1;
	elseif ((z <= -7e-12) || !(z <= 1.6e+54))
		tmp = Float64(t_2 - Float64(a * Float64(x * t)));
	else
		tmp = Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -5.6e+56)
		tmp = t_2;
	elseif (z <= -1.55e+18)
		tmp = t_1;
	elseif ((z <= -7e-12) || ~((z <= 1.6e+54)))
		tmp = t_2 - (a * (x * t));
	else
		tmp = (t * ((b * i) - (x * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+56], t$95$2, If[LessEqual[z, -1.55e+18], t$95$1, If[Or[LessEqual[z, -7e-12], N[Not[LessEqual[z, 1.6e+54]], $MachinePrecision]], N[(t$95$2 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.60000000000000017e56

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -5.60000000000000017e56 < z < -1.55e18

   1. Initial program 60.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1.55e18 < z < -7.0000000000000001e-12 or 1.6e54 < z

   1. Initial program 68.3%

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

   3. Taylor expanded in y around 0 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. *-commutative 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in j around 0 66.7%

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

       1. +-commutative 66.7%

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

       2. mul-1-neg 66.7%

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

       3. associate-*r* 70.0%

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

       4. distribute-lft-neg-in 70.0%

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

       5. mul-1-neg 70.0%

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

       6. associate-*r* 73.7%

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

       7. distribute-rgt-in 77.3%

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

       8. mul-1-neg 77.3%

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

       9. unsub-neg 77.3%

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

       10. +-commutative 77.3%

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

       11. mul-1-neg 77.3%

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

       12. unsub-neg 77.3%

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

       13. *-commutative 77.3%

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

       14. *-commutative 77.3%

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

   11. Simplified 77.3%

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

   if -7.0000000000000001e-12 < z < 1.6e54

   1. Initial program 80.9%

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

   3. Taylor expanded in z around 0 70.4%

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

      1. associate--l+ 70.4%

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

      2. cancel-sign-sub-inv 70.4%

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

      3. metadata-eval 70.4%

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

      4. *-lft-identity 70.4%

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

      5. +-commutative 70.4%

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

      6. associate-+r+ 70.4%

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

   5. Simplified 72.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-12} \lor \neg \left(z \leq 1.6 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+181} \lor \neg \left(t \leq 6.2 \cdot 10^{+130}\right):\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + t \cdot \frac{b \cdot i - x \cdot a}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.58e+181) (not (<= t 6.2e+130)))
   (* j (+ (- (* a c) (* y i)) (* t (/ (- (* b i) (* x a)) j))))
   (+
    (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j))))
    (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.58e+181) || !(t <= 6.2e+130)) {
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)));
	} else {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.58d+181)) .or. (.not. (t <= 6.2d+130))) then
        tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)))
    else
        tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.58e+181) || !(t <= 6.2e+130)) {
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)));
	} else {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.58e+181) or not (t <= 6.2e+130):
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)))
	else:
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.58e+181) || !(t <= 6.2e+130))
		tmp = Float64(j * Float64(Float64(Float64(a * c) - Float64(y * i)) + Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / j))));
	else
		tmp = Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.58e+181) || ~((t <= 6.2e+130)))
		tmp = j * (((a * c) - (y * i)) + (t * (((b * i) - (x * a)) / j)));
	else
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.58e+181], N[Not[LessEqual[t, 6.2e+130]], $MachinePrecision]], N[(j * N[(N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.58000000000000002e181 or 6.1999999999999999e130 < t

   1. Initial program 59.3%

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

   3. Taylor expanded in z around 0 59.6%

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

      1. associate--l+ 59.6%

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

      2. cancel-sign-sub-inv 59.6%

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

      3. metadata-eval 59.6%

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

      4. *-lft-identity 59.6%

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

      5. +-commutative 59.6%

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

      6. associate-+r+ 59.6%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in j around -inf 76.8%

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

      1. associate-*r* 76.8%

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

      2. mul-1-neg 76.8%

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

      3. +-commutative 76.8%

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

      4. mul-1-neg 76.8%

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

      5. *-commutative 76.8%

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

      6. unsub-neg 76.8%

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

      7. mul-1-neg 76.8%

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

      8. associate-/l* 78.6%

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

      9. distribute-rgt-neg-in 78.6%

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

      10. *-commutative 78.6%

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

      11. *-commutative 78.6%

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

      12. *-commutative 78.6%

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

   8. Simplified 78.6%

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

   if -1.58000000000000002e181 < t < 6.1999999999999999e130

   1. Initial program 77.9%

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

   3. Taylor expanded in y around 0 79.8%

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

   5. Simplified 80.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+181} \lor \neg \left(t \leq 6.2 \cdot 10^{+130}\right):\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + t \cdot \frac{b \cdot i - x \cdot a}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.72 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-95}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= x -1.72e-43)
     (- (* z (- (* x y) (* b c))) (* a (* x t)))
     (if (<= x 2.2e-95)
       (+ t_2 t_1)
       (if (<= x 7.8e+105)
         (+ (* t (- (* b i) (* x a))) t_2)
         (+ (* x (- (* y z) (* t 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 * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -1.72e-43) {
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t));
	} else if (x <= 2.2e-95) {
		tmp = t_2 + t_1;
	} else if (x <= 7.8e+105) {
		tmp = (t * ((b * i) - (x * a))) + t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (x <= (-1.72d-43)) then
        tmp = (z * ((x * y) - (b * c))) - (a * (x * t))
    else if (x <= 2.2d-95) then
        tmp = t_2 + t_1
    else if (x <= 7.8d+105) then
        tmp = (t * ((b * i) - (x * a))) + t_2
    else
        tmp = (x * ((y * z) - (t * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -1.72e-43) {
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t));
	} else if (x <= 2.2e-95) {
		tmp = t_2 + t_1;
	} else if (x <= 7.8e+105) {
		tmp = (t * ((b * i) - (x * a))) + t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if x <= -1.72e-43:
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t))
	elif x <= 2.2e-95:
		tmp = t_2 + t_1
	elif x <= 7.8e+105:
		tmp = (t * ((b * i) - (x * a))) + t_2
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -1.72e-43)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(x * t)));
	elseif (x <= 2.2e-95)
		tmp = Float64(t_2 + t_1);
	elseif (x <= 7.8e+105)
		tmp = Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + t_2);
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -1.72e-43)
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t));
	elseif (x <= 2.2e-95)
		tmp = t_2 + t_1;
	elseif (x <= 7.8e+105)
		tmp = (t * ((b * i) - (x * a))) + t_2;
	else
		tmp = (x * ((y * z) - (t * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.72e-43], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-95], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[x, 7.8e+105], N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.72000000000000005e-43

   1. Initial program 70.2%

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

   3. Taylor expanded in y around 0 68.6%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in j around 0 65.2%

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

       1. +-commutative 65.2%

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

       2. mul-1-neg 65.2%

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

       3. associate-*r* 70.3%

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

       4. distribute-lft-neg-in 70.3%

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

       5. mul-1-neg 70.3%

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

       6. associate-*r* 71.9%

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

       7. distribute-rgt-in 73.5%

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

       8. mul-1-neg 73.5%

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

       9. unsub-neg 73.5%

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

       10. +-commutative 73.5%

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

       11. mul-1-neg 73.5%

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

       12. unsub-neg 73.5%

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

       13. *-commutative 73.5%

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

       14. *-commutative 73.5%

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

   11. Simplified 73.5%

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

   if -1.72000000000000005e-43 < x < 2.1999999999999999e-95

   1. Initial program 73.0%

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

   3. Taylor expanded in x around 0 78.2%

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

   if 2.1999999999999999e-95 < x < 7.79999999999999957e105

   1. Initial program 73.9%

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

   3. Taylor expanded in z around 0 74.2%

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

      1. associate--l+ 74.2%

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

      2. cancel-sign-sub-inv 74.2%

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

      3. metadata-eval 74.2%

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

      4. *-lft-identity 74.2%

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

      5. +-commutative 74.2%

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

      6. associate-+r+ 74.2%

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

   5. Simplified 74.3%

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

   if 7.79999999999999957e105 < x

   1. Initial program 79.6%

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

   3. Taylor expanded in j around 0 71.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.365 \cdot 10^{-114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* c (* a j))))
   (if (<= z -2.4e+89)
     (* c (* z (- b)))
     (if (<= z -7.9e-44)
       t_1
       (if (<= z -1.365e-114)
         t_2
         (if (<= z -2.15e-238) t_1 (if (<= z 3.7e+47) t_2 (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = c * (a * j);
	double tmp;
	if (z <= -2.4e+89) {
		tmp = c * (z * -b);
	} else if (z <= -7.9e-44) {
		tmp = t_1;
	} else if (z <= -1.365e-114) {
		tmp = t_2;
	} else if (z <= -2.15e-238) {
		tmp = t_1;
	} else if (z <= 3.7e+47) {
		tmp = t_2;
	} else {
		tmp = x * (y * z);
	}
	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 = i * (y * -j)
    t_2 = c * (a * j)
    if (z <= (-2.4d+89)) then
        tmp = c * (z * -b)
    else if (z <= (-7.9d-44)) then
        tmp = t_1
    else if (z <= (-1.365d-114)) then
        tmp = t_2
    else if (z <= (-2.15d-238)) then
        tmp = t_1
    else if (z <= 3.7d+47) then
        tmp = t_2
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = c * (a * j);
	double tmp;
	if (z <= -2.4e+89) {
		tmp = c * (z * -b);
	} else if (z <= -7.9e-44) {
		tmp = t_1;
	} else if (z <= -1.365e-114) {
		tmp = t_2;
	} else if (z <= -2.15e-238) {
		tmp = t_1;
	} else if (z <= 3.7e+47) {
		tmp = t_2;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = c * (a * j)
	tmp = 0
	if z <= -2.4e+89:
		tmp = c * (z * -b)
	elif z <= -7.9e-44:
		tmp = t_1
	elif z <= -1.365e-114:
		tmp = t_2
	elif z <= -2.15e-238:
		tmp = t_1
	elif z <= 3.7e+47:
		tmp = t_2
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (z <= -2.4e+89)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= -7.9e-44)
		tmp = t_1;
	elseif (z <= -1.365e-114)
		tmp = t_2;
	elseif (z <= -2.15e-238)
		tmp = t_1;
	elseif (z <= 3.7e+47)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (z <= -2.4e+89)
		tmp = c * (z * -b);
	elseif (z <= -7.9e-44)
		tmp = t_1;
	elseif (z <= -1.365e-114)
		tmp = t_2;
	elseif (z <= -2.15e-238)
		tmp = t_1;
	elseif (z <= 3.7e+47)
		tmp = t_2;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+89], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.9e-44], t$95$1, If[LessEqual[z, -1.365e-114], t$95$2, If[LessEqual[z, -2.15e-238], t$95$1, If[LessEqual[z, 3.7e+47], t$95$2, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000004e89

   1. Initial program 60.5%

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

   3. Taylor expanded in y around 0 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in c around inf 55.2%

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

      1. +-commutative 55.2%

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

      2. mul-1-neg 55.2%

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

      3. unsub-neg 55.2%

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

      4. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   9. Taylor expanded in j around 0 52.0%

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

       1. mul-1-neg 52.0%

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

       2. distribute-rgt-neg-in 52.0%

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

   11. Simplified 52.0%

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

   if -2.40000000000000004e89 < z < -7.8999999999999995e-44 or -1.36500000000000008e-114 < z < -2.14999999999999984e-238

   1. Initial program 75.4%

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

   3. Taylor expanded in y around 0 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in t around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. *-commutative 72.4%

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

      3. distribute-rgt-neg-in 72.4%

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

   8. Simplified 72.4%

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

   9. Taylor expanded in i around inf 43.6%

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

       1. mul-1-neg 43.6%

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

       2. distribute-rgt-neg-in 43.6%

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

       3. *-commutative 43.6%

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

       4. distribute-rgt-neg-in 43.6%

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

   11. Simplified 43.6%

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

   if -7.8999999999999995e-44 < z < -1.36500000000000008e-114 or -2.14999999999999984e-238 < z < 3.70000000000000041e47

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0 84.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in c around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

   8. Simplified 47.5%

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

   9. Taylor expanded in j around inf 35.8%

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

       1. *-commutative 35.8%

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

       2. associate-*l* 40.5%

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

   11. Simplified 40.5%

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

   if 3.70000000000000041e47 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 49.9%

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

      1. *-commutative 49.9%

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

   8. Simplified 49.9%

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

   9. Taylor expanded in z around inf 43.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-44}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq -1.365 \cdot 10^{-114}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+190} \lor \neg \left(b \leq -2.5 \cdot 10^{+136} \lor \neg \left(b \leq -3.4 \cdot 10^{+41}\right) \land b \leq 4.4 \cdot 10^{+136}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.7e+190)
         (not
          (or (<= b -2.5e+136) (and (not (<= b -3.4e+41)) (<= b 4.4e+136)))))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.7e+190) || !((b <= -2.5e+136) || (!(b <= -3.4e+41) && (b <= 4.4e+136)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.7d+190)) .or. (.not. (b <= (-2.5d+136)) .or. (.not. (b <= (-3.4d+41))) .and. (b <= 4.4d+136))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.7e+190) || !((b <= -2.5e+136) || (!(b <= -3.4e+41) && (b <= 4.4e+136)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.7e+190) or not ((b <= -2.5e+136) or (not (b <= -3.4e+41) and (b <= 4.4e+136))):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.7e+190) || !((b <= -2.5e+136) || (!(b <= -3.4e+41) && (b <= 4.4e+136))))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.7e+190) || ~(((b <= -2.5e+136) || (~((b <= -3.4e+41)) && (b <= 4.4e+136)))))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.7e+190], N[Not[Or[LessEqual[b, -2.5e+136], And[N[Not[LessEqual[b, -3.4e+41]], $MachinePrecision], LessEqual[b, 4.4e+136]]]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e190 or -2.5000000000000001e136 < b < -3.39999999999999998e41 or 4.3999999999999999e136 < b

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   if -1.7e190 < b < -2.5000000000000001e136 or -3.39999999999999998e41 < b < 4.3999999999999999e136

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. *-commutative 49.8%

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

      5. *-commutative 49.8%

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

   5. Simplified 49.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+190} \lor \neg \left(b \leq -2.5 \cdot 10^{+136} \lor \neg \left(b \leq -3.4 \cdot 10^{+41}\right) \land b \leq 4.4 \cdot 10^{+136}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -7e+104)
     t_1
     (if (<= i -1.6e+17)
       (* b (- (* t i) (* z c)))
       (if (<= i 2.4e-257)
         (* a (* x (- (/ (* c j) x) t)))
         (if (<= i 3.4e+32) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -7e+104) {
		tmp = t_1;
	} else if (i <= -1.6e+17) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 2.4e-257) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (i <= 3.4e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-7d+104)) then
        tmp = t_1
    else if (i <= (-1.6d+17)) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 2.4d-257) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (i <= 3.4d+32) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -7e+104) {
		tmp = t_1;
	} else if (i <= -1.6e+17) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 2.4e-257) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (i <= 3.4e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -7e+104:
		tmp = t_1
	elif i <= -1.6e+17:
		tmp = b * ((t * i) - (z * c))
	elif i <= 2.4e-257:
		tmp = a * (x * (((c * j) / x) - t))
	elif i <= 3.4e+32:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -7e+104)
		tmp = t_1;
	elseif (i <= -1.6e+17)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 2.4e-257)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (i <= 3.4e+32)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -7e+104)
		tmp = t_1;
	elseif (i <= -1.6e+17)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 2.4e-257)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (i <= 3.4e+32)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7e+104], t$95$1, If[LessEqual[i, -1.6e+17], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e-257], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e+32], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.0000000000000003e104 or 3.39999999999999979e32 < i

   1. Initial program 59.9%

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

   3. Taylor expanded in i around inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. neg-mul-1 64.3%

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

      3. cancel-sign-sub 64.3%

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

      4. +-commutative 64.3%

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

      5. mul-1-neg 64.3%

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

      6. unsub-neg 64.3%

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

      7. *-commutative 64.3%

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

      8. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -7.0000000000000003e104 < i < -1.6e17

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -1.6e17 < i < 2.40000000000000017e-257

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 60.8%

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

   if 2.40000000000000017e-257 < i < 3.39999999999999979e32

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

Alternative 14: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.7e+104)
     t_1
     (if (<= i -3.6e+17)
       (* b (- (* t i) (* z c)))
       (if (<= i 1.55e-257)
         (* a (- (* c j) (* x t)))
         (if (<= i 3e+32) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.7e+104) {
		tmp = t_1;
	} else if (i <= -3.6e+17) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 1.55e-257) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 3e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.7d+104)) then
        tmp = t_1
    else if (i <= (-3.6d+17)) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 1.55d-257) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 3d+32) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.7e+104) {
		tmp = t_1;
	} else if (i <= -3.6e+17) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 1.55e-257) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 3e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.7e+104:
		tmp = t_1
	elif i <= -3.6e+17:
		tmp = b * ((t * i) - (z * c))
	elif i <= 1.55e-257:
		tmp = a * ((c * j) - (x * t))
	elif i <= 3e+32:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.7e+104)
		tmp = t_1;
	elseif (i <= -3.6e+17)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 1.55e-257)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 3e+32)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.7e+104)
		tmp = t_1;
	elseif (i <= -3.6e+17)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 1.55e-257)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 3e+32)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.7e+104], t$95$1, If[LessEqual[i, -3.6e+17], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.55e-257], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e+32], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.6999999999999998e104 or 3e32 < i

   1. Initial program 59.9%

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

   3. Taylor expanded in i around inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. neg-mul-1 64.3%

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

      3. cancel-sign-sub 64.3%

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

      4. +-commutative 64.3%

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

      5. mul-1-neg 64.3%

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

      6. unsub-neg 64.3%

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

      7. *-commutative 64.3%

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

      8. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -1.6999999999999998e104 < i < -3.6e17

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -3.6e17 < i < 1.55000000000000004e-257

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   if 1.55000000000000004e-257 < i < 3e32

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.7 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -7.1 \cdot 10^{+117}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= i -7.1e+117)
     (* j (* y (- i)))
     (if (<= i -6.5e+17)
       t_1
       (if (<= i 3.3e-258)
         (* a (- (* c j) (* x t)))
         (if (<= i 5e+32) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (i <= -7.1e+117) {
		tmp = j * (y * -i);
	} else if (i <= -6.5e+17) {
		tmp = t_1;
	} else if (i <= 3.3e-258) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (i <= (-7.1d+117)) then
        tmp = j * (y * -i)
    else if (i <= (-6.5d+17)) then
        tmp = t_1
    else if (i <= 3.3d-258) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 5d+32) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (i <= -7.1e+117) {
		tmp = j * (y * -i);
	} else if (i <= -6.5e+17) {
		tmp = t_1;
	} else if (i <= 3.3e-258) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if i <= -7.1e+117:
		tmp = j * (y * -i)
	elif i <= -6.5e+17:
		tmp = t_1
	elif i <= 3.3e-258:
		tmp = a * ((c * j) - (x * t))
	elif i <= 5e+32:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (i <= -7.1e+117)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (i <= -6.5e+17)
		tmp = t_1;
	elseif (i <= 3.3e-258)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 5e+32)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (i <= -7.1e+117)
		tmp = j * (y * -i);
	elseif (i <= -6.5e+17)
		tmp = t_1;
	elseif (i <= 3.3e-258)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 5e+32)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.1e+117], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.5e+17], t$95$1, If[LessEqual[i, 3.3e-258], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e+32], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.09999999999999995e117

   1. Initial program 61.6%

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

   3. Taylor expanded in j around inf 62.2%

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

      1. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in a around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-rgt-neg-in 56.8%

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

   8. Simplified 56.8%

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

   if -7.09999999999999995e117 < i < -6.5e17 or 4.9999999999999997e32 < i

   1. Initial program 64.2%

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

   3. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   if -6.5e17 < i < 3.3e-258

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   if 3.3e-258 < i < 4.9999999999999997e32

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.1 \cdot 10^{+117}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -1.365 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= z -3.4e+116)
     (* c (* z (- b)))
     (if (<= z -1.365e-114)
       t_1
       (if (<= z -1.15e-185)
         (* i (* y (- j)))
         (if (<= z 8.2e+70) t_1 (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -3.4e+116) {
		tmp = c * (z * -b);
	} else if (z <= -1.365e-114) {
		tmp = t_1;
	} else if (z <= -1.15e-185) {
		tmp = i * (y * -j);
	} else if (z <= 8.2e+70) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (z <= (-3.4d+116)) then
        tmp = c * (z * -b)
    else if (z <= (-1.365d-114)) then
        tmp = t_1
    else if (z <= (-1.15d-185)) then
        tmp = i * (y * -j)
    else if (z <= 8.2d+70) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -3.4e+116) {
		tmp = c * (z * -b);
	} else if (z <= -1.365e-114) {
		tmp = t_1;
	} else if (z <= -1.15e-185) {
		tmp = i * (y * -j);
	} else if (z <= 8.2e+70) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if z <= -3.4e+116:
		tmp = c * (z * -b)
	elif z <= -1.365e-114:
		tmp = t_1
	elif z <= -1.15e-185:
		tmp = i * (y * -j)
	elif z <= 8.2e+70:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (z <= -3.4e+116)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= -1.365e-114)
		tmp = t_1;
	elseif (z <= -1.15e-185)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= 8.2e+70)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (z <= -3.4e+116)
		tmp = c * (z * -b);
	elseif (z <= -1.365e-114)
		tmp = t_1;
	elseif (z <= -1.15e-185)
		tmp = i * (y * -j);
	elseif (z <= 8.2e+70)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+116], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.365e-114], t$95$1, If[LessEqual[z, -1.15e-185], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+70], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000023e116

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in c around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in j around 0 52.2%

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

       1. mul-1-neg 52.2%

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

       2. distribute-rgt-neg-in 52.2%

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

   11. Simplified 52.2%

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

   if -3.40000000000000023e116 < z < -1.36500000000000008e-114 or -1.15e-185 < z < 8.2000000000000004e70

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   if -1.36500000000000008e-114 < z < -1.15e-185

   1. Initial program 62.7%

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

   3. Taylor expanded in y around 0 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in t around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in i around inf 55.0%

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

       1. mul-1-neg 55.0%

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

       2. distribute-rgt-neg-in 55.0%

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

       3. *-commutative 55.0%

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

       4. distribute-rgt-neg-in 55.0%

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

   11. Simplified 55.0%

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

   if 8.2000000000000004e70 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in y around 0 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 50.5%

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

      1. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   9. Taylor expanded in z around inf 46.5%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -1.365 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-29} \lor \neg \left(z \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -2.9e-29) (not (<= z 3e+47))) (* x (* y z)) (* c (* a 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 ((z <= -2.9e-29) || !(z <= 3e+47)) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * 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 ((z <= (-2.9d-29)) .or. (.not. (z <= 3d+47))) then
        tmp = x * (y * z)
    else
        tmp = c * (a * 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 ((z <= -2.9e-29) || !(z <= 3e+47)) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -2.9e-29) or not (z <= 3e+47):
		tmp = x * (y * z)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -2.9e-29) || !(z <= 3e+47))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -2.9e-29) || ~((z <= 3e+47)))
		tmp = x * (y * z);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -2.9e-29], N[Not[LessEqual[z, 3e+47]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.90000000000000024e-29 or 3.0000000000000001e47 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in y around 0 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   9. Taylor expanded in z around inf 36.6%

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

   if -2.90000000000000024e-29 < z < 3.0000000000000001e47

   1. Initial program 79.9%

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

   3. Taylor expanded in y around 0 80.5%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in c around inf 42.5%

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

      1. +-commutative 42.5%

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

      2. mul-1-neg 42.5%

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

      3. unsub-neg 42.5%

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

      4. *-commutative 42.5%

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

   8. Simplified 42.5%

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

   9. Taylor expanded in j around inf 31.3%

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

       1. *-commutative 31.3%

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

       2. associate-*l* 36.0%

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

   11. Simplified 36.0%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-29} \lor \neg \left(z \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -86000000 \lor \neg \left(c \leq 1.2 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -86000000.0) (not (<= c 1.2e-50))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -86000000.0) || !(c <= 1.2e-50)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-86000000.0d0)) .or. (.not. (c <= 1.2d-50))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -86000000.0) || !(c <= 1.2e-50)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -86000000.0) or not (c <= 1.2e-50):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -86000000.0) || !(c <= 1.2e-50))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -86000000.0) || ~((c <= 1.2e-50)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -86000000.0], N[Not[LessEqual[c, 1.2e-50]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.6e7 or 1.20000000000000001e-50 < c

   1. Initial program 71.6%

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

   3. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

      5. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in j around inf 39.6%

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

   if -8.6e7 < c < 1.20000000000000001e-50

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0 55.0%

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

   4. Taylor expanded in t around inf 28.8%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -86000000 \lor \neg \left(c \leq 1.2 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -8e+78)
   (* c (* z (- b)))
   (if (<= z 4e+46) (* c (* a j)) (* x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -8e+78) {
		tmp = c * (z * -b);
	} else if (z <= 4e+46) {
		tmp = c * (a * j);
	} else {
		tmp = x * (y * z);
	}
	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 (z <= (-8d+78)) then
        tmp = c * (z * -b)
    else if (z <= 4d+46) then
        tmp = c * (a * j)
    else
        tmp = x * (y * z)
    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 (z <= -8e+78) {
		tmp = c * (z * -b);
	} else if (z <= 4e+46) {
		tmp = c * (a * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -8e+78:
		tmp = c * (z * -b)
	elif z <= 4e+46:
		tmp = c * (a * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -8e+78)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= 4e+46)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -8e+78)
		tmp = c * (z * -b);
	elseif (z <= 4e+46)
		tmp = c * (a * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -8e+78], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+46], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000007e78

   1. Initial program 59.3%

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

   3. Taylor expanded in y around 0 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in c around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   9. Taylor expanded in j around 0 51.0%

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

       1. mul-1-neg 51.0%

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

       2. distribute-rgt-neg-in 51.0%

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

   11. Simplified 51.0%

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

   if -8.00000000000000007e78 < z < 4e46

   1. Initial program 80.7%

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

   3. Taylor expanded in y around 0 78.8%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in c around inf 40.2%

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

      1. +-commutative 40.2%

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

      2. mul-1-neg 40.2%

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

      3. unsub-neg 40.2%

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

      4. *-commutative 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in j around inf 30.5%

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

       1. *-commutative 30.5%

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

       2. associate-*l* 33.4%

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

   11. Simplified 33.4%

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

   if 4e46 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 49.9%

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

      1. *-commutative 49.9%

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

   8. Simplified 49.9%

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

   9. Taylor expanded in z around inf 43.1%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.15e+110)
   (* y (* x z))
   (if (<= z 2.9e+46) (* c (* a j)) (* x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.15e+110) {
		tmp = y * (x * z);
	} else if (z <= 2.9e+46) {
		tmp = c * (a * j);
	} else {
		tmp = x * (y * z);
	}
	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 (z <= (-1.15d+110)) then
        tmp = y * (x * z)
    else if (z <= 2.9d+46) then
        tmp = c * (a * j)
    else
        tmp = x * (y * z)
    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 (z <= -1.15e+110) {
		tmp = y * (x * z);
	} else if (z <= 2.9e+46) {
		tmp = c * (a * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.15e+110:
		tmp = y * (x * z)
	elif z <= 2.9e+46:
		tmp = c * (a * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.15e+110)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 2.9e+46)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.15e+110)
		tmp = y * (x * z);
	elseif (z <= 2.9e+46)
		tmp = c * (a * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.15e+110], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+46], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e110

   1. Initial program 62.4%

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

   3. Taylor expanded in y around 0 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

   8. Simplified 44.1%

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

   9. Taylor expanded in z around inf 37.3%

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

       1. *-commutative 37.3%

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

       2. associate-*r* 41.6%

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

   11. Simplified 41.6%

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

   if -1.15e110 < z < 2.9000000000000002e46

   1. Initial program 79.3%

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

   3. Taylor expanded in y around 0 78.1%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in c around inf 41.1%

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

      1. +-commutative 41.1%

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

      2. mul-1-neg 41.1%

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

      3. unsub-neg 41.1%

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

      4. *-commutative 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in j around inf 31.0%

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

       1. *-commutative 31.0%

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

       2. associate-*l* 33.9%

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

   11. Simplified 33.9%

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

   if 2.9000000000000002e46 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 49.9%

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

      1. *-commutative 49.9%

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

   8. Simplified 49.9%

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

   9. Taylor expanded in z around inf 43.1%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.0% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

3. Taylor expanded in a around inf 41.9%

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

   1. +-commutative 41.9%

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

   2. mul-1-neg 41.9%

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

   3. unsub-neg 41.9%

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

   4. *-commutative 41.9%

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

   5. *-commutative 41.9%

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

5. Simplified 41.9%

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

6. Taylor expanded in j around inf 25.2%

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

Developer target: 59.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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