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

Percentage Accurate: 72.9% → 81.7%

Time: 37.3s

Alternatives: 24

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.9% 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: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.2%

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

   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 c around inf 55.6%

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

4. Final simplification 82.9%

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

Alternative 2: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{if}\;j \leq -7.6 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* i (* t b)) (* z (- (* x y) (* b c)))))
        (t_2 (- (* x (* y z)) (* j (- (* y i) (* a c))))))
   (if (<= j -7.6e+113)
     t_2
     (if (<= j -4.1e+20)
       (* c (- (* a j) (* z b)))
       (if (<= j -1.5e-70)
         t_1
         (if (<= j -5.2e-112)
           (* x (- (* y z) (* t a)))
           (if (<= j 6e-255)
             t_1
             (if (<= j 8e-191)
               (* t (- (* b i) (* x a)))
               (if (<= j 2.65e+138) 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 = (i * (t * b)) + (z * ((x * y) - (b * c)));
	double t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)));
	double tmp;
	if (j <= -7.6e+113) {
		tmp = t_2;
	} else if (j <= -4.1e+20) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -1.5e-70) {
		tmp = t_1;
	} else if (j <= -5.2e-112) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 6e-255) {
		tmp = t_1;
	} else if (j <= 8e-191) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.65e+138) {
		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 = (i * (t * b)) + (z * ((x * y) - (b * c)))
    t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)))
    if (j <= (-7.6d+113)) then
        tmp = t_2
    else if (j <= (-4.1d+20)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-1.5d-70)) then
        tmp = t_1
    else if (j <= (-5.2d-112)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 6d-255) then
        tmp = t_1
    else if (j <= 8d-191) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.65d+138) 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 = (i * (t * b)) + (z * ((x * y) - (b * c)));
	double t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)));
	double tmp;
	if (j <= -7.6e+113) {
		tmp = t_2;
	} else if (j <= -4.1e+20) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -1.5e-70) {
		tmp = t_1;
	} else if (j <= -5.2e-112) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 6e-255) {
		tmp = t_1;
	} else if (j <= 8e-191) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.65e+138) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * (t * b)) + (z * ((x * y) - (b * c)))
	t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)))
	tmp = 0
	if j <= -7.6e+113:
		tmp = t_2
	elif j <= -4.1e+20:
		tmp = c * ((a * j) - (z * b))
	elif j <= -1.5e-70:
		tmp = t_1
	elif j <= -5.2e-112:
		tmp = x * ((y * z) - (t * a))
	elif j <= 6e-255:
		tmp = t_1
	elif j <= 8e-191:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.65e+138:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(t * b)) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	t_2 = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	tmp = 0.0
	if (j <= -7.6e+113)
		tmp = t_2;
	elseif (j <= -4.1e+20)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -1.5e-70)
		tmp = t_1;
	elseif (j <= -5.2e-112)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 6e-255)
		tmp = t_1;
	elseif (j <= 8e-191)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.65e+138)
		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 = (i * (t * b)) + (z * ((x * y) - (b * c)));
	t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)));
	tmp = 0.0;
	if (j <= -7.6e+113)
		tmp = t_2;
	elseif (j <= -4.1e+20)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -1.5e-70)
		tmp = t_1;
	elseif (j <= -5.2e-112)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 6e-255)
		tmp = t_1;
	elseif (j <= 8e-191)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.65e+138)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.6e+113], t$95$2, If[LessEqual[j, -4.1e+20], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.5e-70], t$95$1, If[LessEqual[j, -5.2e-112], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-255], t$95$1, If[LessEqual[j, 8e-191], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.65e+138], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.6000000000000007e113 or 2.64999999999999992e138 < j

   1. Initial program 66.8%

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

      1. +-commutative 66.8%

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

      2. fma-def 68.1%

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

      3. *-commutative 68.1%

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

      4. *-commutative 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in b around 0 74.3%

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

   5. Taylor expanded in y around inf 80.8%

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

   if -7.6000000000000007e113 < j < -4.1e20

   1. Initial program 56.0%

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

      1. associate-+l- 56.0%

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

      2. *-commutative 56.0%

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

      3. sub-neg 56.0%

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

      4. sub-neg 56.0%

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

      5. *-commutative 56.0%

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

   3. Simplified 56.0%

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

   4. Taylor expanded in c around inf 64.7%

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

   if -4.1e20 < j < -1.5000000000000001e-70 or -5.19999999999999983e-112 < j < 6.00000000000000004e-255 or 8.0000000000000002e-191 < j < 2.64999999999999992e138

   1. Initial program 71.6%

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

      1. associate-+l- 71.6%

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

      2. *-commutative 71.6%

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

      3. sub-neg 71.6%

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

      4. sub-neg 71.6%

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

      5. *-commutative 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in j around 0 73.6%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in a around 0 66.5%

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

   if -1.5000000000000001e-70 < j < -5.19999999999999983e-112

   1. Initial program 82.3%

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

      1. associate-+l- 82.3%

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

      2. *-commutative 82.3%

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

      3. sub-neg 82.3%

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

      4. sub-neg 82.3%

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

      5. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in j around 0 88.2%

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

   5. Taylor expanded in x around inf 83.2%

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

   if 6.00000000000000004e-255 < j < 8.0000000000000002e-191

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in j around 0 87.5%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

   9. Simplified 84.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 3: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+227}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-238}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-153}:\\ \;\;\;\;t_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+230}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b)))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ t_2 (* x (- (* y z) (* t a)))))
        (t_4 (* a (- (* c j) (* x t)))))
   (if (<= a -1.65e+227)
     t_4
     (if (<= a -4.3e-75)
       t_3
       (if (<= a 3.8e-238)
         (+ t_2 (* b (- (* t i) (* z c))))
         (if (<= a 1.05e-153)
           (+ t_1 (* z (- (* x y) (* b c))))
           (if (<= a 7e-69)
             t_3
             (if (<= a 7.6e+230) (- t_1 (* j (- (* y i) (* a c)))) 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 = i * (t * b);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (x * ((y * z) - (t * a)));
	double t_4 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.65e+227) {
		tmp = t_4;
	} else if (a <= -4.3e-75) {
		tmp = t_3;
	} else if (a <= 3.8e-238) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if (a <= 1.05e-153) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (a <= 7e-69) {
		tmp = t_3;
	} else if (a <= 7.6e+230) {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	} 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 = i * (t * b)
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 + (x * ((y * z) - (t * a)))
    t_4 = a * ((c * j) - (x * t))
    if (a <= (-1.65d+227)) then
        tmp = t_4
    else if (a <= (-4.3d-75)) then
        tmp = t_3
    else if (a <= 3.8d-238) then
        tmp = t_2 + (b * ((t * i) - (z * c)))
    else if (a <= 1.05d-153) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    else if (a <= 7d-69) then
        tmp = t_3
    else if (a <= 7.6d+230) then
        tmp = t_1 - (j * ((y * i) - (a * c)))
    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 = i * (t * b);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (x * ((y * z) - (t * a)));
	double t_4 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.65e+227) {
		tmp = t_4;
	} else if (a <= -4.3e-75) {
		tmp = t_3;
	} else if (a <= 3.8e-238) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if (a <= 1.05e-153) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else if (a <= 7e-69) {
		tmp = t_3;
	} else if (a <= 7.6e+230) {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 + (x * ((y * z) - (t * a)))
	t_4 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.65e+227:
		tmp = t_4
	elif a <= -4.3e-75:
		tmp = t_3
	elif a <= 3.8e-238:
		tmp = t_2 + (b * ((t * i) - (z * c)))
	elif a <= 1.05e-153:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	elif a <= 7e-69:
		tmp = t_3
	elif a <= 7.6e+230:
		tmp = t_1 - (j * ((y * i) - (a * c)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_4 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.65e+227)
		tmp = t_4;
	elseif (a <= -4.3e-75)
		tmp = t_3;
	elseif (a <= 3.8e-238)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 1.05e-153)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (a <= 7e-69)
		tmp = t_3;
	elseif (a <= 7.6e+230)
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 + (x * ((y * z) - (t * a)));
	t_4 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.65e+227)
		tmp = t_4;
	elseif (a <= -4.3e-75)
		tmp = t_3;
	elseif (a <= 3.8e-238)
		tmp = t_2 + (b * ((t * i) - (z * c)));
	elseif (a <= 1.05e-153)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	elseif (a <= 7e-69)
		tmp = t_3;
	elseif (a <= 7.6e+230)
		tmp = t_1 - (j * ((y * i) - (a * c)));
	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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+227], t$95$4, If[LessEqual[a, -4.3e-75], t$95$3, If[LessEqual[a, 3.8e-238], N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-153], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-69], t$95$3, If[LessEqual[a, 7.6e+230], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.6499999999999999e227 or 7.6e230 < a

   1. Initial program 41.3%

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

      1. associate-+l- 41.3%

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

      2. *-commutative 41.3%

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

      3. sub-neg 41.3%

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

      4. sub-neg 41.3%

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

      5. *-commutative 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in a around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

   6. Simplified 83.8%

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

   if -1.6499999999999999e227 < a < -4.2999999999999999e-75 or 1.05000000000000002e-153 < a < 7.0000000000000003e-69

   1. Initial program 80.7%

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

      1. +-commutative 80.7%

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

      2. fma-def 80.7%

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

      3. *-commutative 80.7%

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

      4. *-commutative 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in b around 0 75.7%

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

   if -4.2999999999999999e-75 < a < 3.7999999999999997e-238

   1. Initial program 76.7%

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

      1. +-commutative 76.7%

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

      2. fma-def 76.7%

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

      3. *-commutative 76.7%

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

      4. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around 0 72.0%

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

   if 3.7999999999999997e-238 < a < 1.05000000000000002e-153

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. sub-neg 76.8%

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

      4. sub-neg 76.8%

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

      5. *-commutative 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in j around 0 82.7%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in a around 0 81.3%

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

   if 7.0000000000000003e-69 < a < 7.6e230

   1. Initial program 66.0%

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

      1. +-commutative 66.0%

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

      2. fma-def 68.8%

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

      3. *-commutative 68.8%

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

      4. *-commutative 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in z around 0 69.8%

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

   5. Taylor expanded in j around inf 69.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+227}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-238}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+230}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 4: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;j \leq -1.15 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+130}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.06 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* i (* t b)) (* z (- (* x y) (* b c)))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= j -1.15e+232)
     t_2
     (if (<= j -1.8e+130)
       (* i (- (* t b) (* y j)))
       (if (<= j -1.06e+21)
         t_2
         (if (<= j 6.6e-255)
           t_1
           (if (<= j 1.85e-190)
             (* t (- (* b i) (* x a)))
             (if (<= j 9.5e+127) 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 = (i * (t * b)) + (z * ((x * y) - (b * c)));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (j <= -1.15e+232) {
		tmp = t_2;
	} else if (j <= -1.8e+130) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= -1.06e+21) {
		tmp = t_2;
	} else if (j <= 6.6e-255) {
		tmp = t_1;
	} else if (j <= 1.85e-190) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 9.5e+127) {
		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 = (i * (t * b)) + (z * ((x * y) - (b * c)))
    t_2 = c * ((a * j) - (z * b))
    if (j <= (-1.15d+232)) then
        tmp = t_2
    else if (j <= (-1.8d+130)) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= (-1.06d+21)) then
        tmp = t_2
    else if (j <= 6.6d-255) then
        tmp = t_1
    else if (j <= 1.85d-190) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 9.5d+127) 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 = (i * (t * b)) + (z * ((x * y) - (b * c)));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (j <= -1.15e+232) {
		tmp = t_2;
	} else if (j <= -1.8e+130) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= -1.06e+21) {
		tmp = t_2;
	} else if (j <= 6.6e-255) {
		tmp = t_1;
	} else if (j <= 1.85e-190) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 9.5e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * (t * b)) + (z * ((x * y) - (b * c)))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if j <= -1.15e+232:
		tmp = t_2
	elif j <= -1.8e+130:
		tmp = i * ((t * b) - (y * j))
	elif j <= -1.06e+21:
		tmp = t_2
	elif j <= 6.6e-255:
		tmp = t_1
	elif j <= 1.85e-190:
		tmp = t * ((b * i) - (x * a))
	elif j <= 9.5e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(t * b)) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (j <= -1.15e+232)
		tmp = t_2;
	elseif (j <= -1.8e+130)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= -1.06e+21)
		tmp = t_2;
	elseif (j <= 6.6e-255)
		tmp = t_1;
	elseif (j <= 1.85e-190)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 9.5e+127)
		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 = (i * (t * b)) + (z * ((x * y) - (b * c)));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (j <= -1.15e+232)
		tmp = t_2;
	elseif (j <= -1.8e+130)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= -1.06e+21)
		tmp = t_2;
	elseif (j <= 6.6e-255)
		tmp = t_1;
	elseif (j <= 1.85e-190)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 9.5e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.15e+232], t$95$2, If[LessEqual[j, -1.8e+130], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.06e+21], t$95$2, If[LessEqual[j, 6.6e-255], t$95$1, If[LessEqual[j, 1.85e-190], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+127], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.15000000000000003e232 or -1.8000000000000001e130 < j < -1.06e21 or 9.49999999999999975e127 < j

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

      4. sub-neg 64.6%

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

      5. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in c around inf 62.1%

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

   if -1.15000000000000003e232 < j < -1.8000000000000001e130

   1. Initial program 67.3%

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

      1. associate-+l- 67.3%

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

      2. *-commutative 67.3%

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

      3. sub-neg 67.3%

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

      4. sub-neg 67.3%

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

      5. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in i around inf 67.6%

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

      1. distribute-lft-out-- 67.6%

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

   6. Simplified 67.6%

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

   if -1.06e21 < j < 6.59999999999999976e-255 or 1.8500000000000001e-190 < j < 9.49999999999999975e127

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in j around 0 75.1%

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

   6. Simplified 74.2%

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

   7. Taylor expanded in a around 0 64.5%

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

   if 6.59999999999999976e-255 < j < 1.8500000000000001e-190

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in j around 0 87.5%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

   9. Simplified 84.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{+232}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+130}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.06 \cdot 10^{+21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+127}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_3 := t_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-179}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+138}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b)))
        (t_2 (- (* x (* y z)) (* j (- (* y i) (* a c)))))
        (t_3 (+ t_1 (* z (- (* x y) (* b c))))))
   (if (<= j -4.6e+113)
     t_2
     (if (<= j -1.05e+21)
       (* c (- (* a j) (* z b)))
       (if (<= j -6e-179)
         (+ t_1 (* x (- (* y z) (* t a))))
         (if (<= j 7.2e-255)
           t_3
           (if (<= j 3.2e-190)
             (* t (- (* b i) (* x a)))
             (if (<= j 2.7e+138) t_3 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 = i * (t * b);
	double t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)));
	double t_3 = t_1 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -4.6e+113) {
		tmp = t_2;
	} else if (j <= -1.05e+21) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -6e-179) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (j <= 7.2e-255) {
		tmp = t_3;
	} else if (j <= 3.2e-190) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.7e+138) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = i * (t * b)
    t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)))
    t_3 = t_1 + (z * ((x * y) - (b * c)))
    if (j <= (-4.6d+113)) then
        tmp = t_2
    else if (j <= (-1.05d+21)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-6d-179)) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (j <= 7.2d-255) then
        tmp = t_3
    else if (j <= 3.2d-190) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.7d+138) then
        tmp = t_3
    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 = i * (t * b);
	double t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)));
	double t_3 = t_1 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -4.6e+113) {
		tmp = t_2;
	} else if (j <= -1.05e+21) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -6e-179) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (j <= 7.2e-255) {
		tmp = t_3;
	} else if (j <= 3.2e-190) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.7e+138) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)))
	t_3 = t_1 + (z * ((x * y) - (b * c)))
	tmp = 0
	if j <= -4.6e+113:
		tmp = t_2
	elif j <= -1.05e+21:
		tmp = c * ((a * j) - (z * b))
	elif j <= -6e-179:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif j <= 7.2e-255:
		tmp = t_3
	elif j <= 3.2e-190:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.7e+138:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	t_3 = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (j <= -4.6e+113)
		tmp = t_2;
	elseif (j <= -1.05e+21)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -6e-179)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (j <= 7.2e-255)
		tmp = t_3;
	elseif (j <= 3.2e-190)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.7e+138)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	t_2 = (x * (y * z)) - (j * ((y * i) - (a * c)));
	t_3 = t_1 + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (j <= -4.6e+113)
		tmp = t_2;
	elseif (j <= -1.05e+21)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -6e-179)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (j <= 7.2e-255)
		tmp = t_3;
	elseif (j <= 3.2e-190)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.7e+138)
		tmp = t_3;
	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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.6e+113], t$95$2, If[LessEqual[j, -1.05e+21], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-179], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e-255], t$95$3, If[LessEqual[j, 3.2e-190], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+138], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.59999999999999993e113 or 2.70000000000000009e138 < j

   1. Initial program 66.8%

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

      1. +-commutative 66.8%

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

      2. fma-def 68.1%

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

      3. *-commutative 68.1%

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

      4. *-commutative 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in b around 0 74.3%

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

   5. Taylor expanded in y around inf 80.8%

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

   if -4.59999999999999993e113 < j < -1.05e21

   1. Initial program 56.0%

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

      1. associate-+l- 56.0%

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

      2. *-commutative 56.0%

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

      3. sub-neg 56.0%

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

      4. sub-neg 56.0%

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

      5. *-commutative 56.0%

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

   3. Simplified 56.0%

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

   4. Taylor expanded in c around inf 64.7%

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

   if -1.05e21 < j < -6.00000000000000012e-179

   1. Initial program 77.6%

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

      1. associate-+l- 77.6%

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

      2. *-commutative 77.6%

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

      3. sub-neg 77.6%

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

      4. sub-neg 77.6%

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

      5. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in j around 0 80.0%

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

   5. Taylor expanded in c around 0 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r* 76.1%

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

      3. neg-mul-1 76.1%

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

   7. Simplified 76.1%

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

   if -6.00000000000000012e-179 < j < 7.2000000000000004e-255 or 3.2000000000000001e-190 < j < 2.70000000000000009e138

   1. Initial program 70.4%

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

      1. associate-+l- 70.4%

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

      2. *-commutative 70.4%

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

      3. sub-neg 70.4%

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

      4. sub-neg 70.4%

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

      5. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in j around 0 73.0%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in a around 0 68.1%

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

   if 7.2000000000000004e-255 < j < 3.2000000000000001e-190

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in j around 0 87.5%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

   9. Simplified 84.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-179}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 6: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ t_3 := t_2 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-179}:\\ \;\;\;\;t_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+138}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* y i) (* a c))))
        (t_2 (* i (* t b)))
        (t_3 (+ t_2 (* z (- (* x y) (* b c))))))
   (if (<= j -1.7e+129)
     (- t_2 t_1)
     (if (<= j -6.8e+20)
       (* c (- (* a j) (* z b)))
       (if (<= j -7e-179)
         (+ t_2 (* x (- (* y z) (* t a))))
         (if (<= j 6e-255)
           t_3
           (if (<= j 8e-191)
             (* t (- (* b i) (* x a)))
             (if (<= j 2.7e+138) t_3 (- (* x (* y z)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((y * i) - (a * c));
	double t_2 = i * (t * b);
	double t_3 = t_2 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -1.7e+129) {
		tmp = t_2 - t_1;
	} else if (j <= -6.8e+20) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -7e-179) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else if (j <= 6e-255) {
		tmp = t_3;
	} else if (j <= 8e-191) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.7e+138) {
		tmp = t_3;
	} else {
		tmp = (x * (y * z)) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((y * i) - (a * c))
    t_2 = i * (t * b)
    t_3 = t_2 + (z * ((x * y) - (b * c)))
    if (j <= (-1.7d+129)) then
        tmp = t_2 - t_1
    else if (j <= (-6.8d+20)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-7d-179)) then
        tmp = t_2 + (x * ((y * z) - (t * a)))
    else if (j <= 6d-255) then
        tmp = t_3
    else if (j <= 8d-191) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.7d+138) then
        tmp = t_3
    else
        tmp = (x * (y * z)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((y * i) - (a * c));
	double t_2 = i * (t * b);
	double t_3 = t_2 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -1.7e+129) {
		tmp = t_2 - t_1;
	} else if (j <= -6.8e+20) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -7e-179) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else if (j <= 6e-255) {
		tmp = t_3;
	} else if (j <= 8e-191) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.7e+138) {
		tmp = t_3;
	} else {
		tmp = (x * (y * z)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((y * i) - (a * c))
	t_2 = i * (t * b)
	t_3 = t_2 + (z * ((x * y) - (b * c)))
	tmp = 0
	if j <= -1.7e+129:
		tmp = t_2 - t_1
	elif j <= -6.8e+20:
		tmp = c * ((a * j) - (z * b))
	elif j <= -7e-179:
		tmp = t_2 + (x * ((y * z) - (t * a)))
	elif j <= 6e-255:
		tmp = t_3
	elif j <= 8e-191:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.7e+138:
		tmp = t_3
	else:
		tmp = (x * (y * z)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(y * i) - Float64(a * c)))
	t_2 = Float64(i * Float64(t * b))
	t_3 = Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (j <= -1.7e+129)
		tmp = Float64(t_2 - t_1);
	elseif (j <= -6.8e+20)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -7e-179)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (j <= 6e-255)
		tmp = t_3;
	elseif (j <= 8e-191)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.7e+138)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * Float64(y * z)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((y * i) - (a * c));
	t_2 = i * (t * b);
	t_3 = t_2 + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (j <= -1.7e+129)
		tmp = t_2 - t_1;
	elseif (j <= -6.8e+20)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -7e-179)
		tmp = t_2 + (x * ((y * z) - (t * a)));
	elseif (j <= 6e-255)
		tmp = t_3;
	elseif (j <= 8e-191)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.7e+138)
		tmp = t_3;
	else
		tmp = (x * (y * z)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+129], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[j, -6.8e+20], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7e-179], N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-255], t$95$3, If[LessEqual[j, 8e-191], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+138], t$95$3, N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.70000000000000009e129

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. fma-def 73.6%

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

      3. *-commutative 73.6%

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

      4. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in z around 0 79.0%

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

   5. Taylor expanded in j around inf 76.3%

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

   if -1.70000000000000009e129 < j < -6.8e20

   1. Initial program 58.6%

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

      1. associate-+l- 58.6%

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

      2. *-commutative 58.6%

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

      3. sub-neg 58.6%

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

      4. sub-neg 58.6%

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

      5. *-commutative 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in c around inf 66.2%

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

   if -6.8e20 < j < -7.00000000000000049e-179

   1. Initial program 77.6%

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

      1. associate-+l- 77.6%

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

      2. *-commutative 77.6%

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

      3. sub-neg 77.6%

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

      4. sub-neg 77.6%

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

      5. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in j around 0 80.0%

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

   5. Taylor expanded in c around 0 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r* 76.1%

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

      3. neg-mul-1 76.1%

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

   7. Simplified 76.1%

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

   if -7.00000000000000049e-179 < j < 6.00000000000000004e-255 or 8.0000000000000002e-191 < j < 2.70000000000000009e138

   1. Initial program 70.4%

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

      1. associate-+l- 70.4%

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

      2. *-commutative 70.4%

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

      3. sub-neg 70.4%

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

      4. sub-neg 70.4%

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

      5. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in j around 0 73.0%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in a around 0 68.1%

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

   if 6.00000000000000004e-255 < j < 8.0000000000000002e-191

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in j around 0 87.5%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

   9. Simplified 84.9%

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

   if 2.70000000000000009e138 < j

   1. Initial program 60.3%

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

      1. +-commutative 60.3%

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

      2. fma-def 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in b around 0 72.6%

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

   5. Taylor expanded in y around inf 85.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+129}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-179}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 7: 61.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t_2\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-170}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-255}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b)))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_1 (* z (- (* x y) (* b c))))))
   (if (<= j -3.6e+20)
     (+ (* j (- (* a c) (* y i))) t_2)
     (if (<= j -2e-170)
       (+ t_1 t_2)
       (if (<= j -3.5e-178)
         (* a (- (* c j) (* x t)))
         (if (<= j 4.7e-255)
           t_3
           (if (<= j 8e-191)
             (* t (- (* b i) (* x a)))
             (if (<= j 2.65e+138)
               t_3
               (- (* x (* y z)) (* 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 t_1 = i * (t * b);
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_1 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -3.6e+20) {
		tmp = (j * ((a * c) - (y * i))) + t_2;
	} else if (j <= -2e-170) {
		tmp = t_1 + t_2;
	} else if (j <= -3.5e-178) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 4.7e-255) {
		tmp = t_3;
	} else if (j <= 8e-191) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.65e+138) {
		tmp = t_3;
	} else {
		tmp = (x * (y * z)) - (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (t * b)
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_1 + (z * ((x * y) - (b * c)))
    if (j <= (-3.6d+20)) then
        tmp = (j * ((a * c) - (y * i))) + t_2
    else if (j <= (-2d-170)) then
        tmp = t_1 + t_2
    else if (j <= (-3.5d-178)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= 4.7d-255) then
        tmp = t_3
    else if (j <= 8d-191) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.65d+138) then
        tmp = t_3
    else
        tmp = (x * (y * z)) - (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 t_1 = i * (t * b);
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_1 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -3.6e+20) {
		tmp = (j * ((a * c) - (y * i))) + t_2;
	} else if (j <= -2e-170) {
		tmp = t_1 + t_2;
	} else if (j <= -3.5e-178) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 4.7e-255) {
		tmp = t_3;
	} else if (j <= 8e-191) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.65e+138) {
		tmp = t_3;
	} else {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_1 + (z * ((x * y) - (b * c)))
	tmp = 0
	if j <= -3.6e+20:
		tmp = (j * ((a * c) - (y * i))) + t_2
	elif j <= -2e-170:
		tmp = t_1 + t_2
	elif j <= -3.5e-178:
		tmp = a * ((c * j) - (x * t))
	elif j <= 4.7e-255:
		tmp = t_3
	elif j <= 8e-191:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.65e+138:
		tmp = t_3
	else:
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (j <= -3.6e+20)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_2);
	elseif (j <= -2e-170)
		tmp = Float64(t_1 + t_2);
	elseif (j <= -3.5e-178)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= 4.7e-255)
		tmp = t_3;
	elseif (j <= 8e-191)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.65e+138)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * Float64(y * z)) - 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)
	t_1 = i * (t * b);
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_1 + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (j <= -3.6e+20)
		tmp = (j * ((a * c) - (y * i))) + t_2;
	elseif (j <= -2e-170)
		tmp = t_1 + t_2;
	elseif (j <= -3.5e-178)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= 4.7e-255)
		tmp = t_3;
	elseif (j <= 8e-191)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.65e+138)
		tmp = t_3;
	else
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.6e+20], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[j, -2e-170], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[j, -3.5e-178], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.7e-255], t$95$3, If[LessEqual[j, 8e-191], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.65e+138], t$95$3, N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.6e20

   1. Initial program 66.7%

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

      1. +-commutative 66.7%

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

      2. fma-def 68.3%

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

      3. *-commutative 68.3%

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

      4. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in b around 0 68.2%

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

   if -3.6e20 < j < -1.99999999999999997e-170

   1. Initial program 78.1%

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

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. sub-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in j around 0 82.8%

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

   5. Taylor expanded in c around 0 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*r* 78.7%

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

      3. neg-mul-1 78.7%

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

   7. Simplified 78.7%

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

   if -1.99999999999999997e-170 < j < -3.49999999999999983e-178

   1. Initial program 69.1%

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

      1. associate-+l- 69.1%

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

      2. *-commutative 69.1%

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

      3. sub-neg 69.1%

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

      4. sub-neg 69.1%

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

      5. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   if -3.49999999999999983e-178 < j < 4.6999999999999997e-255 or 8.0000000000000002e-191 < j < 2.64999999999999992e138

   1. Initial program 70.4%

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

      1. associate-+l- 70.4%

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

      2. *-commutative 70.4%

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

      3. sub-neg 70.4%

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

      4. sub-neg 70.4%

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

      5. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in j around 0 73.0%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in a around 0 68.1%

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

   if 4.6999999999999997e-255 < j < 8.0000000000000002e-191

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in j around 0 87.5%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

   9. Simplified 84.9%

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

   if 2.64999999999999992e138 < j

   1. Initial program 60.3%

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

      1. +-commutative 60.3%

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

      2. fma-def 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in b around 0 72.6%

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

   5. Taylor expanded in y around inf 85.3%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 8: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c))))))
   (if (<= j -2.25e+46)
     (+ (* j (- (* a c) (* y i))) t_1)
     (if (<= j 2.35e-104)
       t_2
       (if (<= j 2.8e-91)
         (* c (- (* a j) (* z b)))
         (if (<= j 3.2e+138)
           t_2
           (- (* x (* y z)) (* 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 t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -2.25e+46) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (j <= 2.35e-104) {
		tmp = t_2;
	} else if (j <= 2.8e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 3.2e+138) {
		tmp = t_2;
	} else {
		tmp = (x * (y * z)) - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    if (j <= (-2.25d+46)) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else if (j <= 2.35d-104) then
        tmp = t_2
    else if (j <= 2.8d-91) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 3.2d+138) then
        tmp = t_2
    else
        tmp = (x * (y * z)) - (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 t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -2.25e+46) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (j <= 2.35e-104) {
		tmp = t_2;
	} else if (j <= 2.8e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 3.2e+138) {
		tmp = t_2;
	} else {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -2.25e+46:
		tmp = (j * ((a * c) - (y * i))) + t_1
	elif j <= 2.35e-104:
		tmp = t_2
	elif j <= 2.8e-91:
		tmp = c * ((a * j) - (z * b))
	elif j <= 3.2e+138:
		tmp = t_2
	else:
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -2.25e+46)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	elseif (j <= 2.35e-104)
		tmp = t_2;
	elseif (j <= 2.8e-91)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 3.2e+138)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * Float64(y * z)) - 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)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -2.25e+46)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	elseif (j <= 2.35e-104)
		tmp = t_2;
	elseif (j <= 2.8e-91)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 3.2e+138)
		tmp = t_2;
	else
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.25e+46], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 2.35e-104], t$95$2, If[LessEqual[j, 2.8e-91], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+138], t$95$2, N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.25000000000000005e46

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. fma-def 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in b around 0 71.3%

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

   if -2.25000000000000005e46 < j < 2.35e-104 or 2.8e-91 < j < 3.2000000000000001e138

   1. Initial program 75.2%

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

      1. associate-+l- 75.2%

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

      2. *-commutative 75.2%

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

      3. sub-neg 75.2%

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

      4. sub-neg 75.2%

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

      5. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in j around 0 78.9%

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

   if 2.35e-104 < j < 2.8e-91

   1. Initial program 34.9%

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

      1. associate-+l- 34.9%

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

      2. *-commutative 34.9%

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

      3. sub-neg 34.9%

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

      4. sub-neg 34.9%

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

      5. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in c around inf 78.5%

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

   if 3.2000000000000001e138 < j

   1. Initial program 60.3%

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

      1. +-commutative 60.3%

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

      2. fma-def 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in b around 0 72.6%

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

   5. Taylor expanded in y around inf 85.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 9: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - \left(a \cdot \left(x \cdot t\right) + t_2\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (* j (- (* y i) (* a c)))))
   (if (<= j -1.7e+53)
     (- (* i (* t b)) (+ (* a (* x t)) t_2))
     (if (<= j 2.35e-104)
       t_1
       (if (<= j 2.7e-91)
         (* c (- (* a j) (* z b)))
         (if (<= j 3.5e+138) t_1 (- (* x (* y z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = j * ((y * i) - (a * c));
	double tmp;
	if (j <= -1.7e+53) {
		tmp = (i * (t * b)) - ((a * (x * t)) + t_2);
	} else if (j <= 2.35e-104) {
		tmp = t_1;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 3.5e+138) {
		tmp = t_1;
	} else {
		tmp = (x * (y * z)) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    t_2 = j * ((y * i) - (a * c))
    if (j <= (-1.7d+53)) then
        tmp = (i * (t * b)) - ((a * (x * t)) + t_2)
    else if (j <= 2.35d-104) then
        tmp = t_1
    else if (j <= 2.7d-91) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 3.5d+138) then
        tmp = t_1
    else
        tmp = (x * (y * z)) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = j * ((y * i) - (a * c));
	double tmp;
	if (j <= -1.7e+53) {
		tmp = (i * (t * b)) - ((a * (x * t)) + t_2);
	} else if (j <= 2.35e-104) {
		tmp = t_1;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 3.5e+138) {
		tmp = t_1;
	} else {
		tmp = (x * (y * z)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	t_2 = j * ((y * i) - (a * c))
	tmp = 0
	if j <= -1.7e+53:
		tmp = (i * (t * b)) - ((a * (x * t)) + t_2)
	elif j <= 2.35e-104:
		tmp = t_1
	elif j <= 2.7e-91:
		tmp = c * ((a * j) - (z * b))
	elif j <= 3.5e+138:
		tmp = t_1
	else:
		tmp = (x * (y * z)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(j * Float64(Float64(y * i) - Float64(a * c)))
	tmp = 0.0
	if (j <= -1.7e+53)
		tmp = Float64(Float64(i * Float64(t * b)) - Float64(Float64(a * Float64(x * t)) + t_2));
	elseif (j <= 2.35e-104)
		tmp = t_1;
	elseif (j <= 2.7e-91)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 3.5e+138)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(y * z)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	t_2 = j * ((y * i) - (a * c));
	tmp = 0.0;
	if (j <= -1.7e+53)
		tmp = (i * (t * b)) - ((a * (x * t)) + t_2);
	elseif (j <= 2.35e-104)
		tmp = t_1;
	elseif (j <= 2.7e-91)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 3.5e+138)
		tmp = t_1;
	else
		tmp = (x * (y * z)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+53], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.35e-104], t$95$1, If[LessEqual[j, 2.7e-91], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e+138], t$95$1, N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.69999999999999999e53

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. fma-def 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in z around 0 73.0%

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

   if -1.69999999999999999e53 < j < 2.35e-104 or 2.6999999999999997e-91 < j < 3.4999999999999998e138

   1. Initial program 75.2%

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

      1. associate-+l- 75.2%

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

      2. *-commutative 75.2%

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

      3. sub-neg 75.2%

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

      4. sub-neg 75.2%

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

      5. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in j around 0 78.9%

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

   if 2.35e-104 < j < 2.6999999999999997e-91

   1. Initial program 34.9%

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

      1. associate-+l- 34.9%

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

      2. *-commutative 34.9%

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

      3. sub-neg 34.9%

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

      4. sub-neg 34.9%

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

      5. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in c around inf 78.5%

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

   if 3.4999999999999998e138 < j

   1. Initial program 60.3%

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

      1. +-commutative 60.3%

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

      2. fma-def 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in b around 0 72.6%

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

   5. Taylor expanded in y around inf 85.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - \left(a \cdot \left(x \cdot t\right) + j \cdot \left(y \cdot i - a \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]

Alternative 10: 52.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -5e+88)
     t_3
     (if (<= c -5.8e+47)
       t_2
       (if (<= c -1.2e+40)
         (* a (* x (- t)))
         (if (<= c -2.2e+23)
           (* z (- (* x y) (* b c)))
           (if (<= c -5.5e-141)
             t_2
             (if (<= c -1.2e-250)
               t_1
               (if (<= c 3.4e-294)
                 (* x (- (* y z) (* t a)))
                 (if (<= c 1.7e+43) 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 = t * ((b * i) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5e+88) {
		tmp = t_3;
	} else if (c <= -5.8e+47) {
		tmp = t_2;
	} else if (c <= -1.2e+40) {
		tmp = a * (x * -t);
	} else if (c <= -2.2e+23) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -5.5e-141) {
		tmp = t_2;
	} else if (c <= -1.2e-250) {
		tmp = t_1;
	} else if (c <= 3.4e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.7e+43) {
		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 = t * ((b * i) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-5d+88)) then
        tmp = t_3
    else if (c <= (-5.8d+47)) then
        tmp = t_2
    else if (c <= (-1.2d+40)) then
        tmp = a * (x * -t)
    else if (c <= (-2.2d+23)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-5.5d-141)) then
        tmp = t_2
    else if (c <= (-1.2d-250)) then
        tmp = t_1
    else if (c <= 3.4d-294) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 1.7d+43) 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 = t * ((b * i) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5e+88) {
		tmp = t_3;
	} else if (c <= -5.8e+47) {
		tmp = t_2;
	} else if (c <= -1.2e+40) {
		tmp = a * (x * -t);
	} else if (c <= -2.2e+23) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -5.5e-141) {
		tmp = t_2;
	} else if (c <= -1.2e-250) {
		tmp = t_1;
	} else if (c <= 3.4e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.7e+43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -5e+88:
		tmp = t_3
	elif c <= -5.8e+47:
		tmp = t_2
	elif c <= -1.2e+40:
		tmp = a * (x * -t)
	elif c <= -2.2e+23:
		tmp = z * ((x * y) - (b * c))
	elif c <= -5.5e-141:
		tmp = t_2
	elif c <= -1.2e-250:
		tmp = t_1
	elif c <= 3.4e-294:
		tmp = x * ((y * z) - (t * a))
	elif c <= 1.7e+43:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5e+88)
		tmp = t_3;
	elseif (c <= -5.8e+47)
		tmp = t_2;
	elseif (c <= -1.2e+40)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= -2.2e+23)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -5.5e-141)
		tmp = t_2;
	elseif (c <= -1.2e-250)
		tmp = t_1;
	elseif (c <= 3.4e-294)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 1.7e+43)
		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 = t * ((b * i) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5e+88)
		tmp = t_3;
	elseif (c <= -5.8e+47)
		tmp = t_2;
	elseif (c <= -1.2e+40)
		tmp = a * (x * -t);
	elseif (c <= -2.2e+23)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -5.5e-141)
		tmp = t_2;
	elseif (c <= -1.2e-250)
		tmp = t_1;
	elseif (c <= 3.4e-294)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 1.7e+43)
		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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e+88], t$95$3, If[LessEqual[c, -5.8e+47], t$95$2, If[LessEqual[c, -1.2e+40], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.2e+23], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.5e-141], t$95$2, If[LessEqual[c, -1.2e-250], t$95$1, If[LessEqual[c, 3.4e-294], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+43], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -4.99999999999999997e88 or 1.70000000000000006e43 < c

   1. Initial program 61.1%

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

      1. associate-+l- 61.1%

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

      2. *-commutative 61.1%

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

      3. sub-neg 61.1%

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

      4. sub-neg 61.1%

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

      5. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in c around inf 68.4%

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

   if -4.99999999999999997e88 < c < -5.79999999999999961e47 or -2.20000000000000008e23 < c < -5.4999999999999998e-141

   1. Initial program 72.3%

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

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. sub-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

   6. Simplified 70.0%

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

   if -5.79999999999999961e47 < c < -1.2e40

   1. Initial program 33.3%

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

      1. associate-+l- 33.3%

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

      2. *-commutative 33.3%

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

      3. sub-neg 33.3%

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

      4. sub-neg 33.3%

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

      5. *-commutative 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in c around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   9. Simplified 100.0%

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

   if -1.2e40 < c < -2.20000000000000008e23

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 99.0%

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

   if -5.4999999999999998e-141 < c < -1.1999999999999999e-250 or 3.39999999999999981e-294 < c < 1.70000000000000006e43

   1. Initial program 78.1%

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

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. sub-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in j around 0 63.2%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in t around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

      3. *-commutative 60.8%

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

      4. *-commutative 60.8%

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

   9. Simplified 60.8%

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

   if -1.1999999999999999e-250 < c < 3.39999999999999981e-294

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. sub-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in j around 0 80.0%

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

   5. Taylor expanded in x around inf 80.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 11: 52.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.12 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -1.12e+88)
     t_2
     (if (<= c -3.8e+42)
       t_1
       (if (<= c -1.2e+40)
         (* a (* x (- t)))
         (if (<= c -3.05e+26)
           (* z (- (* x y) (* b c)))
           (if (<= c -5.5e-141)
             t_1
             (if (<= c 4.7e+44) (* t (- (* b i) (* x a))) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.12e+88) {
		tmp = t_2;
	} else if (c <= -3.8e+42) {
		tmp = t_1;
	} else if (c <= -1.2e+40) {
		tmp = a * (x * -t);
	} else if (c <= -3.05e+26) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -5.5e-141) {
		tmp = t_1;
	} else if (c <= 4.7e+44) {
		tmp = t * ((b * i) - (x * a));
	} 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 = y * ((x * z) - (i * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-1.12d+88)) then
        tmp = t_2
    else if (c <= (-3.8d+42)) then
        tmp = t_1
    else if (c <= (-1.2d+40)) then
        tmp = a * (x * -t)
    else if (c <= (-3.05d+26)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-5.5d-141)) then
        tmp = t_1
    else if (c <= 4.7d+44) then
        tmp = t * ((b * i) - (x * a))
    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 = y * ((x * z) - (i * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.12e+88) {
		tmp = t_2;
	} else if (c <= -3.8e+42) {
		tmp = t_1;
	} else if (c <= -1.2e+40) {
		tmp = a * (x * -t);
	} else if (c <= -3.05e+26) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -5.5e-141) {
		tmp = t_1;
	} else if (c <= 4.7e+44) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.12e+88:
		tmp = t_2
	elif c <= -3.8e+42:
		tmp = t_1
	elif c <= -1.2e+40:
		tmp = a * (x * -t)
	elif c <= -3.05e+26:
		tmp = z * ((x * y) - (b * c))
	elif c <= -5.5e-141:
		tmp = t_1
	elif c <= 4.7e+44:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.12e+88)
		tmp = t_2;
	elseif (c <= -3.8e+42)
		tmp = t_1;
	elseif (c <= -1.2e+40)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= -3.05e+26)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -5.5e-141)
		tmp = t_1;
	elseif (c <= 4.7e+44)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.12e+88)
		tmp = t_2;
	elseif (c <= -3.8e+42)
		tmp = t_1;
	elseif (c <= -1.2e+40)
		tmp = a * (x * -t);
	elseif (c <= -3.05e+26)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -5.5e-141)
		tmp = t_1;
	elseif (c <= 4.7e+44)
		tmp = t * ((b * i) - (x * a));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.12e+88], t$95$2, If[LessEqual[c, -3.8e+42], t$95$1, If[LessEqual[c, -1.2e+40], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.05e+26], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.5e-141], t$95$1, If[LessEqual[c, 4.7e+44], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.12000000000000006e88 or 4.70000000000000018e44 < c

   1. Initial program 61.1%

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

      1. associate-+l- 61.1%

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

      2. *-commutative 61.1%

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

      3. sub-neg 61.1%

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

      4. sub-neg 61.1%

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

      5. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in c around inf 68.4%

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

   if -1.12000000000000006e88 < c < -3.7999999999999998e42 or -3.0500000000000001e26 < c < -5.4999999999999998e-141

   1. Initial program 72.3%

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

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. sub-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

   6. Simplified 70.0%

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

   if -3.7999999999999998e42 < c < -1.2e40

   1. Initial program 33.3%

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

      1. associate-+l- 33.3%

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

      2. *-commutative 33.3%

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

      3. sub-neg 33.3%

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

      4. sub-neg 33.3%

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

      5. *-commutative 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in c around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   9. Simplified 100.0%

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

   if -1.2e40 < c < -3.0500000000000001e26

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 99.0%

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

   if -5.4999999999999998e-141 < c < 4.70000000000000018e44

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. sub-neg 79.3%

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

      4. sub-neg 79.3%

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

      5. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in j around 0 64.9%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in t around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

   9. Simplified 57.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 12: 43.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4400000:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -5.8e-81)
     t_1
     (if (<= a 8.5e-155)
       (* c (* z (- b)))
       (if (<= a 4400000.0) (* j (* i (- y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.8e-81) {
		tmp = t_1;
	} else if (a <= 8.5e-155) {
		tmp = c * (z * -b);
	} else if (a <= 4400000.0) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-5.8d-81)) then
        tmp = t_1
    else if (a <= 8.5d-155) then
        tmp = c * (z * -b)
    else if (a <= 4400000.0d0) then
        tmp = j * (i * -y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.8e-81) {
		tmp = t_1;
	} else if (a <= 8.5e-155) {
		tmp = c * (z * -b);
	} else if (a <= 4400000.0) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5.8e-81:
		tmp = t_1
	elif a <= 8.5e-155:
		tmp = c * (z * -b)
	elif a <= 4400000.0:
		tmp = j * (i * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.8e-81)
		tmp = t_1;
	elseif (a <= 8.5e-155)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (a <= 4400000.0)
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5.8e-81)
		tmp = t_1;
	elseif (a <= 8.5e-155)
		tmp = c * (z * -b);
	elseif (a <= 4400000.0)
		tmp = j * (i * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e-81], t$95$1, If[LessEqual[a, 8.5e-155], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4400000.0], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.79999999999999978e-81 or 4.4e6 < a

   1. Initial program 66.3%

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

      1. associate-+l- 66.3%

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

      2. *-commutative 66.3%

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

      3. sub-neg 66.3%

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

      4. sub-neg 66.3%

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

      5. *-commutative 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in a around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

   6. Simplified 55.4%

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

   if -5.79999999999999978e-81 < a < 8.4999999999999996e-155

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. sub-neg 76.8%

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

      4. sub-neg 76.8%

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

      5. *-commutative 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in b around inf 52.1%

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

   5. Taylor expanded in i around 0 39.2%

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

      1. associate-*r* 39.2%

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

      2. neg-mul-1 39.2%

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

      3. *-commutative 39.2%

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

   7. Simplified 39.2%

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

   if 8.4999999999999996e-155 < a < 4.4e6

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in i around inf 63.4%

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

      1. distribute-lft-out-- 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in y around inf 40.4%

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

      1. mul-1-neg 40.4%

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

      2. associate-*r* 49.7%

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

      3. distribute-rgt-neg-in 49.7%

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

   9. Simplified 49.7%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 4400000:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 13: 51.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -1.3e-20)
     t_1
     (if (<= c -5.6e-141)
       (* y (* x z))
       (if (<= c 3e+44) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.3e-20) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = y * (x * z);
	} else if (c <= 3e+44) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-1.3d-20)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = y * (x * z)
    else if (c <= 3d+44) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.3e-20) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = y * (x * z);
	} else if (c <= 3e+44) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.3e-20:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = y * (x * z)
	elif c <= 3e+44:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.3e-20)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 3e+44)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.3e-20)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = y * (x * z);
	elseif (c <= 3e+44)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e-20], t$95$1, If[LessEqual[c, -5.6e-141], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+44], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.29999999999999997e-20 or 2.99999999999999987e44 < c

   1. Initial program 61.9%

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

      1. associate-+l- 61.9%

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

      2. *-commutative 61.9%

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

      3. sub-neg 61.9%

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

      4. sub-neg 61.9%

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

      5. *-commutative 61.9%

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

   3. Simplified 61.9%

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

   4. Taylor expanded in c around inf 63.9%

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

   if -1.29999999999999997e-20 < c < -5.60000000000000023e-141

   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 j around 0 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in y around inf 51.2%

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

   if -5.60000000000000023e-141 < c < 2.99999999999999987e44

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. sub-neg 79.3%

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

      4. sub-neg 79.3%

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

      5. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in j around 0 64.9%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in t around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

   9. Simplified 57.9%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 14: 52.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -1.35e+88)
     t_1
     (if (<= c -5.5e-141)
       (* y (- (* x z) (* i j)))
       (if (<= c 1.35e+45) (* t (- (* b i) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.35e+88) {
		tmp = t_1;
	} else if (c <= -5.5e-141) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.35e+45) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-1.35d+88)) then
        tmp = t_1
    else if (c <= (-5.5d-141)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.35d+45) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.35e+88) {
		tmp = t_1;
	} else if (c <= -5.5e-141) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.35e+45) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.35e+88:
		tmp = t_1
	elif c <= -5.5e-141:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.35e+45:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.35e+88)
		tmp = t_1;
	elseif (c <= -5.5e-141)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.35e+45)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.35e+88)
		tmp = t_1;
	elseif (c <= -5.5e-141)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.35e+45)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.35e+88], t$95$1, If[LessEqual[c, -5.5e-141], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e+45], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.35000000000000008e88 or 1.34999999999999992e45 < c

   1. Initial program 61.1%

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

      1. associate-+l- 61.1%

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

      2. *-commutative 61.1%

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

      3. sub-neg 61.1%

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

      4. sub-neg 61.1%

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

      5. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in c around inf 68.4%

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

   if -1.35000000000000008e88 < c < -5.4999999999999998e-141

   1. Initial program 71.5%

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

      1. associate-+l- 71.5%

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

      2. *-commutative 71.5%

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

      3. sub-neg 71.5%

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

      4. sub-neg 71.5%

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

      5. *-commutative 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

   6. Simplified 62.7%

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

   if -5.4999999999999998e-141 < c < 1.34999999999999992e45

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. sub-neg 79.3%

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

      4. sub-neg 79.3%

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

      5. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in j around 0 64.9%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in t around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

   9. Simplified 57.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 15: 30.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -5.5e+100)
   (* a (* c j))
   (if (<= c -5.5e-141)
     (* y (* x z))
     (if (<= c 1.25e-141)
       (* i (* t b))
       (if (<= c 5.2e+64) (* i (* y (- j))) (* c (* a j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.5e+100) {
		tmp = a * (c * j);
	} else if (c <= -5.5e-141) {
		tmp = y * (x * z);
	} else if (c <= 1.25e-141) {
		tmp = i * (t * b);
	} else if (c <= 5.2e+64) {
		tmp = i * (y * -j);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-5.5d+100)) then
        tmp = a * (c * j)
    else if (c <= (-5.5d-141)) then
        tmp = y * (x * z)
    else if (c <= 1.25d-141) then
        tmp = i * (t * b)
    else if (c <= 5.2d+64) then
        tmp = i * (y * -j)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.5e+100) {
		tmp = a * (c * j);
	} else if (c <= -5.5e-141) {
		tmp = y * (x * z);
	} else if (c <= 1.25e-141) {
		tmp = i * (t * b);
	} else if (c <= 5.2e+64) {
		tmp = i * (y * -j);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.5e+100:
		tmp = a * (c * j)
	elif c <= -5.5e-141:
		tmp = y * (x * z)
	elif c <= 1.25e-141:
		tmp = i * (t * b)
	elif c <= 5.2e+64:
		tmp = i * (y * -j)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.5e+100)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= -5.5e-141)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 1.25e-141)
		tmp = Float64(i * Float64(t * b));
	elseif (c <= 5.2e+64)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.5e+100)
		tmp = a * (c * j);
	elseif (c <= -5.5e-141)
		tmp = y * (x * z);
	elseif (c <= 1.25e-141)
		tmp = i * (t * b);
	elseif (c <= 5.2e+64)
		tmp = i * (y * -j);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -5.5e+100], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.5e-141], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-141], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e+64], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.5000000000000002e100

   1. Initial program 50.3%

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

      1. associate-+l- 50.3%

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

      2. *-commutative 50.3%

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

      3. sub-neg 50.3%

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

      4. sub-neg 50.3%

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

      5. *-commutative 50.3%

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

   3. Simplified 50.3%

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

   4. Taylor expanded in a around inf 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

   6. Simplified 44.3%

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

   7. Taylor expanded in c around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. associate-*l* 39.4%

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

      3. *-commutative 39.4%

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

   9. Simplified 39.4%

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

   if -5.5000000000000002e100 < c < -5.4999999999999998e-141

   1. Initial program 70.3%

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

      1. associate-+l- 70.3%

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

      2. *-commutative 70.3%

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

      3. sub-neg 70.3%

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

      4. sub-neg 70.3%

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

      5. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in j around 0 63.7%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in y around inf 41.1%

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

   if -5.4999999999999998e-141 < c < 1.25e-141

   1. Initial program 80.1%

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

      1. associate-+l- 80.1%

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

      2. *-commutative 80.1%

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

      3. sub-neg 80.1%

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

      4. sub-neg 80.1%

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

      5. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in b around inf 34.5%

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

   5. Taylor expanded in i around inf 36.1%

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

   if 1.25e-141 < c < 5.19999999999999994e64

   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 i around inf 50.2%

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

      1. distribute-lft-out-- 50.2%

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

   6. Simplified 50.2%

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

   7. Taylor expanded in y around inf 31.3%

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

      1. mul-1-neg 31.3%

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

   9. Simplified 31.3%

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

   10. Taylor expanded in y around 0 35.9%

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

   if 5.19999999999999994e64 < c

   1. Initial program 67.5%

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

      1. associate-+l- 67.5%

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

      2. *-commutative 67.5%

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

      3. sub-neg 67.5%

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

      4. sub-neg 67.5%

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

      5. *-commutative 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in a around inf 41.1%

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

      1. +-commutative 41.1%

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

      2. mul-1-neg 41.1%

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

      3. unsub-neg 41.1%

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

   6. Simplified 41.1%

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

   7. Taylor expanded in c around inf 41.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 16: 30.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -2.35 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= b -2.35e-64)
     t_1
     (if (<= b -1.7e-122)
       (* a (* x (- t)))
       (if (<= b 1.6e-293)
         (* i (* y (- j)))
         (if (<= b 4.4e+106) (* c (* a j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (b <= -2.35e-64) {
		tmp = t_1;
	} else if (b <= -1.7e-122) {
		tmp = a * (x * -t);
	} else if (b <= 1.6e-293) {
		tmp = i * (y * -j);
	} else if (b <= 4.4e+106) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (b <= (-2.35d-64)) then
        tmp = t_1
    else if (b <= (-1.7d-122)) then
        tmp = a * (x * -t)
    else if (b <= 1.6d-293) then
        tmp = i * (y * -j)
    else if (b <= 4.4d+106) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (b <= -2.35e-64) {
		tmp = t_1;
	} else if (b <= -1.7e-122) {
		tmp = a * (x * -t);
	} else if (b <= 1.6e-293) {
		tmp = i * (y * -j);
	} else if (b <= 4.4e+106) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if b <= -2.35e-64:
		tmp = t_1
	elif b <= -1.7e-122:
		tmp = a * (x * -t)
	elif b <= 1.6e-293:
		tmp = i * (y * -j)
	elif b <= 4.4e+106:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -2.35e-64)
		tmp = t_1;
	elseif (b <= -1.7e-122)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (b <= 1.6e-293)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 4.4e+106)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (b <= -2.35e-64)
		tmp = t_1;
	elseif (b <= -1.7e-122)
		tmp = a * (x * -t);
	elseif (b <= 1.6e-293)
		tmp = i * (y * -j);
	elseif (b <= 4.4e+106)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.35e-64], t$95$1, If[LessEqual[b, -1.7e-122], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-293], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+106], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.3499999999999999e-64 or 4.39999999999999983e106 < b

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in b around inf 59.1%

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

   5. Taylor expanded in i around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. neg-mul-1 40.0%

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

      3. *-commutative 40.0%

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

   7. Simplified 40.0%

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

   if -2.3499999999999999e-64 < b < -1.6999999999999999e-122

   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 82.8%

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

      1. +-commutative 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in c around 0 83.1%

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

      1. neg-mul-1 83.1%

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

      2. distribute-rgt-neg-in 83.1%

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

   9. Simplified 83.1%

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

   if -1.6999999999999999e-122 < b < 1.60000000000000003e-293

   1. Initial program 71.2%

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

      1. associate-+l- 71.2%

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

      2. *-commutative 71.2%

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

      3. sub-neg 71.2%

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

      4. sub-neg 71.2%

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

      5. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

   6. Simplified 50.6%

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

   7. Taylor expanded in y around inf 40.8%

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

      1. mul-1-neg 40.8%

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

   9. Simplified 40.8%

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

   10. Taylor expanded in y around 0 43.3%

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

   if 1.60000000000000003e-293 < b < 4.39999999999999983e106

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. sub-neg 67.7%

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

      4. sub-neg 67.7%

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

      5. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in c around inf 36.2%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 17: 30.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -1.62 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= b -1.62e-65)
     t_1
     (if (<= b -2.8e-123)
       (* a (* x (- t)))
       (if (<= b 1.16e-293)
         (* j (* i (- y)))
         (if (<= b 1.55e+107) (* c (* a j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (b <= -1.62e-65) {
		tmp = t_1;
	} else if (b <= -2.8e-123) {
		tmp = a * (x * -t);
	} else if (b <= 1.16e-293) {
		tmp = j * (i * -y);
	} else if (b <= 1.55e+107) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (b <= (-1.62d-65)) then
        tmp = t_1
    else if (b <= (-2.8d-123)) then
        tmp = a * (x * -t)
    else if (b <= 1.16d-293) then
        tmp = j * (i * -y)
    else if (b <= 1.55d+107) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (b <= -1.62e-65) {
		tmp = t_1;
	} else if (b <= -2.8e-123) {
		tmp = a * (x * -t);
	} else if (b <= 1.16e-293) {
		tmp = j * (i * -y);
	} else if (b <= 1.55e+107) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if b <= -1.62e-65:
		tmp = t_1
	elif b <= -2.8e-123:
		tmp = a * (x * -t)
	elif b <= 1.16e-293:
		tmp = j * (i * -y)
	elif b <= 1.55e+107:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -1.62e-65)
		tmp = t_1;
	elseif (b <= -2.8e-123)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (b <= 1.16e-293)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (b <= 1.55e+107)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (b <= -1.62e-65)
		tmp = t_1;
	elseif (b <= -2.8e-123)
		tmp = a * (x * -t);
	elseif (b <= 1.16e-293)
		tmp = j * (i * -y);
	elseif (b <= 1.55e+107)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.62e-65], t$95$1, If[LessEqual[b, -2.8e-123], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.16e-293], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+107], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6200000000000001e-65 or 1.55000000000000013e107 < b

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in b around inf 59.1%

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

   5. Taylor expanded in i around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. neg-mul-1 40.0%

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

      3. *-commutative 40.0%

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

   7. Simplified 40.0%

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

   if -1.6200000000000001e-65 < b < -2.7999999999999999e-123

   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 82.8%

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

      1. +-commutative 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in c around 0 83.1%

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

      1. neg-mul-1 83.1%

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

      2. distribute-rgt-neg-in 83.1%

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

   9. Simplified 83.1%

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

   if -2.7999999999999999e-123 < b < 1.16e-293

   1. Initial program 71.2%

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

      1. associate-+l- 71.2%

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

      2. *-commutative 71.2%

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

      3. sub-neg 71.2%

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

      4. sub-neg 71.2%

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

      5. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

   6. Simplified 50.6%

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

   7. Taylor expanded in y around inf 40.8%

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

      1. mul-1-neg 40.8%

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

      2. associate-*r* 45.9%

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

      3. distribute-rgt-neg-in 45.9%

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

   9. Simplified 45.9%

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

   if 1.16e-293 < b < 1.55000000000000013e107

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. sub-neg 67.7%

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

      4. sub-neg 67.7%

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

      5. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in c around inf 36.2%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.62 \cdot 10^{-65}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 18: 31.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;j \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 10^{+59}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= j -7.8e+20)
     (* a (* c j))
     (if (<= j 1.5e-17)
       t_1
       (if (<= j 1e+59)
         (* y (* x z))
         (if (<= j 3.7e+126) t_1 (* c (* a j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (j <= -7.8e+20) {
		tmp = a * (c * j);
	} else if (j <= 1.5e-17) {
		tmp = t_1;
	} else if (j <= 1e+59) {
		tmp = y * (x * z);
	} else if (j <= 3.7e+126) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (j <= (-7.8d+20)) then
        tmp = a * (c * j)
    else if (j <= 1.5d-17) then
        tmp = t_1
    else if (j <= 1d+59) then
        tmp = y * (x * z)
    else if (j <= 3.7d+126) then
        tmp = t_1
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (j <= -7.8e+20) {
		tmp = a * (c * j);
	} else if (j <= 1.5e-17) {
		tmp = t_1;
	} else if (j <= 1e+59) {
		tmp = y * (x * z);
	} else if (j <= 3.7e+126) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if j <= -7.8e+20:
		tmp = a * (c * j)
	elif j <= 1.5e-17:
		tmp = t_1
	elif j <= 1e+59:
		tmp = y * (x * z)
	elif j <= 3.7e+126:
		tmp = t_1
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (j <= -7.8e+20)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 1.5e-17)
		tmp = t_1;
	elseif (j <= 1e+59)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.7e+126)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (j <= -7.8e+20)
		tmp = a * (c * j);
	elseif (j <= 1.5e-17)
		tmp = t_1;
	elseif (j <= 1e+59)
		tmp = y * (x * z);
	elseif (j <= 3.7e+126)
		tmp = t_1;
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.8e+20], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e-17], t$95$1, If[LessEqual[j, 1e+59], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e+126], t$95$1, N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.8e20

   1. Initial program 66.7%

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

      1. associate-+l- 66.7%

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

      2. *-commutative 66.7%

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

      3. sub-neg 66.7%

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

      4. sub-neg 66.7%

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

      5. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in a around inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

   6. Simplified 50.1%

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

   7. Taylor expanded in c around inf 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-*l* 44.0%

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

      3. *-commutative 44.0%

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

   9. Simplified 44.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -7.8e20 < j < 1.50000000000000003e-17 or 9.99999999999999972e58 < j < 3.6999999999999998e126

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 50.0%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 32.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.50000000000000003e-17 < j < 9.99999999999999972e58

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 86.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 86.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 86.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 86.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 86.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 85.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   6. Simplified 71.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(-a, x, i \cdot b\right), z \cdot \left(y \cdot x - c \cdot b\right)\right)} \]

   7. Taylor expanded in y around inf 32.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 3.6999999999999998e126 < j

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 10^{+59}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 19: 45.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-135} \lor \neg \left(z \leq 8.6 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.35e-135) (not (<= z 8.6e+33)))
   (* c (- (* a j) (* z b)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.35e-135) || !(z <= 8.6e+33)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-1.35d-135)) .or. (.not. (z <= 8.6d+33))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.35e-135) || !(z <= 8.6e+33)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -1.35e-135) or not (z <= 8.6e+33):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.35e-135) || !(z <= 8.6e+33))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -1.35e-135) || ~((z <= 8.6e+33)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -1.35e-135], N[Not[LessEqual[z, 8.6e+33]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999999e-135 or 8.60000000000000057e33 < z

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 49.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -1.34999999999999999e-135 < z < 8.60000000000000057e33

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 82.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 82.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 82.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 82.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 82.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 52.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 52.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-135} \lor \neg \left(z \leq 8.6 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 20: 30.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -8.2e+43)
   (* a (* c j))
   (if (<= j -4.2e-257)
     (* a (* x (- t)))
     (if (<= j 4.3e+126) (* i (* t b)) (* c (* a j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8.2e+43) {
		tmp = a * (c * j);
	} else if (j <= -4.2e-257) {
		tmp = a * (x * -t);
	} else if (j <= 4.3e+126) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-8.2d+43)) then
        tmp = a * (c * j)
    else if (j <= (-4.2d-257)) then
        tmp = a * (x * -t)
    else if (j <= 4.3d+126) then
        tmp = i * (t * b)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8.2e+43) {
		tmp = a * (c * j);
	} else if (j <= -4.2e-257) {
		tmp = a * (x * -t);
	} else if (j <= 4.3e+126) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -8.2e+43:
		tmp = a * (c * j)
	elif j <= -4.2e-257:
		tmp = a * (x * -t)
	elif j <= 4.3e+126:
		tmp = i * (t * b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -8.2e+43)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -4.2e-257)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (j <= 4.3e+126)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -8.2e+43)
		tmp = a * (c * j);
	elseif (j <= -4.2e-257)
		tmp = a * (x * -t);
	elseif (j <= 4.3e+126)
		tmp = i * (t * b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -8.2e+43], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e-257], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.3e+126], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.2000000000000001e43

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

      2. associate-*l* 45.9%

         \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

      3. *-commutative 45.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   9. Simplified 45.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -8.2000000000000001e43 < j < -4.2000000000000002e-257

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 42.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 42.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 31.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 31.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 31.3%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   9. Simplified 31.3%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   if -4.2000000000000002e-257 < j < 4.3000000000000002e126

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 53.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 33.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 4.3000000000000002e126 < j

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 21: 30.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-257}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -7.5e+44)
   (* a (* c j))
   (if (<= j -5.3e-257)
     (* (* t a) (- x))
     (if (<= j 8.6e+126) (* i (* t b)) (* c (* a j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -7.5e+44) {
		tmp = a * (c * j);
	} else if (j <= -5.3e-257) {
		tmp = (t * a) * -x;
	} else if (j <= 8.6e+126) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-7.5d+44)) then
        tmp = a * (c * j)
    else if (j <= (-5.3d-257)) then
        tmp = (t * a) * -x
    else if (j <= 8.6d+126) then
        tmp = i * (t * b)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -7.5e+44) {
		tmp = a * (c * j);
	} else if (j <= -5.3e-257) {
		tmp = (t * a) * -x;
	} else if (j <= 8.6e+126) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -7.5e+44:
		tmp = a * (c * j)
	elif j <= -5.3e-257:
		tmp = (t * a) * -x
	elif j <= 8.6e+126:
		tmp = i * (t * b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -7.5e+44)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -5.3e-257)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (j <= 8.6e+126)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -7.5e+44)
		tmp = a * (c * j);
	elseif (j <= -5.3e-257)
		tmp = (t * a) * -x;
	elseif (j <= 8.6e+126)
		tmp = i * (t * b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -7.5e+44], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.3e-257], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[j, 8.6e+126], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.50000000000000027e44

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

      2. associate-*l* 45.9%

         \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

      3. *-commutative 45.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   9. Simplified 45.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -7.50000000000000027e44 < j < -5.3e-257

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 72.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot t\right) \cdot b} \]

   6. Simplified 73.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(-a, x, i \cdot b\right), z \cdot \left(y \cdot x - c \cdot b\right)\right)} \]

   7. Taylor expanded in a around inf 31.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 31.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 31.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 30.3%

         \[\leadsto \color{blue}{\left(\left(-a\right) \cdot x\right) \cdot t} \]

      5. *-commutative 30.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(-a\right)\right)} \cdot t \]

      6. associate-*l* 31.7%

         \[\leadsto \color{blue}{x \cdot \left(\left(-a\right) \cdot t\right)} \]

      7. distribute-lft-neg-in 31.7%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      8. distribute-rgt-neg-in 31.7%

         \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]

   9. Simplified 31.7%

      \[\leadsto \color{blue}{x \cdot \left(a \cdot \left(-t\right)\right)} \]

   if -5.3e-257 < j < 8.60000000000000041e126

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 53.6%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 33.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 8.60000000000000041e126 < j

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-257}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 22: 30.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -7.6e+20)
   (* a (* c j))
   (if (<= j 3.2e+126) (* i (* t b)) (* c (* a j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -7.6e+20) {
		tmp = a * (c * j);
	} else if (j <= 3.2e+126) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-7.6d+20)) then
        tmp = a * (c * j)
    else if (j <= 3.2d+126) then
        tmp = i * (t * b)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -7.6e+20) {
		tmp = a * (c * j);
	} else if (j <= 3.2e+126) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -7.6e+20:
		tmp = a * (c * j)
	elif j <= 3.2e+126:
		tmp = i * (t * b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -7.6e+20)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 3.2e+126)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -7.6e+20)
		tmp = a * (c * j);
	elseif (j <= 3.2e+126)
		tmp = i * (t * b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -7.6e+20], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+126], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.6e20

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 42.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

      2. associate-*l* 44.0%

         \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

      3. *-commutative 44.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   9. Simplified 44.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -7.6e20 < j < 3.1999999999999998e126

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 29.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 3.1999999999999998e126 < j

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 50.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 23: 23.1% 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 69.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 69.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 69.9%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 40.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 40.0%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 25.5%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 25.5%

      \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

   2. associate-*l* 25.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   3. *-commutative 25.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

9. Simplified 25.1%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

10. Final simplification 25.1%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 24: 23.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* c (* a j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * 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 = c * (a * 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 c * (a * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return c * (a * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(c * Float64(a * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = c * (a * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 69.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 69.9%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 40.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 40.0%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 25.5%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

8. Final simplification 25.5%

   \[\leadsto c \cdot \left(a \cdot j\right) \]

Developer target: 58.6% 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 2023279 
(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)))))