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

Percentage Accurate: 73.4% → 81.8%

Time: 19.6s

Alternatives: 18

Speedup: 0.5×

• 58.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.4% 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: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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))) - (x * ((t * a) - (y * z)))) - (j * ((y * i) - (a * c)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $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 94.3%

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

   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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around inf 56.0%

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

      1. distribute-lft-out-- 56.0%

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

      2. *-commutative 56.0%

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

   6. Simplified 56.0%

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

   7. Taylor expanded in t around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. *-commutative 56.0%

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

      3. distribute-rgt-neg-out 56.0%

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

      4. neg-mul-1 56.0%

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

      5. neg-mul-1 56.0%

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

      6. sub-neg 56.0%

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

      7. +-commutative 56.0%

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

      8. distribute-neg-in 56.0%

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

      9. remove-double-neg 56.0%

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

      10. sub-neg 56.0%

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

   9. Simplified 56.0%

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

4. Final simplification 86.5%

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

Alternative 2: 51.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* z (- (* x y) (* b c))))
        (t_4 (* i (- (* t b) (* y j)))))
   (if (<= i -4.1e+27)
     t_4
     (if (<= i -3.2e-95)
       t_3
       (if (<= i -2.4e-223)
         t_1
         (if (<= i 1.8e-246)
           (* c (- (* a j) (* z b)))
           (if (<= i 2.85e-232)
             t_1
             (if (<= i 1.22e-134)
               t_3
               (if (<= i 1.02e-65)
                 t_2
                 (if (<= i 8.5e-42) t_3 (if (<= i 9.5e+132) 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 = a * ((c * j) - (x * t));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double t_4 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.1e+27) {
		tmp = t_4;
	} else if (i <= -3.2e-95) {
		tmp = t_3;
	} else if (i <= -2.4e-223) {
		tmp = t_1;
	} else if (i <= 1.8e-246) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.85e-232) {
		tmp = t_1;
	} else if (i <= 1.22e-134) {
		tmp = t_3;
	} else if (i <= 1.02e-65) {
		tmp = t_2;
	} else if (i <= 8.5e-42) {
		tmp = t_3;
	} else if (i <= 9.5e+132) {
		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 = a * ((c * j) - (x * t))
    t_2 = t * ((b * i) - (x * a))
    t_3 = z * ((x * y) - (b * c))
    t_4 = i * ((t * b) - (y * j))
    if (i <= (-4.1d+27)) then
        tmp = t_4
    else if (i <= (-3.2d-95)) then
        tmp = t_3
    else if (i <= (-2.4d-223)) then
        tmp = t_1
    else if (i <= 1.8d-246) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 2.85d-232) then
        tmp = t_1
    else if (i <= 1.22d-134) then
        tmp = t_3
    else if (i <= 1.02d-65) then
        tmp = t_2
    else if (i <= 8.5d-42) then
        tmp = t_3
    else if (i <= 9.5d+132) 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 = a * ((c * j) - (x * t));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double t_4 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.1e+27) {
		tmp = t_4;
	} else if (i <= -3.2e-95) {
		tmp = t_3;
	} else if (i <= -2.4e-223) {
		tmp = t_1;
	} else if (i <= 1.8e-246) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.85e-232) {
		tmp = t_1;
	} else if (i <= 1.22e-134) {
		tmp = t_3;
	} else if (i <= 1.02e-65) {
		tmp = t_2;
	} else if (i <= 8.5e-42) {
		tmp = t_3;
	} else if (i <= 9.5e+132) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = t * ((b * i) - (x * a))
	t_3 = z * ((x * y) - (b * c))
	t_4 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.1e+27:
		tmp = t_4
	elif i <= -3.2e-95:
		tmp = t_3
	elif i <= -2.4e-223:
		tmp = t_1
	elif i <= 1.8e-246:
		tmp = c * ((a * j) - (z * b))
	elif i <= 2.85e-232:
		tmp = t_1
	elif i <= 1.22e-134:
		tmp = t_3
	elif i <= 1.02e-65:
		tmp = t_2
	elif i <= 8.5e-42:
		tmp = t_3
	elif i <= 9.5e+132:
		tmp = t_2
	else:
		tmp = t_4
	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)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_4 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.1e+27)
		tmp = t_4;
	elseif (i <= -3.2e-95)
		tmp = t_3;
	elseif (i <= -2.4e-223)
		tmp = t_1;
	elseif (i <= 1.8e-246)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 2.85e-232)
		tmp = t_1;
	elseif (i <= 1.22e-134)
		tmp = t_3;
	elseif (i <= 1.02e-65)
		tmp = t_2;
	elseif (i <= 8.5e-42)
		tmp = t_3;
	elseif (i <= 9.5e+132)
		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 = a * ((c * j) - (x * t));
	t_2 = t * ((b * i) - (x * a));
	t_3 = z * ((x * y) - (b * c));
	t_4 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.1e+27)
		tmp = t_4;
	elseif (i <= -3.2e-95)
		tmp = t_3;
	elseif (i <= -2.4e-223)
		tmp = t_1;
	elseif (i <= 1.8e-246)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 2.85e-232)
		tmp = t_1;
	elseif (i <= 1.22e-134)
		tmp = t_3;
	elseif (i <= 1.02e-65)
		tmp = t_2;
	elseif (i <= 8.5e-42)
		tmp = t_3;
	elseif (i <= 9.5e+132)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.1e+27], t$95$4, If[LessEqual[i, -3.2e-95], t$95$3, If[LessEqual[i, -2.4e-223], t$95$1, If[LessEqual[i, 1.8e-246], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.85e-232], t$95$1, If[LessEqual[i, 1.22e-134], t$95$3, If[LessEqual[i, 1.02e-65], t$95$2, If[LessEqual[i, 8.5e-42], t$95$3, If[LessEqual[i, 9.5e+132], t$95$2, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.1000000000000002e27 or 9.5000000000000005e132 < i

   1. Initial program 70.0%

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

      1. associate-+l- 70.0%

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

      2. *-commutative 70.0%

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

      3. sub-neg 70.0%

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

      4. sub-neg 70.0%

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

      5. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in i around inf 77.4%

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

      1. distribute-lft-out-- 77.4%

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

      2. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in i around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. *-commutative 77.4%

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

      3. *-commutative 77.4%

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

      4. distribute-rgt-neg-in 77.4%

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

      5. neg-sub0 77.4%

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

      6. associate-+l- 77.4%

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

      7. neg-sub0 77.4%

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

      8. +-commutative 77.4%

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

      9. sub-neg 77.4%

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

   9. Simplified 77.4%

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

   if -4.1000000000000002e27 < i < -3.1999999999999997e-95 or 2.8500000000000001e-232 < i < 1.2199999999999999e-134 or 1.02000000000000004e-65 < i < 8.4999999999999996e-42

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. sub-neg 84.8%

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

      4. sub-neg 84.8%

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

      5. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   if -3.1999999999999997e-95 < i < -2.39999999999999985e-223 or 1.8000000000000001e-246 < i < 2.8500000000000001e-232

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. *-commutative 85.9%

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

      3. sub-neg 85.9%

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

      4. sub-neg 85.9%

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

      5. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in a around inf 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

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

      3. unsub-neg 90.5%

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

      4. *-commutative 90.5%

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

      5. *-commutative 90.5%

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

   6. Simplified 90.5%

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

   if -2.39999999999999985e-223 < i < 1.8000000000000001e-246

   1. Initial program 65.3%

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

      1. associate-+l- 65.3%

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

      2. *-commutative 65.3%

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

      3. sub-neg 65.3%

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

      4. sub-neg 65.3%

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

      5. *-commutative 65.3%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in c around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   if 1.2199999999999999e-134 < i < 1.02000000000000004e-65 or 8.4999999999999996e-42 < i < 9.5000000000000005e132

   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. Step-by-step derivation

      1. associate-+l- 75.4%

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

      2. *-commutative 75.4%

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

      3. sub-neg 75.4%

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

      4. sub-neg 75.4%

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

      5. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around inf 62.8%

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

      1. distribute-lft-out-- 62.8%

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

      2. *-commutative 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in t around 0 62.8%

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

      1. mul-1-neg 62.8%

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

      2. *-commutative 62.8%

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

      3. distribute-rgt-neg-out 62.8%

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

      4. neg-mul-1 62.8%

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

      5. neg-mul-1 62.8%

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

      6. sub-neg 62.8%

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

      7. +-commutative 62.8%

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

      8. distribute-neg-in 62.8%

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

      9. remove-double-neg 62.8%

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

      10. sub-neg 62.8%

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

   9. Simplified 62.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-232}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{-134}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 3: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -2.4e+29)
     t_3
     (if (<= i -3.8e-95)
       t_2
       (if (<= i -1.1e-220)
         t_1
         (if (<= i 1.8e-246)
           (* c (- (* a j) (* z b)))
           (if (<= i 2.6e-232)
             t_1
             (if (<= i 1.15e-135)
               t_2
               (if (<= i 2.3e-65)
                 (- (* t (* b i)) (* t (* x a)))
                 (if (<= i 1.7e-41)
                   t_2
                   (if (<= i 1.85e+130)
                     (* t (- (* b i) (* x a)))
                     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 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.4e+29) {
		tmp = t_3;
	} else if (i <= -3.8e-95) {
		tmp = t_2;
	} else if (i <= -1.1e-220) {
		tmp = t_1;
	} else if (i <= 1.8e-246) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.6e-232) {
		tmp = t_1;
	} else if (i <= 1.15e-135) {
		tmp = t_2;
	} else if (i <= 2.3e-65) {
		tmp = (t * (b * i)) - (t * (x * a));
	} else if (i <= 1.7e-41) {
		tmp = t_2;
	} else if (i <= 1.85e+130) {
		tmp = t * ((b * i) - (x * a));
	} 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 = a * ((c * j) - (x * t))
    t_2 = z * ((x * y) - (b * c))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-2.4d+29)) then
        tmp = t_3
    else if (i <= (-3.8d-95)) then
        tmp = t_2
    else if (i <= (-1.1d-220)) then
        tmp = t_1
    else if (i <= 1.8d-246) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 2.6d-232) then
        tmp = t_1
    else if (i <= 1.15d-135) then
        tmp = t_2
    else if (i <= 2.3d-65) then
        tmp = (t * (b * i)) - (t * (x * a))
    else if (i <= 1.7d-41) then
        tmp = t_2
    else if (i <= 1.85d+130) then
        tmp = t * ((b * i) - (x * a))
    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 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.4e+29) {
		tmp = t_3;
	} else if (i <= -3.8e-95) {
		tmp = t_2;
	} else if (i <= -1.1e-220) {
		tmp = t_1;
	} else if (i <= 1.8e-246) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.6e-232) {
		tmp = t_1;
	} else if (i <= 1.15e-135) {
		tmp = t_2;
	} else if (i <= 2.3e-65) {
		tmp = (t * (b * i)) - (t * (x * a));
	} else if (i <= 1.7e-41) {
		tmp = t_2;
	} else if (i <= 1.85e+130) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * ((x * y) - (b * c))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.4e+29:
		tmp = t_3
	elif i <= -3.8e-95:
		tmp = t_2
	elif i <= -1.1e-220:
		tmp = t_1
	elif i <= 1.8e-246:
		tmp = c * ((a * j) - (z * b))
	elif i <= 2.6e-232:
		tmp = t_1
	elif i <= 1.15e-135:
		tmp = t_2
	elif i <= 2.3e-65:
		tmp = (t * (b * i)) - (t * (x * a))
	elif i <= 1.7e-41:
		tmp = t_2
	elif i <= 1.85e+130:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	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)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.4e+29)
		tmp = t_3;
	elseif (i <= -3.8e-95)
		tmp = t_2;
	elseif (i <= -1.1e-220)
		tmp = t_1;
	elseif (i <= 1.8e-246)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 2.6e-232)
		tmp = t_1;
	elseif (i <= 1.15e-135)
		tmp = t_2;
	elseif (i <= 2.3e-65)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(t * Float64(x * a)));
	elseif (i <= 1.7e-41)
		tmp = t_2;
	elseif (i <= 1.85e+130)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	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));
	t_2 = z * ((x * y) - (b * c));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.4e+29)
		tmp = t_3;
	elseif (i <= -3.8e-95)
		tmp = t_2;
	elseif (i <= -1.1e-220)
		tmp = t_1;
	elseif (i <= 1.8e-246)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 2.6e-232)
		tmp = t_1;
	elseif (i <= 1.15e-135)
		tmp = t_2;
	elseif (i <= 2.3e-65)
		tmp = (t * (b * i)) - (t * (x * a));
	elseif (i <= 1.7e-41)
		tmp = t_2;
	elseif (i <= 1.85e+130)
		tmp = t * ((b * i) - (x * a));
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.4e+29], t$95$3, If[LessEqual[i, -3.8e-95], t$95$2, If[LessEqual[i, -1.1e-220], t$95$1, If[LessEqual[i, 1.8e-246], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e-232], t$95$1, If[LessEqual[i, 1.15e-135], t$95$2, If[LessEqual[i, 2.3e-65], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-41], t$95$2, If[LessEqual[i, 1.85e+130], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.4000000000000001e29 or 1.8500000000000001e130 < i

   1. Initial program 70.0%

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

      1. associate-+l- 70.0%

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

      2. *-commutative 70.0%

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

      3. sub-neg 70.0%

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

      4. sub-neg 70.0%

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

      5. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in i around inf 77.4%

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

      1. distribute-lft-out-- 77.4%

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

      2. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in i around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. *-commutative 77.4%

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

      3. *-commutative 77.4%

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

      4. distribute-rgt-neg-in 77.4%

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

      5. neg-sub0 77.4%

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

      6. associate-+l- 77.4%

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

      7. neg-sub0 77.4%

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

      8. +-commutative 77.4%

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

      9. sub-neg 77.4%

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

   9. Simplified 77.4%

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

   if -2.4000000000000001e29 < i < -3.7999999999999997e-95 or 2.59999999999999996e-232 < i < 1.15e-135 or 2.3e-65 < i < 1.6999999999999999e-41

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. sub-neg 84.8%

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

      4. sub-neg 84.8%

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

      5. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   if -3.7999999999999997e-95 < i < -1.09999999999999993e-220 or 1.8000000000000001e-246 < i < 2.59999999999999996e-232

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. *-commutative 85.9%

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

      3. sub-neg 85.9%

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

      4. sub-neg 85.9%

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

      5. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in a around inf 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

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

      3. unsub-neg 90.5%

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

      4. *-commutative 90.5%

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

      5. *-commutative 90.5%

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

   6. Simplified 90.5%

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

   if -1.09999999999999993e-220 < i < 1.8000000000000001e-246

   1. Initial program 65.3%

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

      1. associate-+l- 65.3%

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

      2. *-commutative 65.3%

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

      3. sub-neg 65.3%

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

      4. sub-neg 65.3%

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

      5. *-commutative 65.3%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in c around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   if 1.15e-135 < i < 2.3e-65

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. *-commutative 88.5%

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

      3. sub-neg 88.5%

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

      4. sub-neg 88.5%

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

      5. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in t around inf 72.4%

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

      1. distribute-lft-out-- 72.4%

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

      2. *-commutative 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in t around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. *-commutative 72.4%

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

      3. distribute-rgt-neg-out 72.4%

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

      4. neg-mul-1 72.4%

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

      5. neg-mul-1 72.4%

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

      6. sub-neg 72.4%

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

      7. +-commutative 72.4%

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

      8. distribute-neg-in 72.4%

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

      9. remove-double-neg 72.4%

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

      10. sub-neg 72.4%

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

   9. Simplified 72.4%

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

       1. sub-neg 72.4%

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

       2. distribute-lft-in 72.5%

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

       3. distribute-rgt-neg-in 72.5%

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

   11. Applied egg-rr 72.5%

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

   if 1.6999999999999999e-41 < i < 1.8500000000000001e130

   1. Initial program 68.6%

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

      1. associate-+l- 68.6%

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

      2. *-commutative 68.6%

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

      3. sub-neg 68.6%

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

      4. sub-neg 68.6%

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

      5. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in t around inf 57.8%

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

      1. distribute-lft-out-- 57.8%

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

      2. *-commutative 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in t around 0 57.8%

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

      1. mul-1-neg 57.8%

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

      2. *-commutative 57.8%

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

      3. distribute-rgt-neg-out 57.8%

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

      4. neg-mul-1 57.8%

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

      5. neg-mul-1 57.8%

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

      6. sub-neg 57.8%

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

      7. +-commutative 57.8%

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

      8. distribute-neg-in 57.8%

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

      9. remove-double-neg 57.8%

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

      10. sub-neg 57.8%

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

   9. Simplified 57.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-232}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 4: 49.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -1.4e+64)
     t_3
     (if (<= t -6.5e-80)
       t_2
       (if (<= t -4.1e-282)
         t_1
         (if (<= t 5e-250)
           t_2
           (if (<= t 1.7e-229)
             t_1
             (if (<= t 1.7e-145) t_2 (if (<= t 4.9e+42) t_1 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 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.4e+64) {
		tmp = t_3;
	} else if (t <= -6.5e-80) {
		tmp = t_2;
	} else if (t <= -4.1e-282) {
		tmp = t_1;
	} else if (t <= 5e-250) {
		tmp = t_2;
	} else if (t <= 1.7e-229) {
		tmp = t_1;
	} else if (t <= 1.7e-145) {
		tmp = t_2;
	} else if (t <= 4.9e+42) {
		tmp = t_1;
	} 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 = c * ((a * j) - (z * b))
    t_2 = i * ((t * b) - (y * j))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-1.4d+64)) then
        tmp = t_3
    else if (t <= (-6.5d-80)) then
        tmp = t_2
    else if (t <= (-4.1d-282)) then
        tmp = t_1
    else if (t <= 5d-250) then
        tmp = t_2
    else if (t <= 1.7d-229) then
        tmp = t_1
    else if (t <= 1.7d-145) then
        tmp = t_2
    else if (t <= 4.9d+42) then
        tmp = t_1
    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 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.4e+64) {
		tmp = t_3;
	} else if (t <= -6.5e-80) {
		tmp = t_2;
	} else if (t <= -4.1e-282) {
		tmp = t_1;
	} else if (t <= 5e-250) {
		tmp = t_2;
	} else if (t <= 1.7e-229) {
		tmp = t_1;
	} else if (t <= 1.7e-145) {
		tmp = t_2;
	} else if (t <= 4.9e+42) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = i * ((t * b) - (y * j))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.4e+64:
		tmp = t_3
	elif t <= -6.5e-80:
		tmp = t_2
	elif t <= -4.1e-282:
		tmp = t_1
	elif t <= 5e-250:
		tmp = t_2
	elif t <= 1.7e-229:
		tmp = t_1
	elif t <= 1.7e-145:
		tmp = t_2
	elif t <= 4.9e+42:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.4e+64)
		tmp = t_3;
	elseif (t <= -6.5e-80)
		tmp = t_2;
	elseif (t <= -4.1e-282)
		tmp = t_1;
	elseif (t <= 5e-250)
		tmp = t_2;
	elseif (t <= 1.7e-229)
		tmp = t_1;
	elseif (t <= 1.7e-145)
		tmp = t_2;
	elseif (t <= 4.9e+42)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = i * ((t * b) - (y * j));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.4e+64)
		tmp = t_3;
	elseif (t <= -6.5e-80)
		tmp = t_2;
	elseif (t <= -4.1e-282)
		tmp = t_1;
	elseif (t <= 5e-250)
		tmp = t_2;
	elseif (t <= 1.7e-229)
		tmp = t_1;
	elseif (t <= 1.7e-145)
		tmp = t_2;
	elseif (t <= 4.9e+42)
		tmp = t_1;
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+64], t$95$3, If[LessEqual[t, -6.5e-80], t$95$2, If[LessEqual[t, -4.1e-282], t$95$1, If[LessEqual[t, 5e-250], t$95$2, If[LessEqual[t, 1.7e-229], t$95$1, If[LessEqual[t, 1.7e-145], t$95$2, If[LessEqual[t, 4.9e+42], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.40000000000000012e64 or 4.9000000000000002e42 < t

   1. Initial program 67.1%

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

      1. associate-+l- 67.1%

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

      2. *-commutative 67.1%

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

      3. sub-neg 67.1%

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

      4. sub-neg 67.1%

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

      5. *-commutative 67.1%

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

   3. Simplified 67.1%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. distribute-lft-out-- 75.8%

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

      2. *-commutative 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. *-commutative 75.8%

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

      3. distribute-rgt-neg-out 75.8%

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

      4. neg-mul-1 75.8%

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

      5. neg-mul-1 75.8%

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

      6. sub-neg 75.8%

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

      7. +-commutative 75.8%

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

      8. distribute-neg-in 75.8%

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

      9. remove-double-neg 75.8%

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

      10. sub-neg 75.8%

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

   9. Simplified 75.8%

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

   if -1.40000000000000012e64 < t < -6.49999999999999984e-80 or -4.09999999999999977e-282 < t < 5.00000000000000027e-250 or 1.7e-229 < t < 1.6999999999999999e-145

   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. Step-by-step derivation

      1. associate-+l- 84.5%

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

      2. *-commutative 84.5%

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

      3. sub-neg 84.5%

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

      4. sub-neg 84.5%

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

      5. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in i around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

      2. *-commutative 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in i around 0 62.0%

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

      1. mul-1-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. *-commutative 62.0%

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

      4. distribute-rgt-neg-in 62.0%

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

      5. neg-sub0 62.0%

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

      6. associate-+l- 62.0%

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

      7. neg-sub0 62.0%

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

      8. +-commutative 62.0%

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

      9. sub-neg 62.0%

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

   9. Simplified 62.0%

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

   if -6.49999999999999984e-80 < t < -4.09999999999999977e-282 or 5.00000000000000027e-250 < t < 1.7e-229 or 1.6999999999999999e-145 < t < 4.9000000000000002e42

   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. Step-by-step derivation

      1. associate-+l- 79.6%

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

      2. *-commutative 79.6%

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

      3. sub-neg 79.6%

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

      4. sub-neg 79.6%

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

      5. *-commutative 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in c around inf 57.1%

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

      1. *-commutative 57.1%

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

      2. *-commutative 57.1%

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

   6. Simplified 57.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-282}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-250}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 5: 51.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -1.15e+64)
     t_3
     (if (<= t -1.3e-79)
       t_2
       (if (<= t -4e-214)
         t_1
         (if (<= t 1.15e-252)
           (* y (- (* x z) (* i j)))
           (if (<= t 4.7e-228)
             t_1
             (if (<= t 1.35e-145) t_2 (if (<= t 9e+39) t_1 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 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.15e+64) {
		tmp = t_3;
	} else if (t <= -1.3e-79) {
		tmp = t_2;
	} else if (t <= -4e-214) {
		tmp = t_1;
	} else if (t <= 1.15e-252) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.7e-228) {
		tmp = t_1;
	} else if (t <= 1.35e-145) {
		tmp = t_2;
	} else if (t <= 9e+39) {
		tmp = t_1;
	} 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 = c * ((a * j) - (z * b))
    t_2 = i * ((t * b) - (y * j))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-1.15d+64)) then
        tmp = t_3
    else if (t <= (-1.3d-79)) then
        tmp = t_2
    else if (t <= (-4d-214)) then
        tmp = t_1
    else if (t <= 1.15d-252) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.7d-228) then
        tmp = t_1
    else if (t <= 1.35d-145) then
        tmp = t_2
    else if (t <= 9d+39) then
        tmp = t_1
    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 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.15e+64) {
		tmp = t_3;
	} else if (t <= -1.3e-79) {
		tmp = t_2;
	} else if (t <= -4e-214) {
		tmp = t_1;
	} else if (t <= 1.15e-252) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.7e-228) {
		tmp = t_1;
	} else if (t <= 1.35e-145) {
		tmp = t_2;
	} else if (t <= 9e+39) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = i * ((t * b) - (y * j))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.15e+64:
		tmp = t_3
	elif t <= -1.3e-79:
		tmp = t_2
	elif t <= -4e-214:
		tmp = t_1
	elif t <= 1.15e-252:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.7e-228:
		tmp = t_1
	elif t <= 1.35e-145:
		tmp = t_2
	elif t <= 9e+39:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.15e+64)
		tmp = t_3;
	elseif (t <= -1.3e-79)
		tmp = t_2;
	elseif (t <= -4e-214)
		tmp = t_1;
	elseif (t <= 1.15e-252)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.7e-228)
		tmp = t_1;
	elseif (t <= 1.35e-145)
		tmp = t_2;
	elseif (t <= 9e+39)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = i * ((t * b) - (y * j));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.15e+64)
		tmp = t_3;
	elseif (t <= -1.3e-79)
		tmp = t_2;
	elseif (t <= -4e-214)
		tmp = t_1;
	elseif (t <= 1.15e-252)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.7e-228)
		tmp = t_1;
	elseif (t <= 1.35e-145)
		tmp = t_2;
	elseif (t <= 9e+39)
		tmp = t_1;
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+64], t$95$3, If[LessEqual[t, -1.3e-79], t$95$2, If[LessEqual[t, -4e-214], t$95$1, If[LessEqual[t, 1.15e-252], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e-228], t$95$1, If[LessEqual[t, 1.35e-145], t$95$2, If[LessEqual[t, 9e+39], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e64 or 8.99999999999999991e39 < t

   1. Initial program 67.1%

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

      1. associate-+l- 67.1%

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

      2. *-commutative 67.1%

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

      3. sub-neg 67.1%

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

      4. sub-neg 67.1%

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

      5. *-commutative 67.1%

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

   3. Simplified 67.1%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. distribute-lft-out-- 75.8%

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

      2. *-commutative 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. *-commutative 75.8%

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

      3. distribute-rgt-neg-out 75.8%

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

      4. neg-mul-1 75.8%

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

      5. neg-mul-1 75.8%

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

      6. sub-neg 75.8%

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

      7. +-commutative 75.8%

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

      8. distribute-neg-in 75.8%

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

      9. remove-double-neg 75.8%

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

      10. sub-neg 75.8%

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

   9. Simplified 75.8%

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

   if -1.15e64 < t < -1.29999999999999997e-79 or 4.7000000000000002e-228 < t < 1.35e-145

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. sub-neg 78.8%

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

      4. sub-neg 78.8%

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

      5. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in i around inf 65.6%

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

      1. distribute-lft-out-- 65.6%

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

      2. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in i around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. *-commutative 65.6%

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

      3. *-commutative 65.6%

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

      4. distribute-rgt-neg-in 65.6%

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

      5. neg-sub0 65.6%

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

      6. associate-+l- 65.6%

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

      7. neg-sub0 65.6%

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

      8. +-commutative 65.6%

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

      9. sub-neg 65.6%

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

   9. Simplified 65.6%

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

   if -1.29999999999999997e-79 < t < -3.99999999999999965e-214 or 1.1499999999999999e-252 < t < 4.7000000000000002e-228 or 1.35e-145 < t < 8.99999999999999991e39

   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. Step-by-step derivation

      1. associate-+l- 77.9%

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

      2. *-commutative 77.9%

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

      3. sub-neg 77.9%

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

      4. sub-neg 77.9%

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

      5. *-commutative 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in c around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if -3.99999999999999965e-214 < t < 1.1499999999999999e-252

   1. Initial program 91.6%

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

      1. associate-+l- 91.6%

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

      2. *-commutative 91.6%

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

      3. sub-neg 91.6%

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

      4. sub-neg 91.6%

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

      5. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   6. Simplified 60.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-79}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-145}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 6: 64.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+152} \lor \neg \left(a \leq 3.4 \cdot 10^{+100}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.4e+152) (not (<= a 3.4e+100)))
   (* a (- (* c j) (* x t)))
   (- (* b (- (* t i) (* z c))) (* j (- (* y i) (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.4e+152) || !(a <= 3.4e+100)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.4d+152)) .or. (.not. (a <= 3.4d+100))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.4e+152) || !(a <= 3.4e+100)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.4e+152) or not (a <= 3.4e+100):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.4e+152) || !(a <= 3.4e+100))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.4e+152) || ~((a <= 3.4e+100)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.4e+152], N[Not[LessEqual[a, 3.4e+100]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4000000000000001e152 or 3.39999999999999994e100 < a

   1. Initial program 57.5%

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

      1. associate-+l- 57.5%

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

      2. *-commutative 57.5%

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

      3. sub-neg 57.5%

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

      4. sub-neg 57.5%

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

      5. *-commutative 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in a around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

   6. Simplified 72.6%

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

   if -1.4000000000000001e152 < a < 3.39999999999999994e100

   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. Step-by-step derivation

      1. associate-+l- 81.5%

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

      2. *-commutative 81.5%

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

      3. sub-neg 81.5%

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

      4. sub-neg 81.5%

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

      5. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in x around 0 69.4%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+152} \lor \neg \left(a \leq 3.4 \cdot 10^{+100}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 7: 70.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -410 \lor \neg \left(j \leq 1.62 \cdot 10^{-62}\right):\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (or (<= j -410.0) (not (<= j 1.62e-62)))
     (- t_1 (* j (- (* y i) (* a c))))
     (- t_1 (* x (- (* t a) (* 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 = b * ((t * i) - (z * c));
	double tmp;
	if ((j <= -410.0) || !(j <= 1.62e-62)) {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (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 = b * ((t * i) - (z * c))
    if ((j <= (-410.0d0)) .or. (.not. (j <= 1.62d-62))) then
        tmp = t_1 - (j * ((y * i) - (a * c)))
    else
        tmp = t_1 - (x * ((t * a) - (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 = b * ((t * i) - (z * c));
	double tmp;
	if ((j <= -410.0) || !(j <= 1.62e-62)) {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if (j <= -410.0) or not (j <= 1.62e-62):
		tmp = t_1 - (j * ((y * i) - (a * c)))
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	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 ((j <= -410.0) || !(j <= 1.62e-62))
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	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 ((j <= -410.0) || ~((j <= 1.62e-62)))
		tmp = t_1 - (j * ((y * i) - (a * c)));
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	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[Or[LessEqual[j, -410.0], N[Not[LessEqual[j, 1.62e-62]], $MachinePrecision]], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if j < -410 or 1.6199999999999999e-62 < j

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. sub-neg 75.7%

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

      4. sub-neg 75.7%

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

      5. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 72.5%

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

   if -410 < j < 1.6199999999999999e-62

   1. Initial program 74.4%

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

      1. associate-+l- 74.4%

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

      2. *-commutative 74.4%

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

      3. sub-neg 74.4%

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

      4. sub-neg 74.4%

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

      5. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in j around 0 79.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -410 \lor \neg \left(j \leq 1.62 \cdot 10^{-62}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]

Alternative 8: 29.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := -c \cdot \left(z \cdot b\right)\\ t_3 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (- (* c (* z b)))) (t_3 (* t (* b i))))
   (if (<= i -2.3e+80)
     t_3
     (if (<= i -6.2e+27)
       (* (* y j) (- i))
       (if (<= i -1.6e-115)
         t_2
         (if (<= i -1.5e-255)
           t_1
           (if (<= i 1.25e-246)
             t_2
             (if (<= i 3e-122)
               (* x (* y z))
               (if (<= i 2.65e-20)
                 t_3
                 (if (<= i 3.4e+42) t_1 (* 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 t_1 = a * (c * j);
	double t_2 = -(c * (z * b));
	double t_3 = t * (b * i);
	double tmp;
	if (i <= -2.3e+80) {
		tmp = t_3;
	} else if (i <= -6.2e+27) {
		tmp = (y * j) * -i;
	} else if (i <= -1.6e-115) {
		tmp = t_2;
	} else if (i <= -1.5e-255) {
		tmp = t_1;
	} else if (i <= 1.25e-246) {
		tmp = t_2;
	} else if (i <= 3e-122) {
		tmp = x * (y * z);
	} else if (i <= 2.65e-20) {
		tmp = t_3;
	} else if (i <= 3.4e+42) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = -(c * (z * b))
    t_3 = t * (b * i)
    if (i <= (-2.3d+80)) then
        tmp = t_3
    else if (i <= (-6.2d+27)) then
        tmp = (y * j) * -i
    else if (i <= (-1.6d-115)) then
        tmp = t_2
    else if (i <= (-1.5d-255)) then
        tmp = t_1
    else if (i <= 1.25d-246) then
        tmp = t_2
    else if (i <= 3d-122) then
        tmp = x * (y * z)
    else if (i <= 2.65d-20) then
        tmp = t_3
    else if (i <= 3.4d+42) then
        tmp = t_1
    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 t_1 = a * (c * j);
	double t_2 = -(c * (z * b));
	double t_3 = t * (b * i);
	double tmp;
	if (i <= -2.3e+80) {
		tmp = t_3;
	} else if (i <= -6.2e+27) {
		tmp = (y * j) * -i;
	} else if (i <= -1.6e-115) {
		tmp = t_2;
	} else if (i <= -1.5e-255) {
		tmp = t_1;
	} else if (i <= 1.25e-246) {
		tmp = t_2;
	} else if (i <= 3e-122) {
		tmp = x * (y * z);
	} else if (i <= 2.65e-20) {
		tmp = t_3;
	} else if (i <= 3.4e+42) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = -(c * (z * b))
	t_3 = t * (b * i)
	tmp = 0
	if i <= -2.3e+80:
		tmp = t_3
	elif i <= -6.2e+27:
		tmp = (y * j) * -i
	elif i <= -1.6e-115:
		tmp = t_2
	elif i <= -1.5e-255:
		tmp = t_1
	elif i <= 1.25e-246:
		tmp = t_2
	elif i <= 3e-122:
		tmp = x * (y * z)
	elif i <= 2.65e-20:
		tmp = t_3
	elif i <= 3.4e+42:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(-Float64(c * Float64(z * b)))
	t_3 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -2.3e+80)
		tmp = t_3;
	elseif (i <= -6.2e+27)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (i <= -1.6e-115)
		tmp = t_2;
	elseif (i <= -1.5e-255)
		tmp = t_1;
	elseif (i <= 1.25e-246)
		tmp = t_2;
	elseif (i <= 3e-122)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 2.65e-20)
		tmp = t_3;
	elseif (i <= 3.4e+42)
		tmp = t_1;
	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)
	t_1 = a * (c * j);
	t_2 = -(c * (z * b));
	t_3 = t * (b * i);
	tmp = 0.0;
	if (i <= -2.3e+80)
		tmp = t_3;
	elseif (i <= -6.2e+27)
		tmp = (y * j) * -i;
	elseif (i <= -1.6e-115)
		tmp = t_2;
	elseif (i <= -1.5e-255)
		tmp = t_1;
	elseif (i <= 1.25e-246)
		tmp = t_2;
	elseif (i <= 3e-122)
		tmp = x * (y * z);
	elseif (i <= 2.65e-20)
		tmp = t_3;
	elseif (i <= 3.4e+42)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$3 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.3e+80], t$95$3, If[LessEqual[i, -6.2e+27], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[i, -1.6e-115], t$95$2, If[LessEqual[i, -1.5e-255], t$95$1, If[LessEqual[i, 1.25e-246], t$95$2, If[LessEqual[i, 3e-122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.65e-20], t$95$3, If[LessEqual[i, 3.4e+42], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.30000000000000004e80 or 3.00000000000000004e-122 < i < 2.6500000000000001e-20

   1. Initial program 76.9%

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

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. sub-neg 76.9%

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

      5. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in t around inf 63.3%

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

      1. distribute-lft-out-- 63.3%

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

      2. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in t around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. *-commutative 63.3%

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

      3. distribute-rgt-neg-out 63.3%

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

      4. neg-mul-1 63.3%

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

      5. neg-mul-1 63.3%

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

      6. sub-neg 63.3%

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

      7. +-commutative 63.3%

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

      8. distribute-neg-in 63.3%

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

      9. remove-double-neg 63.3%

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

      10. sub-neg 63.3%

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

   9. Simplified 63.3%

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

   10. Taylor expanded in i around inf 47.0%

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

       1. *-commutative 47.0%

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

       2. *-commutative 47.0%

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

       3. associate-*r* 52.2%

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

       4. *-commutative 52.2%

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

   12. Simplified 52.2%

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

   if -2.30000000000000004e80 < i < -6.19999999999999992e27

   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. Step-by-step derivation

      1. associate-+l- 62.7%

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

      2. *-commutative 62.7%

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

      3. sub-neg 62.7%

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

      4. sub-neg 62.7%

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

      5. *-commutative 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in i around inf 87.3%

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

      1. distribute-lft-out-- 87.3%

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

      2. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in j around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. *-commutative 74.9%

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

      3. distribute-rgt-neg-in 74.9%

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

   9. Simplified 74.9%

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

   if -6.19999999999999992e27 < i < -1.6e-115 or -1.50000000000000001e-255 < i < 1.2499999999999999e-246

   1. Initial program 71.4%

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

      1. associate-+l- 71.4%

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

      2. *-commutative 71.4%

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

      3. sub-neg 71.4%

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

      4. sub-neg 71.4%

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

      5. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in c around inf 59.9%

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

      1. *-commutative 59.9%

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

      2. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in j around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-in 45.4%

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

   9. Simplified 45.4%

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

   if -1.6e-115 < i < -1.50000000000000001e-255 or 2.6500000000000001e-20 < i < 3.39999999999999975e42

   1. Initial program 72.2%

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

      1. associate-+l- 72.2%

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

      2. *-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in a around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in j around inf 51.5%

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

      1. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if 1.2499999999999999e-246 < i < 3.00000000000000004e-122

   1. Initial program 93.3%

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

      1. associate-+l- 93.3%

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

      2. *-commutative 93.3%

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

      3. sub-neg 93.3%

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

      4. sub-neg 93.3%

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

      5. *-commutative 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   7. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   9. Simplified 45.5%

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

   10. Taylor expanded in z around 0 45.5%

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

   if 3.39999999999999975e42 < i

   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. Step-by-step derivation

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. sub-neg 71.1%

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

      4. sub-neg 71.1%

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

      5. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

      2. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in a around 0 55.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;-c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{-246}:\\ \;\;\;\;-c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 9: 29.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.08 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;-c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= i -1.08e+80)
     t_2
     (if (<= i -7.5e+28)
       (* (* y j) (- i))
       (if (<= i -1.9e-115)
         (* z (* b (- c)))
         (if (<= i -7.5e-256)
           t_1
           (if (<= i 6.5e-247)
             (- (* c (* z b)))
             (if (<= i 3.4e-124)
               (* x (* y z))
               (if (<= i 3.2e-20)
                 t_2
                 (if (<= i 3.5e+42) t_1 (* 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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.08e+80) {
		tmp = t_2;
	} else if (i <= -7.5e+28) {
		tmp = (y * j) * -i;
	} else if (i <= -1.9e-115) {
		tmp = z * (b * -c);
	} else if (i <= -7.5e-256) {
		tmp = t_1;
	} else if (i <= 6.5e-247) {
		tmp = -(c * (z * b));
	} else if (i <= 3.4e-124) {
		tmp = x * (y * z);
	} else if (i <= 3.2e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = t * (b * i)
    if (i <= (-1.08d+80)) then
        tmp = t_2
    else if (i <= (-7.5d+28)) then
        tmp = (y * j) * -i
    else if (i <= (-1.9d-115)) then
        tmp = z * (b * -c)
    else if (i <= (-7.5d-256)) then
        tmp = t_1
    else if (i <= 6.5d-247) then
        tmp = -(c * (z * b))
    else if (i <= 3.4d-124) then
        tmp = x * (y * z)
    else if (i <= 3.2d-20) then
        tmp = t_2
    else if (i <= 3.5d+42) then
        tmp = t_1
    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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.08e+80) {
		tmp = t_2;
	} else if (i <= -7.5e+28) {
		tmp = (y * j) * -i;
	} else if (i <= -1.9e-115) {
		tmp = z * (b * -c);
	} else if (i <= -7.5e-256) {
		tmp = t_1;
	} else if (i <= 6.5e-247) {
		tmp = -(c * (z * b));
	} else if (i <= 3.4e-124) {
		tmp = x * (y * z);
	} else if (i <= 3.2e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if i <= -1.08e+80:
		tmp = t_2
	elif i <= -7.5e+28:
		tmp = (y * j) * -i
	elif i <= -1.9e-115:
		tmp = z * (b * -c)
	elif i <= -7.5e-256:
		tmp = t_1
	elif i <= 6.5e-247:
		tmp = -(c * (z * b))
	elif i <= 3.4e-124:
		tmp = x * (y * z)
	elif i <= 3.2e-20:
		tmp = t_2
	elif i <= 3.5e+42:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -1.08e+80)
		tmp = t_2;
	elseif (i <= -7.5e+28)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (i <= -1.9e-115)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (i <= -7.5e-256)
		tmp = t_1;
	elseif (i <= 6.5e-247)
		tmp = Float64(-Float64(c * Float64(z * b)));
	elseif (i <= 3.4e-124)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 3.2e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	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)
	t_1 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (i <= -1.08e+80)
		tmp = t_2;
	elseif (i <= -7.5e+28)
		tmp = (y * j) * -i;
	elseif (i <= -1.9e-115)
		tmp = z * (b * -c);
	elseif (i <= -7.5e-256)
		tmp = t_1;
	elseif (i <= 6.5e-247)
		tmp = -(c * (z * b));
	elseif (i <= 3.4e-124)
		tmp = x * (y * z);
	elseif (i <= 3.2e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.08e+80], t$95$2, If[LessEqual[i, -7.5e+28], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[i, -1.9e-115], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.5e-256], t$95$1, If[LessEqual[i, 6.5e-247], (-N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), If[LessEqual[i, 3.4e-124], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e-20], t$95$2, If[LessEqual[i, 3.5e+42], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -1.08e80 or 3.4000000000000001e-124 < i < 3.1999999999999997e-20

   1. Initial program 76.9%

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

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. sub-neg 76.9%

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

      5. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in t around inf 63.3%

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

      1. distribute-lft-out-- 63.3%

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

      2. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in t around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. *-commutative 63.3%

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

      3. distribute-rgt-neg-out 63.3%

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

      4. neg-mul-1 63.3%

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

      5. neg-mul-1 63.3%

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

      6. sub-neg 63.3%

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

      7. +-commutative 63.3%

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

      8. distribute-neg-in 63.3%

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

      9. remove-double-neg 63.3%

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

      10. sub-neg 63.3%

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

   9. Simplified 63.3%

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

   10. Taylor expanded in i around inf 47.0%

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

       1. *-commutative 47.0%

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

       2. *-commutative 47.0%

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

       3. associate-*r* 52.2%

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

       4. *-commutative 52.2%

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

   12. Simplified 52.2%

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

   if -1.08e80 < i < -7.4999999999999998e28

   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. Step-by-step derivation

      1. associate-+l- 62.7%

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

      2. *-commutative 62.7%

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

      3. sub-neg 62.7%

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

      4. sub-neg 62.7%

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

      5. *-commutative 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in i around inf 87.3%

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

      1. distribute-lft-out-- 87.3%

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

      2. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in j around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. *-commutative 74.9%

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

      3. distribute-rgt-neg-in 74.9%

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

   9. Simplified 74.9%

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

   if -7.4999999999999998e28 < i < -1.89999999999999996e-115

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. sub-neg 77.7%

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

      4. sub-neg 77.7%

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

      5. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. *-commutative 64.7%

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

      2. *-commutative 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in y around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. distribute-lft-neg-out 46.1%

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

      3. *-commutative 46.1%

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

   9. Simplified 46.1%

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

   if -1.89999999999999996e-115 < i < -7.50000000000000005e-256 or 3.1999999999999997e-20 < i < 3.50000000000000023e42

   1. Initial program 72.2%

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

      1. associate-+l- 72.2%

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

      2. *-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in a around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in j around inf 51.5%

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

      1. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if -7.50000000000000005e-256 < i < 6.4999999999999996e-247

   1. Initial program 64.4%

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

      1. associate-+l- 64.4%

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

      2. *-commutative 64.4%

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

      3. sub-neg 64.4%

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

      4. sub-neg 64.4%

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

      5. *-commutative 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in c around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. *-commutative 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in j around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. distribute-rgt-neg-in 48.0%

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

   9. Simplified 48.0%

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

   if 6.4999999999999996e-247 < i < 3.4000000000000001e-124

   1. Initial program 93.3%

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

      1. associate-+l- 93.3%

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

      2. *-commutative 93.3%

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

      3. sub-neg 93.3%

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

      4. sub-neg 93.3%

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

      5. *-commutative 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   7. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   9. Simplified 45.5%

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

   10. Taylor expanded in z around 0 45.5%

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

   if 3.50000000000000023e42 < i

   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. Step-by-step derivation

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. sub-neg 71.1%

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

      4. sub-neg 71.1%

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

      5. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

      2. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in a around 0 55.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.08 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;-c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 10: 29.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.3 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= i -1.3e+87)
     t_2
     (if (<= i -1.42e-275)
       t_1
       (if (<= i 5.5e-292)
         (* a (- (* x t)))
         (if (<= i 3.2e-275)
           t_1
           (if (<= i 2.45e-120)
             (* x (* y z))
             (if (<= i 6e-20) t_2 (if (<= i 3.5e+42) t_1 (* 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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.3e+87) {
		tmp = t_2;
	} else if (i <= -1.42e-275) {
		tmp = t_1;
	} else if (i <= 5.5e-292) {
		tmp = a * -(x * t);
	} else if (i <= 3.2e-275) {
		tmp = t_1;
	} else if (i <= 2.45e-120) {
		tmp = x * (y * z);
	} else if (i <= 6e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = t * (b * i)
    if (i <= (-1.3d+87)) then
        tmp = t_2
    else if (i <= (-1.42d-275)) then
        tmp = t_1
    else if (i <= 5.5d-292) then
        tmp = a * -(x * t)
    else if (i <= 3.2d-275) then
        tmp = t_1
    else if (i <= 2.45d-120) then
        tmp = x * (y * z)
    else if (i <= 6d-20) then
        tmp = t_2
    else if (i <= 3.5d+42) then
        tmp = t_1
    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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.3e+87) {
		tmp = t_2;
	} else if (i <= -1.42e-275) {
		tmp = t_1;
	} else if (i <= 5.5e-292) {
		tmp = a * -(x * t);
	} else if (i <= 3.2e-275) {
		tmp = t_1;
	} else if (i <= 2.45e-120) {
		tmp = x * (y * z);
	} else if (i <= 6e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if i <= -1.3e+87:
		tmp = t_2
	elif i <= -1.42e-275:
		tmp = t_1
	elif i <= 5.5e-292:
		tmp = a * -(x * t)
	elif i <= 3.2e-275:
		tmp = t_1
	elif i <= 2.45e-120:
		tmp = x * (y * z)
	elif i <= 6e-20:
		tmp = t_2
	elif i <= 3.5e+42:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -1.3e+87)
		tmp = t_2;
	elseif (i <= -1.42e-275)
		tmp = t_1;
	elseif (i <= 5.5e-292)
		tmp = Float64(a * Float64(-Float64(x * t)));
	elseif (i <= 3.2e-275)
		tmp = t_1;
	elseif (i <= 2.45e-120)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 6e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	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)
	t_1 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (i <= -1.3e+87)
		tmp = t_2;
	elseif (i <= -1.42e-275)
		tmp = t_1;
	elseif (i <= 5.5e-292)
		tmp = a * -(x * t);
	elseif (i <= 3.2e-275)
		tmp = t_1;
	elseif (i <= 2.45e-120)
		tmp = x * (y * z);
	elseif (i <= 6e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.3e+87], t$95$2, If[LessEqual[i, -1.42e-275], t$95$1, If[LessEqual[i, 5.5e-292], N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, 3.2e-275], t$95$1, If[LessEqual[i, 2.45e-120], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e-20], t$95$2, If[LessEqual[i, 3.5e+42], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.29999999999999999e87 or 2.4500000000000002e-120 < i < 6.00000000000000057e-20

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. sub-neg 77.7%

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

      4. sub-neg 77.7%

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

      5. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

      2. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in t around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. *-commutative 63.7%

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

      3. distribute-rgt-neg-out 63.7%

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

      4. neg-mul-1 63.7%

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

      5. neg-mul-1 63.7%

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

      6. sub-neg 63.7%

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

      7. +-commutative 63.7%

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

      8. distribute-neg-in 63.7%

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

      9. remove-double-neg 63.7%

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

      10. sub-neg 63.7%

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

   9. Simplified 63.7%

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

   10. Taylor expanded in i around inf 46.9%

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

       1. *-commutative 46.9%

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

       2. *-commutative 46.9%

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

       3. associate-*r* 52.2%

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

       4. *-commutative 52.2%

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

   12. Simplified 52.2%

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

   if -1.29999999999999999e87 < i < -1.41999999999999997e-275 or 5.50000000000000006e-292 < i < 3.2e-275 or 6.00000000000000057e-20 < i < 3.50000000000000023e42

   1. Initial program 70.5%

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

      1. associate-+l- 70.5%

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

      2. *-commutative 70.5%

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

      3. sub-neg 70.5%

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

      4. sub-neg 70.5%

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

      5. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in a around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in j around inf 35.2%

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

      1. *-commutative 35.2%

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

   9. Simplified 35.2%

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

   if -1.41999999999999997e-275 < i < 5.50000000000000006e-292

   1. Initial program 50.5%

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

      1. associate-+l- 50.5%

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

      2. *-commutative 50.5%

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

      3. sub-neg 50.5%

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

      4. sub-neg 50.5%

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

      5. *-commutative 50.5%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in a around inf 60.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. 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%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in j around 0 61.3%

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

      1. mul-1-neg 61.3%

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

      2. *-commutative 61.3%

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

      3. distribute-rgt-neg-in 61.3%

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

      4. distribute-rgt-neg-in 61.3%

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

   9. Simplified 61.3%

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

   if 3.2e-275 < i < 2.4500000000000002e-120

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. *-commutative 94.5%

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

      3. sub-neg 94.5%

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

      4. sub-neg 94.5%

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

      5. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in y around inf 42.8%

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

      1. *-commutative 42.8%

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

   9. Simplified 42.8%

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

   10. Taylor expanded in z around 0 42.8%

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

   if 3.50000000000000023e42 < i

   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. Step-by-step derivation

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. sub-neg 71.1%

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

      4. sub-neg 71.1%

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

      5. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

      2. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in a around 0 55.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 11: 29.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -c \cdot \left(z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ t_3 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.55 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* c (* z b)))) (t_2 (* a (* c j))) (t_3 (* t (* b i))))
   (if (<= i -4e+27)
     t_3
     (if (<= i -2.55e-113)
       t_1
       (if (<= i -1e-255)
         t_2
         (if (<= i 1.65e-246)
           t_1
           (if (<= i 2.3e-119)
             (* x (* y z))
             (if (<= i 3.4e-20)
               t_3
               (if (<= i 3.4e+42) t_2 (* 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 t_1 = -(c * (z * b));
	double t_2 = a * (c * j);
	double t_3 = t * (b * i);
	double tmp;
	if (i <= -4e+27) {
		tmp = t_3;
	} else if (i <= -2.55e-113) {
		tmp = t_1;
	} else if (i <= -1e-255) {
		tmp = t_2;
	} else if (i <= 1.65e-246) {
		tmp = t_1;
	} else if (i <= 2.3e-119) {
		tmp = x * (y * z);
	} else if (i <= 3.4e-20) {
		tmp = t_3;
	} else if (i <= 3.4e+42) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = -(c * (z * b))
    t_2 = a * (c * j)
    t_3 = t * (b * i)
    if (i <= (-4d+27)) then
        tmp = t_3
    else if (i <= (-2.55d-113)) then
        tmp = t_1
    else if (i <= (-1d-255)) then
        tmp = t_2
    else if (i <= 1.65d-246) then
        tmp = t_1
    else if (i <= 2.3d-119) then
        tmp = x * (y * z)
    else if (i <= 3.4d-20) then
        tmp = t_3
    else if (i <= 3.4d+42) then
        tmp = t_2
    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 t_1 = -(c * (z * b));
	double t_2 = a * (c * j);
	double t_3 = t * (b * i);
	double tmp;
	if (i <= -4e+27) {
		tmp = t_3;
	} else if (i <= -2.55e-113) {
		tmp = t_1;
	} else if (i <= -1e-255) {
		tmp = t_2;
	} else if (i <= 1.65e-246) {
		tmp = t_1;
	} else if (i <= 2.3e-119) {
		tmp = x * (y * z);
	} else if (i <= 3.4e-20) {
		tmp = t_3;
	} else if (i <= 3.4e+42) {
		tmp = t_2;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -(c * (z * b))
	t_2 = a * (c * j)
	t_3 = t * (b * i)
	tmp = 0
	if i <= -4e+27:
		tmp = t_3
	elif i <= -2.55e-113:
		tmp = t_1
	elif i <= -1e-255:
		tmp = t_2
	elif i <= 1.65e-246:
		tmp = t_1
	elif i <= 2.3e-119:
		tmp = x * (y * z)
	elif i <= 3.4e-20:
		tmp = t_3
	elif i <= 3.4e+42:
		tmp = t_2
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(-Float64(c * Float64(z * b)))
	t_2 = Float64(a * Float64(c * j))
	t_3 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -4e+27)
		tmp = t_3;
	elseif (i <= -2.55e-113)
		tmp = t_1;
	elseif (i <= -1e-255)
		tmp = t_2;
	elseif (i <= 1.65e-246)
		tmp = t_1;
	elseif (i <= 2.3e-119)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 3.4e-20)
		tmp = t_3;
	elseif (i <= 3.4e+42)
		tmp = t_2;
	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)
	t_1 = -(c * (z * b));
	t_2 = a * (c * j);
	t_3 = t * (b * i);
	tmp = 0.0;
	if (i <= -4e+27)
		tmp = t_3;
	elseif (i <= -2.55e-113)
		tmp = t_1;
	elseif (i <= -1e-255)
		tmp = t_2;
	elseif (i <= 1.65e-246)
		tmp = t_1;
	elseif (i <= 2.3e-119)
		tmp = x * (y * z);
	elseif (i <= 3.4e-20)
		tmp = t_3;
	elseif (i <= 3.4e+42)
		tmp = t_2;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = (-N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+27], t$95$3, If[LessEqual[i, -2.55e-113], t$95$1, If[LessEqual[i, -1e-255], t$95$2, If[LessEqual[i, 1.65e-246], t$95$1, If[LessEqual[i, 2.3e-119], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e-20], t$95$3, If[LessEqual[i, 3.4e+42], t$95$2, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.0000000000000001e27 or 2.29999999999999993e-119 < i < 3.3999999999999997e-20

   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. Step-by-step derivation

      1. associate-+l- 75.4%

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

      2. *-commutative 75.4%

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

      3. sub-neg 75.4%

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

      4. sub-neg 75.4%

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

      5. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

      2. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   7. Taylor expanded in t around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. *-commutative 58.3%

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

      3. distribute-rgt-neg-out 58.3%

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

      4. neg-mul-1 58.3%

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

      5. neg-mul-1 58.3%

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

      6. sub-neg 58.3%

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

      7. +-commutative 58.3%

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

      8. distribute-neg-in 58.3%

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

      9. remove-double-neg 58.3%

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

      10. sub-neg 58.3%

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

   9. Simplified 58.3%

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

   10. Taylor expanded in i around inf 43.7%

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

       1. *-commutative 43.7%

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

       2. *-commutative 43.7%

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

       3. associate-*r* 48.3%

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

       4. *-commutative 48.3%

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

   12. Simplified 48.3%

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

   if -4.0000000000000001e27 < i < -2.54999999999999989e-113 or -1e-255 < i < 1.65e-246

   1. Initial program 71.4%

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

      1. associate-+l- 71.4%

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

      2. *-commutative 71.4%

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

      3. sub-neg 71.4%

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

      4. sub-neg 71.4%

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

      5. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in c around inf 59.9%

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

      1. *-commutative 59.9%

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

      2. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in j around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-in 45.4%

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

   9. Simplified 45.4%

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

   if -2.54999999999999989e-113 < i < -1e-255 or 3.3999999999999997e-20 < i < 3.39999999999999975e42

   1. Initial program 72.2%

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

      1. associate-+l- 72.2%

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

      2. *-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in a around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in j around inf 51.5%

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

      1. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if 1.65e-246 < i < 2.29999999999999993e-119

   1. Initial program 93.3%

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

      1. associate-+l- 93.3%

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

      2. *-commutative 93.3%

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

      3. sub-neg 93.3%

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

      4. sub-neg 93.3%

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

      5. *-commutative 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   7. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   9. Simplified 45.5%

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

   10. Taylor expanded in z around 0 45.5%

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

   if 3.39999999999999975e42 < i

   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. Step-by-step derivation

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. sub-neg 71.1%

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

      4. sub-neg 71.1%

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

      5. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in t around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

      2. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in a around 0 55.6%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.55 \cdot 10^{-113}:\\ \;\;\;\;-c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-246}:\\ \;\;\;\;-c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 12: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+41}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.2e+64)
     t_2
     (if (<= b -9e+41)
       (* (* y j) (- i))
       (if (<= b 1.15e-37)
         t_1
         (if (<= b 9.8e+86)
           (* i (- (* t b) (* y j)))
           (if (<= b 1.8e+123) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e+64) {
		tmp = t_2;
	} else if (b <= -9e+41) {
		tmp = (y * j) * -i;
	} else if (b <= 1.15e-37) {
		tmp = t_1;
	} else if (b <= 9.8e+86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.8e+123) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.2d+64)) then
        tmp = t_2
    else if (b <= (-9d+41)) then
        tmp = (y * j) * -i
    else if (b <= 1.15d-37) then
        tmp = t_1
    else if (b <= 9.8d+86) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= 1.8d+123) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e+64) {
		tmp = t_2;
	} else if (b <= -9e+41) {
		tmp = (y * j) * -i;
	} else if (b <= 1.15e-37) {
		tmp = t_1;
	} else if (b <= 9.8e+86) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.8e+123) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.2e+64:
		tmp = t_2
	elif b <= -9e+41:
		tmp = (y * j) * -i
	elif b <= 1.15e-37:
		tmp = t_1
	elif b <= 9.8e+86:
		tmp = i * ((t * b) - (y * j))
	elif b <= 1.8e+123:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.2e+64)
		tmp = t_2;
	elseif (b <= -9e+41)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (b <= 1.15e-37)
		tmp = t_1;
	elseif (b <= 9.8e+86)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= 1.8e+123)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.2e+64)
		tmp = t_2;
	elseif (b <= -9e+41)
		tmp = (y * j) * -i;
	elseif (b <= 1.15e-37)
		tmp = t_1;
	elseif (b <= 9.8e+86)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= 1.8e+123)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+64], t$95$2, If[LessEqual[b, -9e+41], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[b, 1.15e-37], t$95$1, If[LessEqual[b, 9.8e+86], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+123], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.19999999999999994e64 or 1.79999999999999999e123 < b

   1. Initial program 74.4%

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

      1. associate-+l- 74.4%

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

      2. *-commutative 74.4%

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

      3. sub-neg 74.4%

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

      4. sub-neg 74.4%

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

      5. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in b around inf 76.5%

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

   if -5.19999999999999994e64 < b < -9.0000000000000002e41

   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. Step-by-step derivation

      1. associate-+l- 83.1%

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

      2. *-commutative 83.1%

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

      3. sub-neg 83.1%

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

      4. sub-neg 83.1%

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

      5. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in i around inf 99.7%

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

      1. distribute-lft-out-- 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in j around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. *-commutative 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

   9. Simplified 99.7%

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

   if -9.0000000000000002e41 < b < 1.15e-37 or 9.7999999999999999e86 < b < 1.79999999999999999e123

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 54.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 54.1%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   if 1.15e-37 < b < 9.7999999999999999e86

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 58.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 58.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 58.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{t \cdot b}\right)\right) \]

   6. Simplified 58.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - t \cdot b\right)\right)} \]

   7. Taylor expanded in i around 0 58.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.4%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y - b \cdot t\right)} \]

      2. *-commutative 58.4%

         \[\leadsto -i \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right) \]

      3. *-commutative 58.4%

         \[\leadsto -i \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right) \]

      4. distribute-rgt-neg-in 58.4%

         \[\leadsto \color{blue}{i \cdot \left(-\left(y \cdot j - t \cdot b\right)\right)} \]

      5. neg-sub0 58.4%

         \[\leadsto i \cdot \color{blue}{\left(0 - \left(y \cdot j - t \cdot b\right)\right)} \]

      6. associate-+l- 58.4%

         \[\leadsto i \cdot \color{blue}{\left(\left(0 - y \cdot j\right) + t \cdot b\right)} \]

      7. neg-sub0 58.4%

         \[\leadsto i \cdot \left(\color{blue}{\left(-y \cdot j\right)} + t \cdot b\right) \]

      8. +-commutative 58.4%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + \left(-y \cdot j\right)\right)} \]

      9. sub-neg 58.4%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   9. Simplified 58.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+41}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 13: 40.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.02 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.46 \cdot 10^{+29}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.02e+80)
   (* t (* b i))
   (if (<= i -1.46e+29)
     (* (* y j) (- i))
     (if (<= i -2.25e-94)
       (* z (* b (- c)))
       (if (<= i 1.12e+22) (* a (- (* c j) (* x t))) (* 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 (i <= -1.02e+80) {
		tmp = t * (b * i);
	} else if (i <= -1.46e+29) {
		tmp = (y * j) * -i;
	} else if (i <= -2.25e-94) {
		tmp = z * (b * -c);
	} else if (i <= 1.12e+22) {
		tmp = a * ((c * j) - (x * t));
	} 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 (i <= (-1.02d+80)) then
        tmp = t * (b * i)
    else if (i <= (-1.46d+29)) then
        tmp = (y * j) * -i
    else if (i <= (-2.25d-94)) then
        tmp = z * (b * -c)
    else if (i <= 1.12d+22) then
        tmp = a * ((c * j) - (x * t))
    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 (i <= -1.02e+80) {
		tmp = t * (b * i);
	} else if (i <= -1.46e+29) {
		tmp = (y * j) * -i;
	} else if (i <= -2.25e-94) {
		tmp = z * (b * -c);
	} else if (i <= 1.12e+22) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.02e+80:
		tmp = t * (b * i)
	elif i <= -1.46e+29:
		tmp = (y * j) * -i
	elif i <= -2.25e-94:
		tmp = z * (b * -c)
	elif i <= 1.12e+22:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.02e+80)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= -1.46e+29)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (i <= -2.25e-94)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (i <= 1.12e+22)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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 (i <= -1.02e+80)
		tmp = t * (b * i);
	elseif (i <= -1.46e+29)
		tmp = (y * j) * -i;
	elseif (i <= -2.25e-94)
		tmp = z * (b * -c);
	elseif (i <= 1.12e+22)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.02e+80], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.46e+29], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[i, -2.25e-94], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.12e+22], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.02e80

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 67.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 67.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 67.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 67.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in t around 0 67.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 67.8%

         \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. *-commutative 67.8%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right) \]

      3. distribute-rgt-neg-out 67.8%

         \[\leadsto \color{blue}{t \cdot \left(-\left(a \cdot x - i \cdot b\right)\right)} \]

      4. neg-mul-1 67.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

      5. neg-mul-1 67.8%

         \[\leadsto t \cdot \color{blue}{\left(-\left(a \cdot x - i \cdot b\right)\right)} \]

      6. sub-neg 67.8%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + \left(-i \cdot b\right)\right)}\right) \]

      7. +-commutative 67.8%

         \[\leadsto t \cdot \left(-\color{blue}{\left(\left(-i \cdot b\right) + a \cdot x\right)}\right) \]

      8. distribute-neg-in 67.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(-\left(-i \cdot b\right)\right) + \left(-a \cdot x\right)\right)} \]

      9. remove-double-neg 67.8%

         \[\leadsto t \cdot \left(\color{blue}{i \cdot b} + \left(-a \cdot x\right)\right) \]

      10. sub-neg 67.8%

          \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   9. Simplified 67.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   10. Taylor expanded in i around inf 52.6%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 52.6%

          \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

       2. *-commutative 52.6%

          \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

       3. associate-*r* 61.0%

          \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

       4. *-commutative 61.0%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   12. Simplified 61.0%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -1.02e80 < i < -1.46e29

   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. Step-by-step derivation

      1. associate-+l- 62.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 87.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 87.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 87.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{t \cdot b}\right)\right) \]

   6. Simplified 87.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - t \cdot b\right)\right)} \]

   7. Taylor expanded in j around inf 74.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 74.9%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 74.9%

         \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

      3. distribute-rgt-neg-in 74.9%

         \[\leadsto \color{blue}{i \cdot \left(-y \cdot j\right)} \]

   9. Simplified 74.9%

      \[\leadsto \color{blue}{i \cdot \left(-y \cdot j\right)} \]

   if -1.46e29 < i < -2.2500000000000001e-94

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 68.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 68.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 68.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   6. Simplified 68.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   7. Taylor expanded in y around 0 48.9%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-lft-neg-out 48.9%

         \[\leadsto z \cdot \color{blue}{\left(\left(-b\right) \cdot c\right)} \]

      3. *-commutative 48.9%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 48.9%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if -2.2500000000000001e-94 < i < 1.12e22

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 78.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 78.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 78.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 78.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 53.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 53.0%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 53.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   if 1.12e22 < i

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 65.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 65.5%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 65.5%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 65.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in a around 0 54.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.02 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.46 \cdot 10^{+29}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 14: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= i -1.4e+87)
     t_2
     (if (<= i 3e-275)
       t_1
       (if (<= i 2.5e-121)
         (* x (* y z))
         (if (<= i 2.55e-20) t_2 (if (<= i 3.5e+42) t_1 (* 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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.4e+87) {
		tmp = t_2;
	} else if (i <= 3e-275) {
		tmp = t_1;
	} else if (i <= 2.5e-121) {
		tmp = x * (y * z);
	} else if (i <= 2.55e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = t * (b * i)
    if (i <= (-1.4d+87)) then
        tmp = t_2
    else if (i <= 3d-275) then
        tmp = t_1
    else if (i <= 2.5d-121) then
        tmp = x * (y * z)
    else if (i <= 2.55d-20) then
        tmp = t_2
    else if (i <= 3.5d+42) then
        tmp = t_1
    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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.4e+87) {
		tmp = t_2;
	} else if (i <= 3e-275) {
		tmp = t_1;
	} else if (i <= 2.5e-121) {
		tmp = x * (y * z);
	} else if (i <= 2.55e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if i <= -1.4e+87:
		tmp = t_2
	elif i <= 3e-275:
		tmp = t_1
	elif i <= 2.5e-121:
		tmp = x * (y * z)
	elif i <= 2.55e-20:
		tmp = t_2
	elif i <= 3.5e+42:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -1.4e+87)
		tmp = t_2;
	elseif (i <= 3e-275)
		tmp = t_1;
	elseif (i <= 2.5e-121)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 2.55e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	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)
	t_1 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (i <= -1.4e+87)
		tmp = t_2;
	elseif (i <= 3e-275)
		tmp = t_1;
	elseif (i <= 2.5e-121)
		tmp = x * (y * z);
	elseif (i <= 2.55e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+87], t$95$2, If[LessEqual[i, 3e-275], t$95$1, If[LessEqual[i, 2.5e-121], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.55e-20], t$95$2, If[LessEqual[i, 3.5e+42], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.40000000000000008e87 or 2.49999999999999995e-121 < i < 2.55000000000000009e-20

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 77.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 77.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 77.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 77.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 77.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 63.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 63.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 63.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 63.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in t around 0 63.7%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.7%

         \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. *-commutative 63.7%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right) \]

      3. distribute-rgt-neg-out 63.7%

         \[\leadsto \color{blue}{t \cdot \left(-\left(a \cdot x - i \cdot b\right)\right)} \]

      4. neg-mul-1 63.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

      5. neg-mul-1 63.7%

         \[\leadsto t \cdot \color{blue}{\left(-\left(a \cdot x - i \cdot b\right)\right)} \]

      6. sub-neg 63.7%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + \left(-i \cdot b\right)\right)}\right) \]

      7. +-commutative 63.7%

         \[\leadsto t \cdot \left(-\color{blue}{\left(\left(-i \cdot b\right) + a \cdot x\right)}\right) \]

      8. distribute-neg-in 63.7%

         \[\leadsto t \cdot \color{blue}{\left(\left(-\left(-i \cdot b\right)\right) + \left(-a \cdot x\right)\right)} \]

      9. remove-double-neg 63.7%

         \[\leadsto t \cdot \left(\color{blue}{i \cdot b} + \left(-a \cdot x\right)\right) \]

      10. sub-neg 63.7%

          \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   9. Simplified 63.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   10. Taylor expanded in i around inf 46.9%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 46.9%

          \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

       2. *-commutative 46.9%

          \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

       3. associate-*r* 52.2%

          \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

       4. *-commutative 52.2%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   12. Simplified 52.2%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -1.40000000000000008e87 < i < 3e-275 or 2.55000000000000009e-20 < i < 3.50000000000000023e42

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 68.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 68.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 68.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 68.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 68.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 54.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 54.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 54.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 54.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around inf 32.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.7%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 32.7%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if 3e-275 < i < 2.49999999999999995e-121

   1. Initial program 94.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 94.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 94.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 94.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 94.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 94.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 51.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 51.0%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   6. Simplified 51.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   7. Taylor expanded in y around inf 42.8%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.8%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   9. Simplified 42.8%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   10. Taylor expanded in z around 0 42.8%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 3.50000000000000023e42 < i

   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. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 67.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 67.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 67.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in a around 0 55.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 15: 51.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -5.2e+64)
     t_1
     (if (<= b -5.2e+40)
       (* (* y j) (- i))
       (if (<= b 2.95e+116) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e+64) {
		tmp = t_1;
	} else if (b <= -5.2e+40) {
		tmp = (y * j) * -i;
	} else if (b <= 2.95e+116) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-5.2d+64)) then
        tmp = t_1
    else if (b <= (-5.2d+40)) then
        tmp = (y * j) * -i
    else if (b <= 2.95d+116) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e+64) {
		tmp = t_1;
	} else if (b <= -5.2e+40) {
		tmp = (y * j) * -i;
	} else if (b <= 2.95e+116) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.2e+64:
		tmp = t_1
	elif b <= -5.2e+40:
		tmp = (y * j) * -i
	elif b <= 2.95e+116:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.2e+64)
		tmp = t_1;
	elseif (b <= -5.2e+40)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (b <= 2.95e+116)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.2e+64)
		tmp = t_1;
	elseif (b <= -5.2e+40)
		tmp = (y * j) * -i;
	elseif (b <= 2.95e+116)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+64], t$95$1, If[LessEqual[b, -5.2e+40], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[b, 2.95e+116], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.19999999999999994e64 or 2.95e116 < b

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 74.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 76.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -5.19999999999999994e64 < b < -5.2000000000000001e40

   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. Step-by-step derivation

      1. associate-+l- 83.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 83.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 83.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 83.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 83.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 99.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 99.7%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 99.7%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{t \cdot b}\right)\right) \]

   6. Simplified 99.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - t \cdot b\right)\right)} \]

   7. Taylor expanded in j around inf 99.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 99.7%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 99.7%

         \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \color{blue}{i \cdot \left(-y \cdot j\right)} \]

   9. Simplified 99.7%

      \[\leadsto \color{blue}{i \cdot \left(-y \cdot j\right)} \]

   if -5.2000000000000001e40 < b < 2.95e116

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 75.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 75.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 75.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 75.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 75.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 50.2%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 16: 29.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+87} \lor \neg \left(i \leq 1.4 \cdot 10^{-111}\right) \land \left(i \leq 9.2 \cdot 10^{-20} \lor \neg \left(i \leq 3.5 \cdot 10^{+42}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.3e+87)
         (and (not (<= i 1.4e-111)) (or (<= i 9.2e-20) (not (<= i 3.5e+42)))))
   (* b (* t i))
   (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.3e+87) || (!(i <= 1.4e-111) && ((i <= 9.2e-20) || !(i <= 3.5e+42)))) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.3d+87)) .or. (.not. (i <= 1.4d-111)) .and. (i <= 9.2d-20) .or. (.not. (i <= 3.5d+42))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.3e+87) || (!(i <= 1.4e-111) && ((i <= 9.2e-20) || !(i <= 3.5e+42)))) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.3e+87) or (not (i <= 1.4e-111) and ((i <= 9.2e-20) or not (i <= 3.5e+42))):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.3e+87) || (!(i <= 1.4e-111) && ((i <= 9.2e-20) || !(i <= 3.5e+42))))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.3e+87) || (~((i <= 1.4e-111)) && ((i <= 9.2e-20) || ~((i <= 3.5e+42)))))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.3e+87], And[N[Not[LessEqual[i, 1.4e-111]], $MachinePrecision], Or[LessEqual[i, 9.2e-20], N[Not[LessEqual[i, 3.5e+42]], $MachinePrecision]]]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.29999999999999999e87 or 1.39999999999999998e-111 < i < 9.1999999999999997e-20 or 3.50000000000000023e42 < i

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 66.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 66.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 66.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 66.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in a around 0 51.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -1.29999999999999999e87 < i < 1.39999999999999998e-111 or 9.1999999999999997e-20 < i < 3.50000000000000023e42

   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. Step-by-step derivation

      1. associate-+l- 75.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 50.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around inf 29.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 29.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+87} \lor \neg \left(i \leq 1.4 \cdot 10^{-111}\right) \land \left(i \leq 9.2 \cdot 10^{-20} \lor \neg \left(i \leq 3.5 \cdot 10^{+42}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 17: 29.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= i -1.4e+87)
     t_2
     (if (<= i 1.12e-111)
       t_1
       (if (<= i 3.4e-20) t_2 (if (<= i 3.5e+42) t_1 (* 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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.4e+87) {
		tmp = t_2;
	} else if (i <= 1.12e-111) {
		tmp = t_1;
	} else if (i <= 3.4e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = t * (b * i)
    if (i <= (-1.4d+87)) then
        tmp = t_2
    else if (i <= 1.12d-111) then
        tmp = t_1
    else if (i <= 3.4d-20) then
        tmp = t_2
    else if (i <= 3.5d+42) then
        tmp = t_1
    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 t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -1.4e+87) {
		tmp = t_2;
	} else if (i <= 1.12e-111) {
		tmp = t_1;
	} else if (i <= 3.4e-20) {
		tmp = t_2;
	} else if (i <= 3.5e+42) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if i <= -1.4e+87:
		tmp = t_2
	elif i <= 1.12e-111:
		tmp = t_1
	elif i <= 3.4e-20:
		tmp = t_2
	elif i <= 3.5e+42:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -1.4e+87)
		tmp = t_2;
	elseif (i <= 1.12e-111)
		tmp = t_1;
	elseif (i <= 3.4e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	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)
	t_1 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (i <= -1.4e+87)
		tmp = t_2;
	elseif (i <= 1.12e-111)
		tmp = t_1;
	elseif (i <= 3.4e-20)
		tmp = t_2;
	elseif (i <= 3.5e+42)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+87], t$95$2, If[LessEqual[i, 1.12e-111], t$95$1, If[LessEqual[i, 3.4e-20], t$95$2, If[LessEqual[i, 3.5e+42], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.40000000000000008e87 or 1.12000000000000009e-111 < i < 3.3999999999999997e-20

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 78.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 78.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 78.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 78.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 65.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 65.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 65.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in t around 0 65.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 65.1%

         \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. *-commutative 65.1%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right) \]

      3. distribute-rgt-neg-out 65.1%

         \[\leadsto \color{blue}{t \cdot \left(-\left(a \cdot x - i \cdot b\right)\right)} \]

      4. neg-mul-1 65.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

      5. neg-mul-1 65.1%

         \[\leadsto t \cdot \color{blue}{\left(-\left(a \cdot x - i \cdot b\right)\right)} \]

      6. sub-neg 65.1%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + \left(-i \cdot b\right)\right)}\right) \]

      7. +-commutative 65.1%

         \[\leadsto t \cdot \left(-\color{blue}{\left(\left(-i \cdot b\right) + a \cdot x\right)}\right) \]

      8. distribute-neg-in 65.1%

         \[\leadsto t \cdot \color{blue}{\left(\left(-\left(-i \cdot b\right)\right) + \left(-a \cdot x\right)\right)} \]

      9. remove-double-neg 65.1%

         \[\leadsto t \cdot \left(\color{blue}{i \cdot b} + \left(-a \cdot x\right)\right) \]

      10. sub-neg 65.1%

          \[\leadsto t \cdot \color{blue}{\left(i \cdot b - a \cdot x\right)} \]

   9. Simplified 65.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b - a \cdot x\right)} \]

   10. Taylor expanded in i around inf 47.6%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 47.6%

          \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

       2. *-commutative 47.6%

          \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

       3. associate-*r* 53.1%

          \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

       4. *-commutative 53.1%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   12. Simplified 53.1%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -1.40000000000000008e87 < i < 1.12000000000000009e-111 or 3.3999999999999997e-20 < i < 3.50000000000000023e42

   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. Step-by-step derivation

      1. associate-+l- 75.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 75.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 50.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around inf 29.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 29.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if 3.50000000000000023e42 < i

   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. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 67.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 67.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 67.1%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   7. Taylor expanded in a around 0 55.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-111}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 18: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 75.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 75.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 75.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 75.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 75.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 75.1%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 40.6%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.6%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 40.6%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 40.6%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

6. Simplified 40.6%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

7. Taylor expanded in j around inf 22.3%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 22.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 22.3%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Final simplification 22.3%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 58.9% 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 2023290 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (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)))))