Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 81.1%

Time: 31.2s

Alternatives: 29

Speedup: 0.5×

• 57.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around -inf 28.6%

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

   4. Simplified 30.5%

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

   5. Taylor expanded in z around 0 54.8%

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

4. Final simplification 82.0%

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

Alternative 2: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* j (- (* y i) (* t c)))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -9.5e+32)
     t_3
     (if (<= a -7e-265)
       t_1
       (if (<= a 5.2e-255)
         (- t_2 (* c (* z b)))
         (if (<= a 5.7e-210)
           t_1
           (if (<= a 1.55e-142)
             (+ t_2 (* b (- (* a i) (* z c))))
             (if (<= a 5e+108) 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 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -9.5e+32) {
		tmp = t_3;
	} else if (a <= -7e-265) {
		tmp = t_1;
	} else if (a <= 5.2e-255) {
		tmp = t_2 - (c * (z * b));
	} else if (a <= 5.7e-210) {
		tmp = t_1;
	} else if (a <= 1.55e-142) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (a <= 5e+108) {
		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 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-9.5d+32)) then
        tmp = t_3
    else if (a <= (-7d-265)) then
        tmp = t_1
    else if (a <= 5.2d-255) then
        tmp = t_2 - (c * (z * b))
    else if (a <= 5.7d-210) then
        tmp = t_1
    else if (a <= 1.55d-142) then
        tmp = t_2 + (b * ((a * i) - (z * c)))
    else if (a <= 5d+108) 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 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -9.5e+32) {
		tmp = t_3;
	} else if (a <= -7e-265) {
		tmp = t_1;
	} else if (a <= 5.2e-255) {
		tmp = t_2 - (c * (z * b));
	} else if (a <= 5.7e-210) {
		tmp = t_1;
	} else if (a <= 1.55e-142) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (a <= 5e+108) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -9.5e+32:
		tmp = t_3
	elif a <= -7e-265:
		tmp = t_1
	elif a <= 5.2e-255:
		tmp = t_2 - (c * (z * b))
	elif a <= 5.7e-210:
		tmp = t_1
	elif a <= 1.55e-142:
		tmp = t_2 + (b * ((a * i) - (z * c)))
	elif a <= 5e+108:
		tmp = t_1
	else:
		tmp = t_3
	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(j * Float64(Float64(y * i) - Float64(t * c))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9.5e+32)
		tmp = t_3;
	elseif (a <= -7e-265)
		tmp = t_1;
	elseif (a <= 5.2e-255)
		tmp = Float64(t_2 - Float64(c * Float64(z * b)));
	elseif (a <= 5.7e-210)
		tmp = t_1;
	elseif (a <= 1.55e-142)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (a <= 5e+108)
		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 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -9.5e+32)
		tmp = t_3;
	elseif (a <= -7e-265)
		tmp = t_1;
	elseif (a <= 5.2e-255)
		tmp = t_2 - (c * (z * b));
	elseif (a <= 5.7e-210)
		tmp = t_1;
	elseif (a <= 1.55e-142)
		tmp = t_2 + (b * ((a * i) - (z * c)));
	elseif (a <= 5e+108)
		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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+32], t$95$3, If[LessEqual[a, -7e-265], t$95$1, If[LessEqual[a, 5.2e-255], N[(t$95$2 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e-210], t$95$1, If[LessEqual[a, 1.55e-142], N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+108], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.50000000000000006e32 or 4.99999999999999991e108 < a

   1. Initial program 53.1%

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

   2. Taylor expanded in a around inf 73.7%

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

      1. associate-*r* 73.7%

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

      2. neg-mul-1 73.7%

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

      3. cancel-sign-sub 73.7%

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

      4. +-commutative 73.7%

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

      5. mul-1-neg 73.7%

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

      6. unsub-neg 73.7%

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

   4. Simplified 73.7%

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

   if -9.50000000000000006e32 < a < -7.00000000000000031e-265 or 5.20000000000000041e-255 < a < 5.69999999999999971e-210 or 1.55e-142 < a < 4.99999999999999991e108

   1. Initial program 81.0%

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

   2. Taylor expanded in b around 0 73.3%

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

   if -7.00000000000000031e-265 < a < 5.20000000000000041e-255

   1. Initial program 70.4%

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

   2. Taylor expanded in t around 0 68.6%

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

      1. sub-neg 68.6%

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

      2. mul-1-neg 68.6%

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

      3. associate-*r* 68.6%

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

      4. *-commutative 68.6%

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

      5. associate-*r* 68.6%

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

      6. distribute-rgt-neg-in 68.6%

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

      7. mul-1-neg 68.6%

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

      8. distribute-lft-in 68.6%

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

      9. +-commutative 68.6%

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

      10. mul-1-neg 68.6%

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

      11. unsub-neg 68.6%

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

      12. *-commutative 68.6%

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

      13. fma-neg 68.6%

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

      14. distribute-rgt-neg-out 68.6%

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

      15. distribute-rgt-neg-in 68.6%

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

      16. neg-sub0 68.6%

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

      17. distribute-rgt-neg-out 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in a around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

      4. *-commutative 80.9%

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

   7. Simplified 80.9%

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

   if 5.69999999999999971e-210 < a < 1.55e-142

   1. Initial program 78.0%

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

   2. Taylor expanded in t around 0 83.4%

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

      1. sub-neg 83.4%

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

      2. mul-1-neg 83.4%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r* 83.5%

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

      6. distribute-rgt-neg-in 83.5%

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

      7. mul-1-neg 83.5%

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

      8. distribute-lft-in 83.5%

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

      9. +-commutative 83.5%

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

      10. mul-1-neg 83.5%

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

      11. unsub-neg 83.5%

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

      12. *-commutative 83.5%

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

      13. fma-neg 83.5%

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

      14. distribute-rgt-neg-out 83.5%

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

      15. distribute-rgt-neg-in 83.5%

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

      16. neg-sub0 83.5%

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

      17. distribute-rgt-neg-out 83.5%

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

   4. Simplified 83.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 3: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := i \cdot \left(y \cdot j\right)\\ t_3 := \left(i \cdot \left(a \cdot b\right) - t_2\right) + t_1\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+40}:\\ \;\;\;\;t_4 - t_2\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - \left(c \cdot \left(z \cdot b\right) + y \cdot \left(i \cdot j - x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* i (* y j)))
        (t_3 (+ (- (* i (* a b)) t_2) t_1))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -1.75e+40)
     (- t_4 t_2)
     (if (<= x 5.1e-228)
       t_3
       (if (<= x 4.05e-41)
         (+ (* z (- (* x y) (* b c))) t_1)
         (if (<= x 1.6e+22)
           t_3
           (if (<= x 1.95e+94)
             (- (* c (* t j)) (+ (* c (* z b)) (* y (- (* i j) (* x z)))))
             (+ t_4 (* b (- (* a i) (* z c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * (y * j);
	double t_3 = ((i * (a * b)) - t_2) + t_1;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.75e+40) {
		tmp = t_4 - t_2;
	} else if (x <= 5.1e-228) {
		tmp = t_3;
	} else if (x <= 4.05e-41) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else if (x <= 1.6e+22) {
		tmp = t_3;
	} else if (x <= 1.95e+94) {
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))));
	} else {
		tmp = t_4 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = i * (y * j)
    t_3 = ((i * (a * b)) - t_2) + t_1
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-1.75d+40)) then
        tmp = t_4 - t_2
    else if (x <= 5.1d-228) then
        tmp = t_3
    else if (x <= 4.05d-41) then
        tmp = (z * ((x * y) - (b * c))) + t_1
    else if (x <= 1.6d+22) then
        tmp = t_3
    else if (x <= 1.95d+94) then
        tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))))
    else
        tmp = t_4 + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * (y * j);
	double t_3 = ((i * (a * b)) - t_2) + t_1;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.75e+40) {
		tmp = t_4 - t_2;
	} else if (x <= 5.1e-228) {
		tmp = t_3;
	} else if (x <= 4.05e-41) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else if (x <= 1.6e+22) {
		tmp = t_3;
	} else if (x <= 1.95e+94) {
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))));
	} else {
		tmp = t_4 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = i * (y * j)
	t_3 = ((i * (a * b)) - t_2) + t_1
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.75e+40:
		tmp = t_4 - t_2
	elif x <= 5.1e-228:
		tmp = t_3
	elif x <= 4.05e-41:
		tmp = (z * ((x * y) - (b * c))) + t_1
	elif x <= 1.6e+22:
		tmp = t_3
	elif x <= 1.95e+94:
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))))
	else:
		tmp = t_4 + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(i * Float64(y * j))
	t_3 = Float64(Float64(Float64(i * Float64(a * b)) - t_2) + t_1)
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.75e+40)
		tmp = Float64(t_4 - t_2);
	elseif (x <= 5.1e-228)
		tmp = t_3;
	elseif (x <= 4.05e-41)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1);
	elseif (x <= 1.6e+22)
		tmp = t_3;
	elseif (x <= 1.95e+94)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(Float64(c * Float64(z * b)) + Float64(y * Float64(Float64(i * j) - Float64(x * z)))));
	else
		tmp = Float64(t_4 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = i * (y * j);
	t_3 = ((i * (a * b)) - t_2) + t_1;
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.75e+40)
		tmp = t_4 - t_2;
	elseif (x <= 5.1e-228)
		tmp = t_3;
	elseif (x <= 4.05e-41)
		tmp = (z * ((x * y) - (b * c))) + t_1;
	elseif (x <= 1.6e+22)
		tmp = t_3;
	elseif (x <= 1.95e+94)
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))));
	else
		tmp = t_4 + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+40], N[(t$95$4 - t$95$2), $MachinePrecision], If[LessEqual[x, 5.1e-228], t$95$3, If[LessEqual[x, 4.05e-41], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 1.6e+22], t$95$3, If[LessEqual[x, 1.95e+94], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.75e40

   1. Initial program 68.0%

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

   2. Taylor expanded in b around 0 69.7%

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

   3. Taylor expanded in i around inf 75.2%

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

   if -1.75e40 < x < 5.1000000000000002e-228 or 4.05e-41 < x < 1.6e22

   1. Initial program 67.6%

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

   2. Taylor expanded in t around -inf 74.0%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in z around 0 77.3%

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

   if 5.1000000000000002e-228 < x < 4.05e-41

   1. Initial program 73.1%

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

   2. Taylor expanded in t around -inf 84.4%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in i around 0 72.9%

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

      1. associate-*r* 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*r* 70.8%

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

      4. associate-*r* 70.8%

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

      5. *-commutative 70.8%

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

      6. associate-*r* 70.8%

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

      7. distribute-rgt-in 70.8%

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

      8. +-commutative 70.8%

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

      9. mul-1-neg 70.8%

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

      10. unsub-neg 70.8%

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

      11. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if 1.6e22 < x < 1.94999999999999993e94

   1. Initial program 71.9%

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

   2. Taylor expanded in t around -inf 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in a around 0 85.9%

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

   if 1.94999999999999993e94 < x

   1. Initial program 79.9%

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

   2. Taylor expanded in j around 0 82.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-228}:\\ \;\;\;\;\left(i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\left(i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - \left(c \cdot \left(z \cdot b\right) + y \cdot \left(i \cdot j - x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := i \cdot \left(y \cdot j\right)\\ t_3 := \left(i \cdot \left(a \cdot b\right) - t_2\right) + t_1\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;t_4 - t_2\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{-227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;t_4 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_4 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* i (* y j)))
        (t_3 (+ (- (* i (* a b)) t_2) t_1))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -3.9e+40)
     (- t_4 t_2)
     (if (<= x 1.82e-227)
       t_3
       (if (<= x 8.5e-38)
         (+ (* z (- (* x y) (* b c))) t_1)
         (if (<= x 3.9e+24)
           t_3
           (if (<= x 1.16e+107)
             (- t_4 (* j (- (* y i) (* t c))))
             (+ t_4 (* b (- (* a i) (* z c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * (y * j);
	double t_3 = ((i * (a * b)) - t_2) + t_1;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.9e+40) {
		tmp = t_4 - t_2;
	} else if (x <= 1.82e-227) {
		tmp = t_3;
	} else if (x <= 8.5e-38) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else if (x <= 3.9e+24) {
		tmp = t_3;
	} else if (x <= 1.16e+107) {
		tmp = t_4 - (j * ((y * i) - (t * c)));
	} else {
		tmp = t_4 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = i * (y * j)
    t_3 = ((i * (a * b)) - t_2) + t_1
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-3.9d+40)) then
        tmp = t_4 - t_2
    else if (x <= 1.82d-227) then
        tmp = t_3
    else if (x <= 8.5d-38) then
        tmp = (z * ((x * y) - (b * c))) + t_1
    else if (x <= 3.9d+24) then
        tmp = t_3
    else if (x <= 1.16d+107) then
        tmp = t_4 - (j * ((y * i) - (t * c)))
    else
        tmp = t_4 + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * (y * j);
	double t_3 = ((i * (a * b)) - t_2) + t_1;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.9e+40) {
		tmp = t_4 - t_2;
	} else if (x <= 1.82e-227) {
		tmp = t_3;
	} else if (x <= 8.5e-38) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else if (x <= 3.9e+24) {
		tmp = t_3;
	} else if (x <= 1.16e+107) {
		tmp = t_4 - (j * ((y * i) - (t * c)));
	} else {
		tmp = t_4 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = i * (y * j)
	t_3 = ((i * (a * b)) - t_2) + t_1
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.9e+40:
		tmp = t_4 - t_2
	elif x <= 1.82e-227:
		tmp = t_3
	elif x <= 8.5e-38:
		tmp = (z * ((x * y) - (b * c))) + t_1
	elif x <= 3.9e+24:
		tmp = t_3
	elif x <= 1.16e+107:
		tmp = t_4 - (j * ((y * i) - (t * c)))
	else:
		tmp = t_4 + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(i * Float64(y * j))
	t_3 = Float64(Float64(Float64(i * Float64(a * b)) - t_2) + t_1)
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.9e+40)
		tmp = Float64(t_4 - t_2);
	elseif (x <= 1.82e-227)
		tmp = t_3;
	elseif (x <= 8.5e-38)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1);
	elseif (x <= 3.9e+24)
		tmp = t_3;
	elseif (x <= 1.16e+107)
		tmp = Float64(t_4 - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	else
		tmp = Float64(t_4 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = i * (y * j);
	t_3 = ((i * (a * b)) - t_2) + t_1;
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.9e+40)
		tmp = t_4 - t_2;
	elseif (x <= 1.82e-227)
		tmp = t_3;
	elseif (x <= 8.5e-38)
		tmp = (z * ((x * y) - (b * c))) + t_1;
	elseif (x <= 3.9e+24)
		tmp = t_3;
	elseif (x <= 1.16e+107)
		tmp = t_4 - (j * ((y * i) - (t * c)));
	else
		tmp = t_4 + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+40], N[(t$95$4 - t$95$2), $MachinePrecision], If[LessEqual[x, 1.82e-227], t$95$3, If[LessEqual[x, 8.5e-38], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 3.9e+24], t$95$3, If[LessEqual[x, 1.16e+107], N[(t$95$4 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.9000000000000001e40

   1. Initial program 68.0%

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

   2. Taylor expanded in b around 0 69.7%

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

   3. Taylor expanded in i around inf 75.2%

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

   if -3.9000000000000001e40 < x < 1.8199999999999999e-227 or 8.50000000000000046e-38 < x < 3.8999999999999998e24

   1. Initial program 67.6%

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

   2. Taylor expanded in t around -inf 74.0%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in z around 0 77.3%

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

   if 1.8199999999999999e-227 < x < 8.50000000000000046e-38

   1. Initial program 73.1%

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

   2. Taylor expanded in t around -inf 84.4%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in i around 0 72.9%

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

      1. associate-*r* 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*r* 70.8%

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

      4. associate-*r* 70.8%

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

      5. *-commutative 70.8%

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

      6. associate-*r* 70.8%

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

      7. distribute-rgt-in 70.8%

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

      8. +-commutative 70.8%

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

      9. mul-1-neg 70.8%

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

      10. unsub-neg 70.8%

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

      11. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if 3.8999999999999998e24 < x < 1.1600000000000001e107

   1. Initial program 71.9%

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

   2. Taylor expanded in b around 0 85.6%

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

   if 1.1600000000000001e107 < x

   1. Initial program 79.9%

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

   2. Taylor expanded in j around 0 82.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{-227}:\\ \;\;\;\;\left(i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+24}:\\ \;\;\;\;\left(i \cdot \left(a \cdot b\right) - i \cdot \left(y \cdot j\right)\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5: 52.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-267}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 540:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* z (* x y)) (* b (- (* a i) (* z c)))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.02e+35)
     t_2
     (if (<= x -6.2e-267)
       (* i (- (* a b) (* y j)))
       (if (<= x 1.95e-233)
         (* j (- (* t c) (* y i)))
         (if (<= x 540.0)
           t_1
           (if (<= x 7.2e+49)
             (* t (- (* c j) (* x a)))
             (if (<= x 4.2e+142) 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 = (z * (x * y)) + (b * ((a * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.02e+35) {
		tmp = t_2;
	} else if (x <= -6.2e-267) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 1.95e-233) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 540.0) {
		tmp = t_1;
	} else if (x <= 7.2e+49) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 4.2e+142) {
		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 = (z * (x * y)) + (b * ((a * i) - (z * c)))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.02d+35)) then
        tmp = t_2
    else if (x <= (-6.2d-267)) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 1.95d-233) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 540.0d0) then
        tmp = t_1
    else if (x <= 7.2d+49) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 4.2d+142) 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 = (z * (x * y)) + (b * ((a * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.02e+35) {
		tmp = t_2;
	} else if (x <= -6.2e-267) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 1.95e-233) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 540.0) {
		tmp = t_1;
	} else if (x <= 7.2e+49) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 4.2e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * (x * y)) + (b * ((a * i) - (z * c)))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.02e+35:
		tmp = t_2
	elif x <= -6.2e-267:
		tmp = i * ((a * b) - (y * j))
	elif x <= 1.95e-233:
		tmp = j * ((t * c) - (y * i))
	elif x <= 540.0:
		tmp = t_1
	elif x <= 7.2e+49:
		tmp = t * ((c * j) - (x * a))
	elif x <= 4.2e+142:
		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(z * Float64(x * y)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.02e+35)
		tmp = t_2;
	elseif (x <= -6.2e-267)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 1.95e-233)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 540.0)
		tmp = t_1;
	elseif (x <= 7.2e+49)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 4.2e+142)
		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 = (z * (x * y)) + (b * ((a * i) - (z * c)));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.02e+35)
		tmp = t_2;
	elseif (x <= -6.2e-267)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 1.95e-233)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 540.0)
		tmp = t_1;
	elseif (x <= 7.2e+49)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 4.2e+142)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+35], t$95$2, If[LessEqual[x, -6.2e-267], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-233], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 540.0], t$95$1, If[LessEqual[x, 7.2e+49], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+142], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.02000000000000007e35 or 4.2e142 < x

   1. Initial program 71.7%

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

   2. Taylor expanded in t around -inf 60.1%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -1.02000000000000007e35 < x < -6.2000000000000002e-267

   1. Initial program 61.0%

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

   2. Taylor expanded in i around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*r* 54.2%

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

      3. neg-mul-1 54.2%

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

      4. cancel-sign-sub 54.2%

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

      5. +-commutative 54.2%

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

      6. mul-1-neg 54.2%

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

      7. unsub-neg 54.2%

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

   4. Simplified 54.2%

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

   if -6.2000000000000002e-267 < x < 1.9500000000000001e-233

   1. Initial program 74.5%

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

   2. Taylor expanded in j around inf 69.9%

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

   if 1.9500000000000001e-233 < x < 540 or 7.19999999999999993e49 < x < 4.2e142

   1. Initial program 77.3%

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

   2. Taylor expanded in t around 0 59.3%

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

      1. sub-neg 59.3%

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

      2. mul-1-neg 59.3%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-*r* 62.2%

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

      6. distribute-rgt-neg-in 62.2%

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

      7. mul-1-neg 62.2%

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

      8. distribute-lft-in 62.2%

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

      9. +-commutative 62.2%

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

      10. mul-1-neg 62.2%

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

      11. unsub-neg 62.2%

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

      12. *-commutative 62.2%

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

      13. fma-neg 62.2%

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

      14. distribute-rgt-neg-out 62.2%

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

      15. distribute-rgt-neg-in 62.2%

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

      16. neg-sub0 62.2%

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

      17. distribute-rgt-neg-out 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. *-commutative 18.9%

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

      2. associate-*l* 18.9%

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

   7. Simplified 56.6%

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

   if 540 < x < 7.19999999999999993e49

   1. Initial program 63.4%

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

   2. Taylor expanded in t around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   4. Simplified 75.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-267}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 540:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 6: 68.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.12 \cdot 10^{-203}:\\ \;\;\;\;t_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 930000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (- (* a i) (* z c)))))
        (t_3 (- t_1 (* j (- (* y i) (* t c))))))
   (if (<= j -1.5e-54)
     t_3
     (if (<= j -2.2e-176)
       t_2
       (if (<= j -1.12e-203)
         (- t_1 (* i (* y j)))
         (if (<= j 930000000000.0) t_2 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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -1.5e-54) {
		tmp = t_3;
	} else if (j <= -2.2e-176) {
		tmp = t_2;
	} else if (j <= -1.12e-203) {
		tmp = t_1 - (i * (y * j));
	} else if (j <= 930000000000.0) {
		tmp = t_2;
	} 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 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    t_3 = t_1 - (j * ((y * i) - (t * c)))
    if (j <= (-1.5d-54)) then
        tmp = t_3
    else if (j <= (-2.2d-176)) then
        tmp = t_2
    else if (j <= (-1.12d-203)) then
        tmp = t_1 - (i * (y * j))
    else if (j <= 930000000000.0d0) then
        tmp = t_2
    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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -1.5e-54) {
		tmp = t_3;
	} else if (j <= -2.2e-176) {
		tmp = t_2;
	} else if (j <= -1.12e-203) {
		tmp = t_1 - (i * (y * j));
	} else if (j <= 930000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 * ((a * i) - (z * c)))
	t_3 = t_1 - (j * ((y * i) - (t * c)))
	tmp = 0
	if j <= -1.5e-54:
		tmp = t_3
	elif j <= -2.2e-176:
		tmp = t_2
	elif j <= -1.12e-203:
		tmp = t_1 - (i * (y * j))
	elif j <= 930000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	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(a * i) - Float64(z * c))))
	t_3 = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	tmp = 0.0
	if (j <= -1.5e-54)
		tmp = t_3;
	elseif (j <= -2.2e-176)
		tmp = t_2;
	elseif (j <= -1.12e-203)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (j <= 930000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	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 * ((a * i) - (z * c)));
	t_3 = t_1 - (j * ((y * i) - (t * c)));
	tmp = 0.0;
	if (j <= -1.5e-54)
		tmp = t_3;
	elseif (j <= -2.2e-176)
		tmp = t_2;
	elseif (j <= -1.12e-203)
		tmp = t_1 - (i * (y * j));
	elseif (j <= 930000000000.0)
		tmp = t_2;
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e-54], t$95$3, If[LessEqual[j, -2.2e-176], t$95$2, If[LessEqual[j, -1.12e-203], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 930000000000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.50000000000000005e-54 or 9.3e11 < j

   1. Initial program 72.8%

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

   2. Taylor expanded in b around 0 73.6%

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

   if -1.50000000000000005e-54 < j < -2.1999999999999999e-176 or -1.12e-203 < j < 9.3e11

   1. Initial program 68.6%

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

   2. Taylor expanded in j around 0 73.1%

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

   if -2.1999999999999999e-176 < j < -1.12e-203

   1. Initial program 67.1%

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

   2. Taylor expanded in b around 0 78.2%

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

   3. Taylor expanded in i around inf 89.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.12 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 930000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]

Alternative 7: 68.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{-55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-207}:\\ \;\;\;\;t_1 + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 60000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (- (* a i) (* z c)))))
        (t_3 (- t_1 (* j (- (* y i) (* t c))))))
   (if (<= j -4e-55)
     t_3
     (if (<= j -1.75e-158)
       t_2
       (if (<= j -6.5e-207)
         (+ t_1 (* i (- (* a b) (* y j))))
         (if (<= j 60000000000.0) t_2 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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -4e-55) {
		tmp = t_3;
	} else if (j <= -1.75e-158) {
		tmp = t_2;
	} else if (j <= -6.5e-207) {
		tmp = t_1 + (i * ((a * b) - (y * j)));
	} else if (j <= 60000000000.0) {
		tmp = t_2;
	} 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 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    t_3 = t_1 - (j * ((y * i) - (t * c)))
    if (j <= (-4d-55)) then
        tmp = t_3
    else if (j <= (-1.75d-158)) then
        tmp = t_2
    else if (j <= (-6.5d-207)) then
        tmp = t_1 + (i * ((a * b) - (y * j)))
    else if (j <= 60000000000.0d0) then
        tmp = t_2
    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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -4e-55) {
		tmp = t_3;
	} else if (j <= -1.75e-158) {
		tmp = t_2;
	} else if (j <= -6.5e-207) {
		tmp = t_1 + (i * ((a * b) - (y * j)));
	} else if (j <= 60000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 * ((a * i) - (z * c)))
	t_3 = t_1 - (j * ((y * i) - (t * c)))
	tmp = 0
	if j <= -4e-55:
		tmp = t_3
	elif j <= -1.75e-158:
		tmp = t_2
	elif j <= -6.5e-207:
		tmp = t_1 + (i * ((a * b) - (y * j)))
	elif j <= 60000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	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(a * i) - Float64(z * c))))
	t_3 = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	tmp = 0.0
	if (j <= -4e-55)
		tmp = t_3;
	elseif (j <= -1.75e-158)
		tmp = t_2;
	elseif (j <= -6.5e-207)
		tmp = Float64(t_1 + Float64(i * Float64(Float64(a * b) - Float64(y * j))));
	elseif (j <= 60000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	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 * ((a * i) - (z * c)));
	t_3 = t_1 - (j * ((y * i) - (t * c)));
	tmp = 0.0;
	if (j <= -4e-55)
		tmp = t_3;
	elseif (j <= -1.75e-158)
		tmp = t_2;
	elseif (j <= -6.5e-207)
		tmp = t_1 + (i * ((a * b) - (y * j)));
	elseif (j <= 60000000000.0)
		tmp = t_2;
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e-55], t$95$3, If[LessEqual[j, -1.75e-158], t$95$2, If[LessEqual[j, -6.5e-207], N[(t$95$1 + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 60000000000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.99999999999999998e-55 or 6e10 < j

   1. Initial program 72.8%

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

   2. Taylor expanded in b around 0 73.6%

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

   if -3.99999999999999998e-55 < j < -1.75000000000000006e-158 or -6.5000000000000001e-207 < j < 6e10

   1. Initial program 68.3%

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

   2. Taylor expanded in j around 0 73.9%

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

   if -1.75000000000000006e-158 < j < -6.5000000000000001e-207

   1. Initial program 69.6%

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

   2. Taylor expanded in c around 0 92.8%

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

   3. Taylor expanded in i around -inf 92.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 60000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]

Alternative 8: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{if}\;j \leq -7.8 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.55 \cdot 10^{-157}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-202}:\\ \;\;\;\;t_1 + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 85000000:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* j (- (* y i) (* t c))))))
   (if (<= j -7.8e-55)
     t_2
     (if (<= j -2.55e-157)
       (- (- (* c (* t j)) (* x (- (* t a) (* y z)))) (* c (* z b)))
       (if (<= j -1.35e-202)
         (+ t_1 (* i (- (* a b) (* y j))))
         (if (<= j 85000000.0) (+ t_1 (* b (- (* a i) (* z c)))) 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));
	double t_2 = t_1 - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -7.8e-55) {
		tmp = t_2;
	} else if (j <= -2.55e-157) {
		tmp = ((c * (t * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b));
	} else if (j <= -1.35e-202) {
		tmp = t_1 + (i * ((a * b) - (y * j)));
	} else if (j <= 85000000.0) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (j * ((y * i) - (t * c)))
    if (j <= (-7.8d-55)) then
        tmp = t_2
    else if (j <= (-2.55d-157)) then
        tmp = ((c * (t * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b))
    else if (j <= (-1.35d-202)) then
        tmp = t_1 + (i * ((a * b) - (y * j)))
    else if (j <= 85000000.0d0) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -7.8e-55) {
		tmp = t_2;
	} else if (j <= -2.55e-157) {
		tmp = ((c * (t * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b));
	} else if (j <= -1.35e-202) {
		tmp = t_1 + (i * ((a * b) - (y * j)));
	} else if (j <= 85000000.0) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (j * ((y * i) - (t * c)))
	tmp = 0
	if j <= -7.8e-55:
		tmp = t_2
	elif j <= -2.55e-157:
		tmp = ((c * (t * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b))
	elif j <= -1.35e-202:
		tmp = t_1 + (i * ((a * b) - (y * j)))
	elif j <= 85000000.0:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = t_2
	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(j * Float64(Float64(y * i) - Float64(t * c))))
	tmp = 0.0
	if (j <= -7.8e-55)
		tmp = t_2;
	elseif (j <= -2.55e-157)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) - Float64(c * Float64(z * b)));
	elseif (j <= -1.35e-202)
		tmp = Float64(t_1 + Float64(i * Float64(Float64(a * b) - Float64(y * j))));
	elseif (j <= 85000000.0)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (j * ((y * i) - (t * c)));
	tmp = 0.0;
	if (j <= -7.8e-55)
		tmp = t_2;
	elseif (j <= -2.55e-157)
		tmp = ((c * (t * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b));
	elseif (j <= -1.35e-202)
		tmp = t_1 + (i * ((a * b) - (y * j)));
	elseif (j <= 85000000.0)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.8e-55], t$95$2, If[LessEqual[j, -2.55e-157], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.35e-202], N[(t$95$1 + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 85000000.0], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.8e-55 or 8.5e7 < j

   1. Initial program 72.8%

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

   2. Taylor expanded in b around 0 73.6%

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

   if -7.8e-55 < j < -2.54999999999999999e-157

   1. Initial program 78.2%

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

   2. Taylor expanded in i around 0 83.7%

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

   if -2.54999999999999999e-157 < j < -1.3499999999999999e-202

   1. Initial program 69.6%

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

   2. Taylor expanded in c around 0 92.8%

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

   3. Taylor expanded in i around -inf 92.8%

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

   if -1.3499999999999999e-202 < j < 8.5e7

   1. Initial program 66.5%

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

   2. Taylor expanded in j around 0 72.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.8 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq -2.55 \cdot 10^{-157}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 85000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]

Alternative 9: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -23000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq 0.00088:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+14} \lor \neg \left(a \leq 3.2 \cdot 10^{+50}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -23000000.0)
     t_3
     (if (<= a -4e-46)
       t_1
       (if (<= a -2.95e-87)
         (* b (- (* a i) (* z c)))
         (if (<= a 1.25e-126)
           t_2
           (if (<= a 1.95e-32)
             (* t (- (* c j) (* x a)))
             (if (<= a 0.00088)
               t_1
               (if (or (<= a 6.5e+14) (not (<= a 3.2e+50))) 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 = j * ((t * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -23000000.0) {
		tmp = t_3;
	} else if (a <= -4e-46) {
		tmp = t_1;
	} else if (a <= -2.95e-87) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.25e-126) {
		tmp = t_2;
	} else if (a <= 1.95e-32) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= 0.00088) {
		tmp = t_1;
	} else if ((a <= 6.5e+14) || !(a <= 3.2e+50)) {
		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 = j * ((t * c) - (y * i))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-23000000.0d0)) then
        tmp = t_3
    else if (a <= (-4d-46)) then
        tmp = t_1
    else if (a <= (-2.95d-87)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 1.25d-126) then
        tmp = t_2
    else if (a <= 1.95d-32) then
        tmp = t * ((c * j) - (x * a))
    else if (a <= 0.00088d0) then
        tmp = t_1
    else if ((a <= 6.5d+14) .or. (.not. (a <= 3.2d+50))) 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 = j * ((t * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -23000000.0) {
		tmp = t_3;
	} else if (a <= -4e-46) {
		tmp = t_1;
	} else if (a <= -2.95e-87) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.25e-126) {
		tmp = t_2;
	} else if (a <= 1.95e-32) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= 0.00088) {
		tmp = t_1;
	} else if ((a <= 6.5e+14) || !(a <= 3.2e+50)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -23000000.0:
		tmp = t_3
	elif a <= -4e-46:
		tmp = t_1
	elif a <= -2.95e-87:
		tmp = b * ((a * i) - (z * c))
	elif a <= 1.25e-126:
		tmp = t_2
	elif a <= 1.95e-32:
		tmp = t * ((c * j) - (x * a))
	elif a <= 0.00088:
		tmp = t_1
	elif (a <= 6.5e+14) or not (a <= 3.2e+50):
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -23000000.0)
		tmp = t_3;
	elseif (a <= -4e-46)
		tmp = t_1;
	elseif (a <= -2.95e-87)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 1.25e-126)
		tmp = t_2;
	elseif (a <= 1.95e-32)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (a <= 0.00088)
		tmp = t_1;
	elseif ((a <= 6.5e+14) || !(a <= 3.2e+50))
		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 = j * ((t * c) - (y * i));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -23000000.0)
		tmp = t_3;
	elseif (a <= -4e-46)
		tmp = t_1;
	elseif (a <= -2.95e-87)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 1.25e-126)
		tmp = t_2;
	elseif (a <= 1.95e-32)
		tmp = t * ((c * j) - (x * a));
	elseif (a <= 0.00088)
		tmp = t_1;
	elseif ((a <= 6.5e+14) || ~((a <= 3.2e+50)))
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -23000000.0], t$95$3, If[LessEqual[a, -4e-46], t$95$1, If[LessEqual[a, -2.95e-87], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-126], t$95$2, If[LessEqual[a, 1.95e-32], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00088], t$95$1, If[Or[LessEqual[a, 6.5e+14], N[Not[LessEqual[a, 3.2e+50]], $MachinePrecision]], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.3e7 or 8.80000000000000031e-4 < a < 6.5e14 or 3.19999999999999983e50 < a

   1. Initial program 56.8%

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

   2. Taylor expanded in a around inf 70.4%

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

      1. associate-*r* 70.4%

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

      2. neg-mul-1 70.4%

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

      3. cancel-sign-sub 70.4%

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

      4. +-commutative 70.4%

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

      5. mul-1-neg 70.4%

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

      6. unsub-neg 70.4%

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

   4. Simplified 70.4%

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

   if -2.3e7 < a < -4.00000000000000009e-46 or 1.9500000000000001e-32 < a < 8.80000000000000031e-4

   1. Initial program 81.7%

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

   2. Taylor expanded in j around inf 73.5%

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

   if -4.00000000000000009e-46 < a < -2.9499999999999998e-87

   1. Initial program 91.3%

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

      1. associate-+l- 91.3%

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

      2. sub-neg 91.3%

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

      3. sub-neg 91.3%

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

      4. *-commutative 91.3%

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

      5. fma-neg 91.3%

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

      6. *-commutative 91.3%

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

      7. *-commutative 91.3%

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

      8. fma-neg 91.3%

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

      9. distribute-lft-neg-out 91.3%

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

      10. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in b around inf 56.6%

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

   if -2.9499999999999998e-87 < a < 1.25000000000000001e-126 or 6.5e14 < a < 3.19999999999999983e50

   1. Initial program 80.2%

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

   2. Taylor expanded in y around inf 55.7%

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

      1. +-commutative 55.7%

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

      2. mul-1-neg 55.7%

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

      3. unsub-neg 55.7%

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

   4. Simplified 55.7%

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

   if 1.25000000000000001e-126 < a < 1.9500000000000001e-32

   1. Initial program 71.4%

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

   2. Taylor expanded in t around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

   4. Simplified 76.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -23000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq 0.00088:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+14} \lor \neg \left(a \leq 3.2 \cdot 10^{+50}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 10: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.38 \cdot 10^{+222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.15 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.24 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= i -1.38e+222)
     t_3
     (if (<= i -3.15e+189)
       t_2
       (if (<= i -5.8e+85)
         t_3
         (if (<= i -4.2e-45)
           t_1
           (if (<= i -3.8e-262)
             t_2
             (if (<= i 7.2e-183)
               (* t (- (* c j) (* x a)))
               (if (<= i 9.5e-96) t_2 (if (<= i 1.24e+30) 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.38e+222) {
		tmp = t_3;
	} else if (i <= -3.15e+189) {
		tmp = t_2;
	} else if (i <= -5.8e+85) {
		tmp = t_3;
	} else if (i <= -4.2e-45) {
		tmp = t_1;
	} else if (i <= -3.8e-262) {
		tmp = t_2;
	} else if (i <= 7.2e-183) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 9.5e-96) {
		tmp = t_2;
	} else if (i <= 1.24e+30) {
		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 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    t_3 = i * ((a * b) - (y * j))
    if (i <= (-1.38d+222)) then
        tmp = t_3
    else if (i <= (-3.15d+189)) then
        tmp = t_2
    else if (i <= (-5.8d+85)) then
        tmp = t_3
    else if (i <= (-4.2d-45)) then
        tmp = t_1
    else if (i <= (-3.8d-262)) then
        tmp = t_2
    else if (i <= 7.2d-183) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 9.5d-96) then
        tmp = t_2
    else if (i <= 1.24d+30) 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.38e+222) {
		tmp = t_3;
	} else if (i <= -3.15e+189) {
		tmp = t_2;
	} else if (i <= -5.8e+85) {
		tmp = t_3;
	} else if (i <= -4.2e-45) {
		tmp = t_1;
	} else if (i <= -3.8e-262) {
		tmp = t_2;
	} else if (i <= 7.2e-183) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 9.5e-96) {
		tmp = t_2;
	} else if (i <= 1.24e+30) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.38e+222:
		tmp = t_3
	elif i <= -3.15e+189:
		tmp = t_2
	elif i <= -5.8e+85:
		tmp = t_3
	elif i <= -4.2e-45:
		tmp = t_1
	elif i <= -3.8e-262:
		tmp = t_2
	elif i <= 7.2e-183:
		tmp = t * ((c * j) - (x * a))
	elif i <= 9.5e-96:
		tmp = t_2
	elif i <= 1.24e+30:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.38e+222)
		tmp = t_3;
	elseif (i <= -3.15e+189)
		tmp = t_2;
	elseif (i <= -5.8e+85)
		tmp = t_3;
	elseif (i <= -4.2e-45)
		tmp = t_1;
	elseif (i <= -3.8e-262)
		tmp = t_2;
	elseif (i <= 7.2e-183)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 9.5e-96)
		tmp = t_2;
	elseif (i <= 1.24e+30)
		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 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.38e+222)
		tmp = t_3;
	elseif (i <= -3.15e+189)
		tmp = t_2;
	elseif (i <= -5.8e+85)
		tmp = t_3;
	elseif (i <= -4.2e-45)
		tmp = t_1;
	elseif (i <= -3.8e-262)
		tmp = t_2;
	elseif (i <= 7.2e-183)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 9.5e-96)
		tmp = t_2;
	elseif (i <= 1.24e+30)
		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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.38e+222], t$95$3, If[LessEqual[i, -3.15e+189], t$95$2, If[LessEqual[i, -5.8e+85], t$95$3, If[LessEqual[i, -4.2e-45], t$95$1, If[LessEqual[i, -3.8e-262], t$95$2, If[LessEqual[i, 7.2e-183], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e-96], t$95$2, If[LessEqual[i, 1.24e+30], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.38e222 or -3.15000000000000001e189 < i < -5.79999999999999995e85 or 1.24e30 < i

   1. Initial program 65.4%

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

   2. Taylor expanded in i around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-*r* 65.1%

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

      3. neg-mul-1 65.1%

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

      4. cancel-sign-sub 65.1%

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

      5. +-commutative 65.1%

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

      6. mul-1-neg 65.1%

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

      7. unsub-neg 65.1%

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

   4. Simplified 65.1%

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

   if -1.38e222 < i < -3.15000000000000001e189 or -4.1999999999999999e-45 < i < -3.8000000000000002e-262 or 7.2000000000000002e-183 < i < 9.4999999999999993e-96

   1. Initial program 74.2%

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

   2. Taylor expanded in c around inf 56.9%

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

      1. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   if -5.79999999999999995e85 < i < -4.1999999999999999e-45 or 9.4999999999999993e-96 < i < 1.24e30

   1. Initial program 79.6%

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

   2. Taylor expanded in a around inf 63.5%

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

      1. associate-*r* 63.5%

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

      2. neg-mul-1 63.5%

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

      3. cancel-sign-sub 63.5%

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

      4. +-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. unsub-neg 63.5%

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

   4. Simplified 63.5%

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

   if -3.8000000000000002e-262 < i < 7.2000000000000002e-183

   1. Initial program 62.7%

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

   2. Taylor expanded in t around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

   4. Simplified 51.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.38 \cdot 10^{+222}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.15 \cdot 10^{+189}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-96}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.24 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 11: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -3e+39)
     t_1
     (if (<= x -2.45e-265)
       (* i (- (* a b) (* y j)))
       (if (<= x 5.8e-233)
         (* j (- (* t c) (* y i)))
         (if (<= x 6.5e-142)
           (+ (* z (* x y)) (* b (- (* a i) (* z c))))
           (if (<= x 8e+106)
             (- (* x (* y z)) (* j (- (* y i) (* t c))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3e+39) {
		tmp = t_1;
	} else if (x <= -2.45e-265) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 5.8e-233) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 6.5e-142) {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	} else if (x <= 8e+106) {
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-3d+39)) then
        tmp = t_1
    else if (x <= (-2.45d-265)) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 5.8d-233) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 6.5d-142) then
        tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
    else if (x <= 8d+106) then
        tmp = (x * (y * z)) - (j * ((y * i) - (t * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3e+39) {
		tmp = t_1;
	} else if (x <= -2.45e-265) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 5.8e-233) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 6.5e-142) {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	} else if (x <= 8e+106) {
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3e+39:
		tmp = t_1
	elif x <= -2.45e-265:
		tmp = i * ((a * b) - (y * j))
	elif x <= 5.8e-233:
		tmp = j * ((t * c) - (y * i))
	elif x <= 6.5e-142:
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
	elif x <= 8e+106:
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (x <= -3e+39)
		tmp = t_1;
	elseif (x <= -2.45e-265)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 5.8e-233)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 6.5e-142)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 8e+106)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3e+39)
		tmp = t_1;
	elseif (x <= -2.45e-265)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 5.8e-233)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 6.5e-142)
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	elseif (x <= 8e+106)
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+39], t$95$1, If[LessEqual[x, -2.45e-265], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-233], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-142], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+106], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3e39 or 8.00000000000000073e106 < x

   1. Initial program 72.4%

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

   2. Taylor expanded in t around -inf 58.7%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in x around inf 72.6%

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

   if -3e39 < x < -2.45e-265

   1. Initial program 61.0%

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

   2. Taylor expanded in i around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*r* 54.2%

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

      3. neg-mul-1 54.2%

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

      4. cancel-sign-sub 54.2%

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

      5. +-commutative 54.2%

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

      6. mul-1-neg 54.2%

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

      7. unsub-neg 54.2%

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

   4. Simplified 54.2%

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

   if -2.45e-265 < x < 5.79999999999999964e-233

   1. Initial program 74.5%

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

   2. Taylor expanded in j around inf 69.9%

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

   if 5.79999999999999964e-233 < x < 6.50000000000000027e-142

   1. Initial program 73.4%

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

   2. Taylor expanded in t around 0 60.3%

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

      1. sub-neg 60.3%

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

      2. mul-1-neg 60.3%

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

      3. associate-*r* 68.8%

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

      4. *-commutative 68.8%

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

      5. associate-*r* 68.8%

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

      6. distribute-rgt-neg-in 68.8%

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

      7. mul-1-neg 68.8%

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

      8. distribute-lft-in 68.8%

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

      9. +-commutative 68.8%

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

      10. mul-1-neg 68.8%

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

      11. unsub-neg 68.8%

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

      12. *-commutative 68.8%

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

      13. fma-neg 68.8%

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

      14. distribute-rgt-neg-out 68.8%

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

      15. distribute-rgt-neg-in 68.8%

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

      16. neg-sub0 68.8%

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

      17. distribute-rgt-neg-out 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 14.7%

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

      2. associate-*l* 14.8%

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

   7. Simplified 63.7%

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

   if 6.50000000000000027e-142 < x < 8.00000000000000073e106

   1. Initial program 75.9%

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

   2. Taylor expanded in b around 0 69.5%

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

   3. Taylor expanded in y around inf 67.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 12: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -5.6e+140)
   (* c (- (* t j) (* z b)))
   (if (<= c -1.3e-53)
     (+ (* z (* x y)) (* b (- (* a i) (* z c))))
     (if (<= c 4.7e-241)
       (- (* x (* y z)) (* j (- (* y i) (* t c))))
       (if (<= c 1.3e-62)
         (* x (- (* y z) (* t a)))
         (if (<= c 3.2e+177)
           (- (* y (- (* x z) (* i j))) (* c (* z b)))
           (* t (- (* c j) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.6e+140) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= -1.3e-53) {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	} else if (c <= 4.7e-241) {
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	} else if (c <= 1.3e-62) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.2e+177) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-5.6d+140)) then
        tmp = c * ((t * j) - (z * b))
    else if (c <= (-1.3d-53)) then
        tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
    else if (c <= 4.7d-241) then
        tmp = (x * (y * z)) - (j * ((y * i) - (t * c)))
    else if (c <= 1.3d-62) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 3.2d+177) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else
        tmp = t * ((c * j) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.6e+140) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= -1.3e-53) {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	} else if (c <= 4.7e-241) {
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	} else if (c <= 1.3e-62) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.2e+177) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.6e+140:
		tmp = c * ((t * j) - (z * b))
	elif c <= -1.3e-53:
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
	elif c <= 4.7e-241:
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)))
	elif c <= 1.3e-62:
		tmp = x * ((y * z) - (t * a))
	elif c <= 3.2e+177:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.6e+140)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (c <= -1.3e-53)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (c <= 4.7e-241)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (c <= 1.3e-62)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 3.2e+177)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.6e+140)
		tmp = c * ((t * j) - (z * b));
	elseif (c <= -1.3e-53)
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	elseif (c <= 4.7e-241)
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	elseif (c <= 1.3e-62)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 3.2e+177)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -5.6e+140], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-53], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.7e-241], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-62], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+177], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.59999999999999966e140

   1. Initial program 50.7%

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

   2. Taylor expanded in c around inf 79.9%

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

      1. *-commutative 79.9%

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

   4. Simplified 79.9%

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

   if -5.59999999999999966e140 < c < -1.29999999999999998e-53

   1. Initial program 66.5%

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

   2. Taylor expanded in t around 0 68.2%

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

      1. sub-neg 68.2%

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

      2. mul-1-neg 68.2%

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

      3. associate-*r* 68.2%

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

      4. *-commutative 68.2%

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

      5. associate-*r* 68.1%

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

      6. distribute-rgt-neg-in 68.1%

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

      7. mul-1-neg 68.1%

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

      8. distribute-lft-in 68.1%

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

      9. +-commutative 68.1%

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

      10. mul-1-neg 68.1%

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

      11. unsub-neg 68.1%

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

      12. *-commutative 68.1%

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

      13. fma-neg 68.1%

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

      14. distribute-rgt-neg-out 68.1%

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

      15. distribute-rgt-neg-in 68.1%

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

      16. neg-sub0 68.1%

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

      17. distribute-rgt-neg-out 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in z around inf 65.7%

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

      1. *-commutative 36.0%

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

      2. associate-*l* 38.6%

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

   7. Simplified 68.3%

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

   if -1.29999999999999998e-53 < c < 4.6999999999999999e-241

   1. Initial program 81.2%

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

   2. Taylor expanded in b around 0 71.6%

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

   3. Taylor expanded in y around inf 58.9%

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

   if 4.6999999999999999e-241 < c < 1.3e-62

   1. Initial program 77.6%

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

   2. Taylor expanded in t around -inf 65.5%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in x around inf 60.5%

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

   if 1.3e-62 < c < 3.2e177

   1. Initial program 77.3%

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

   2. Taylor expanded in t around 0 72.6%

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

      1. sub-neg 72.6%

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

      2. mul-1-neg 72.6%

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

      3. associate-*r* 68.6%

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

      4. *-commutative 68.6%

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

      5. associate-*r* 74.8%

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

      6. distribute-rgt-neg-in 74.8%

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

      7. mul-1-neg 74.8%

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

      8. distribute-lft-in 74.8%

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

      9. +-commutative 74.8%

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

      10. mul-1-neg 74.8%

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

      11. unsub-neg 74.8%

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

      12. *-commutative 74.8%

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

      13. fma-neg 74.8%

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

      14. distribute-rgt-neg-out 74.8%

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

      15. distribute-rgt-neg-in 74.8%

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

      16. neg-sub0 74.8%

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

      17. distribute-rgt-neg-out 74.8%

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

   4. Simplified 74.8%

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

   5. Taylor expanded in a around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. mul-1-neg 67.0%

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

      3. unsub-neg 67.0%

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

      4. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 3.2e177 < c

   1. Initial program 54.7%

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

   2. Taylor expanded in t around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. mul-1-neg 72.1%

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

      3. unsub-neg 72.1%

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

   4. Simplified 72.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 13: 65.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+113}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -5.8e+113)
     (- t_1 (* c (* z b)))
     (if (<= t -2.55e-33)
       (- (* x (- (* y z) (* t a))) (* i (* y j)))
       (if (<= t 2.8e+52)
         (+ (* y (- (* x z) (* i j))) (* b (- (* a i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.8e+113) {
		tmp = t_1 - (c * (z * b));
	} else if (t <= -2.55e-33) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (t <= 2.8e+52) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-5.8d+113)) then
        tmp = t_1 - (c * (z * b))
    else if (t <= (-2.55d-33)) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (t <= 2.8d+52) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.8e+113) {
		tmp = t_1 - (c * (z * b));
	} else if (t <= -2.55e-33) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (t <= 2.8e+52) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.8e+113:
		tmp = t_1 - (c * (z * b))
	elif t <= -2.55e-33:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif t <= 2.8e+52:
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.8e+113)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (t <= -2.55e-33)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (t <= 2.8e+52)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.8e+113)
		tmp = t_1 - (c * (z * b));
	elseif (t <= -2.55e-33)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (t <= 2.8e+52)
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+113], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.55e-33], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+52], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.79999999999999968e113

   1. Initial program 53.7%

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

   2. Taylor expanded in t around -inf 66.2%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in c around -inf 74.3%

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

   if -5.79999999999999968e113 < t < -2.55000000000000004e-33

   1. Initial program 82.7%

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

   2. Taylor expanded in b around 0 82.7%

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

   3. Taylor expanded in i around inf 70.2%

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

   if -2.55000000000000004e-33 < t < 2.8e52

   1. Initial program 76.8%

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

   2. Taylor expanded in t around 0 68.0%

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

      1. sub-neg 68.0%

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

      2. mul-1-neg 68.0%

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

      3. associate-*r* 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*r* 68.0%

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

      6. distribute-rgt-neg-in 68.0%

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

      7. mul-1-neg 68.0%

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

      8. distribute-lft-in 68.7%

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

      9. +-commutative 68.7%

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

      10. mul-1-neg 68.7%

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

      11. unsub-neg 68.7%

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

      12. *-commutative 68.7%

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

      13. fma-neg 68.7%

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

      14. distribute-rgt-neg-out 68.7%

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

      15. distribute-rgt-neg-in 68.7%

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

      16. neg-sub0 68.7%

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

      17. distribute-rgt-neg-out 68.7%

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

   4. Simplified 68.7%

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

   if 2.8e52 < t

   1. Initial program 64.7%

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

   2. Taylor expanded in t around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

   4. Simplified 66.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 14: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* z (- (* x y) (* b c))) (* t (- (* c j) (* x a))))))
   (if (<= z -1.1e-120)
     t_1
     (if (<= z -2.2e-174)
       (+ (* y (- (* x z) (* i j))) (* b (- (* a i) (* z c))))
       (if (<= z 1.45e+31)
         (- (* x (- (* y z) (* t a))) (* j (- (* y i) (* t c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * ((x * y) - (b * c))) + (t * ((c * j) - (x * a)));
	double tmp;
	if (z <= -1.1e-120) {
		tmp = t_1;
	} else if (z <= -2.2e-174) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (z <= 1.45e+31) {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((x * y) - (b * c))) + (t * ((c * j) - (x * a)))
    if (z <= (-1.1d-120)) then
        tmp = t_1
    else if (z <= (-2.2d-174)) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
    else if (z <= 1.45d+31) then
        tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * ((x * y) - (b * c))) + (t * ((c * j) - (x * a)));
	double tmp;
	if (z <= -1.1e-120) {
		tmp = t_1;
	} else if (z <= -2.2e-174) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (z <= 1.45e+31) {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * ((x * y) - (b * c))) + (t * ((c * j) - (x * a)))
	tmp = 0
	if z <= -1.1e-120:
		tmp = t_1
	elif z <= -2.2e-174:
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
	elif z <= 1.45e+31:
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))))
	tmp = 0.0
	if (z <= -1.1e-120)
		tmp = t_1;
	elseif (z <= -2.2e-174)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (z <= 1.45e+31)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * ((x * y) - (b * c))) + (t * ((c * j) - (x * a)));
	tmp = 0.0;
	if (z <= -1.1e-120)
		tmp = t_1;
	elseif (z <= -2.2e-174)
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	elseif (z <= 1.45e+31)
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-120], t$95$1, If[LessEqual[z, -2.2e-174], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+31], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000006e-120 or 1.45e31 < z

   1. Initial program 65.1%

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

   2. Taylor expanded in t around -inf 65.0%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in i around 0 58.2%

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

      1. associate-*r* 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-*r* 61.8%

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

      4. associate-*r* 61.8%

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

      5. *-commutative 61.8%

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

      6. associate-*r* 68.0%

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

      7. distribute-rgt-in 71.2%

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

      8. +-commutative 71.2%

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

      9. mul-1-neg 71.2%

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

      10. unsub-neg 71.2%

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

      11. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -1.10000000000000006e-120 < z < -2.20000000000000022e-174

   1. Initial program 88.7%

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

   2. Taylor expanded in t around 0 78.2%

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

      1. sub-neg 78.2%

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

      2. mul-1-neg 78.2%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r* 78.2%

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

      6. distribute-rgt-neg-in 78.2%

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

      7. mul-1-neg 78.2%

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

      8. distribute-lft-in 78.2%

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

      9. +-commutative 78.2%

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

      10. mul-1-neg 78.2%

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

      11. unsub-neg 78.2%

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

      12. *-commutative 78.2%

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

      13. fma-neg 78.2%

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

      14. distribute-rgt-neg-out 78.2%

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

      15. distribute-rgt-neg-in 78.2%

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

      16. neg-sub0 78.2%

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

      17. distribute-rgt-neg-out 78.2%

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

   4. Simplified 78.2%

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

   if -2.20000000000000022e-174 < z < 1.45e31

   1. Initial program 75.3%

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

   2. Taylor expanded in b around 0 72.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 15: 56.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -4.5e+32)
   (* c (- (* t j) (* z b)))
   (if (<= c 1.6e-62)
     (- (* x (- (* y z) (* t a))) (* i (* y j)))
     (if (<= c 2.1e+177)
       (- (* y (- (* x z) (* i j))) (* c (* z b)))
       (* t (- (* c j) (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.5e+32) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= 1.6e-62) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (c <= 2.1e+177) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-4.5d+32)) then
        tmp = c * ((t * j) - (z * b))
    else if (c <= 1.6d-62) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (c <= 2.1d+177) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else
        tmp = t * ((c * j) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.5e+32) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= 1.6e-62) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (c <= 2.1e+177) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -4.5e+32:
		tmp = c * ((t * j) - (z * b))
	elif c <= 1.6e-62:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif c <= 2.1e+177:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -4.5e+32)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (c <= 1.6e-62)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (c <= 2.1e+177)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -4.5e+32)
		tmp = c * ((t * j) - (z * b));
	elseif (c <= 1.6e-62)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (c <= 2.1e+177)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -4.5e+32], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e-62], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+177], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.5000000000000003e32

   1. Initial program 55.6%

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

   2. Taylor expanded in c around inf 72.6%

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

      1. *-commutative 72.6%

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

   4. Simplified 72.6%

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

   if -4.5000000000000003e32 < c < 1.60000000000000011e-62

   1. Initial program 78.6%

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

   2. Taylor expanded in b around 0 69.5%

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

   3. Taylor expanded in i around inf 63.4%

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

   if 1.60000000000000011e-62 < c < 2.10000000000000013e177

   1. Initial program 77.3%

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

   2. Taylor expanded in t around 0 72.6%

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

      1. sub-neg 72.6%

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

      2. mul-1-neg 72.6%

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

      3. associate-*r* 68.6%

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

      4. *-commutative 68.6%

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

      5. associate-*r* 74.8%

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

      6. distribute-rgt-neg-in 74.8%

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

      7. mul-1-neg 74.8%

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

      8. distribute-lft-in 74.8%

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

      9. +-commutative 74.8%

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

      10. mul-1-neg 74.8%

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

      11. unsub-neg 74.8%

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

      12. *-commutative 74.8%

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

      13. fma-neg 74.8%

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

      14. distribute-rgt-neg-out 74.8%

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

      15. distribute-rgt-neg-in 74.8%

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

      16. neg-sub0 74.8%

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

      17. distribute-rgt-neg-out 74.8%

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

   4. Simplified 74.8%

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

   5. Taylor expanded in a around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. mul-1-neg 67.0%

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

      3. unsub-neg 67.0%

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

      4. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 2.10000000000000013e177 < c

   1. Initial program 54.7%

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

   2. Taylor expanded in t around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. mul-1-neg 72.1%

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

      3. unsub-neg 72.1%

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

   4. Simplified 72.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 16: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -3.8e+15)
     t_2
     (if (<= a 5.2e-255)
       t_1
       (if (<= a 1.1e-183)
         (* j (- (* t c) (* y i)))
         (if (<= a 2.3e-126)
           t_1
           (if (<= a 1.38e+93) (* t (- (* c j) (* 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 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.8e+15) {
		tmp = t_2;
	} else if (a <= 5.2e-255) {
		tmp = t_1;
	} else if (a <= 1.1e-183) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 2.3e-126) {
		tmp = t_1;
	} else if (a <= 1.38e+93) {
		tmp = t * ((c * j) - (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 = z * ((x * y) - (b * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-3.8d+15)) then
        tmp = t_2
    else if (a <= 5.2d-255) then
        tmp = t_1
    else if (a <= 1.1d-183) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 2.3d-126) then
        tmp = t_1
    else if (a <= 1.38d+93) then
        tmp = t * ((c * j) - (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 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.8e+15) {
		tmp = t_2;
	} else if (a <= 5.2e-255) {
		tmp = t_1;
	} else if (a <= 1.1e-183) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 2.3e-126) {
		tmp = t_1;
	} else if (a <= 1.38e+93) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3.8e+15:
		tmp = t_2
	elif a <= 5.2e-255:
		tmp = t_1
	elif a <= 1.1e-183:
		tmp = j * ((t * c) - (y * i))
	elif a <= 2.3e-126:
		tmp = t_1
	elif a <= 1.38e+93:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.8e+15)
		tmp = t_2;
	elseif (a <= 5.2e-255)
		tmp = t_1;
	elseif (a <= 1.1e-183)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 2.3e-126)
		tmp = t_1;
	elseif (a <= 1.38e+93)
		tmp = Float64(t * Float64(Float64(c * j) - 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 = z * ((x * y) - (b * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3.8e+15)
		tmp = t_2;
	elseif (a <= 5.2e-255)
		tmp = t_1;
	elseif (a <= 1.1e-183)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 2.3e-126)
		tmp = t_1;
	elseif (a <= 1.38e+93)
		tmp = t * ((c * j) - (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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+15], t$95$2, If[LessEqual[a, 5.2e-255], t$95$1, If[LessEqual[a, 1.1e-183], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-126], t$95$1, If[LessEqual[a, 1.38e+93], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.8e15 or 1.38000000000000005e93 < a

   1. Initial program 54.0%

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

   2. Taylor expanded in a around inf 73.2%

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

      1. associate-*r* 73.2%

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

      2. neg-mul-1 73.2%

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

      3. cancel-sign-sub 73.2%

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

      4. +-commutative 73.2%

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

      5. mul-1-neg 73.2%

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

      6. unsub-neg 73.2%

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

   4. Simplified 73.2%

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

   if -3.8e15 < a < 5.20000000000000041e-255 or 1.1e-183 < a < 2.30000000000000011e-126

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf 56.4%

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

   if 5.20000000000000041e-255 < a < 1.1e-183

   1. Initial program 93.9%

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

   2. Taylor expanded in j around inf 76.9%

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

   if 2.30000000000000011e-126 < a < 1.38000000000000005e93

   1. Initial program 73.8%

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

   2. Taylor expanded in t around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 17: 42.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-133} \lor \neg \left(a \leq 2.95 \cdot 10^{-6}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -3.6e+14)
     t_1
     (if (<= a -1.22e-95)
       (* y (* x z))
       (if (or (<= a -2e-133) (not (<= a 2.95e-6))) t_1 (* (* y j) (- i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.6e+14) {
		tmp = t_1;
	} else if (a <= -1.22e-95) {
		tmp = y * (x * z);
	} else if ((a <= -2e-133) || !(a <= 2.95e-6)) {
		tmp = t_1;
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-3.6d+14)) then
        tmp = t_1
    else if (a <= (-1.22d-95)) then
        tmp = y * (x * z)
    else if ((a <= (-2d-133)) .or. (.not. (a <= 2.95d-6))) then
        tmp = t_1
    else
        tmp = (y * j) * -i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.6e+14) {
		tmp = t_1;
	} else if (a <= -1.22e-95) {
		tmp = y * (x * z);
	} else if ((a <= -2e-133) || !(a <= 2.95e-6)) {
		tmp = t_1;
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3.6e+14:
		tmp = t_1
	elif a <= -1.22e-95:
		tmp = y * (x * z)
	elif (a <= -2e-133) or not (a <= 2.95e-6):
		tmp = t_1
	else:
		tmp = (y * j) * -i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.6e+14)
		tmp = t_1;
	elseif (a <= -1.22e-95)
		tmp = Float64(y * Float64(x * z));
	elseif ((a <= -2e-133) || !(a <= 2.95e-6))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * j) * Float64(-i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3.6e+14)
		tmp = t_1;
	elseif (a <= -1.22e-95)
		tmp = y * (x * z);
	elseif ((a <= -2e-133) || ~((a <= 2.95e-6)))
		tmp = t_1;
	else
		tmp = (y * j) * -i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+14], t$95$1, If[LessEqual[a, -1.22e-95], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -2e-133], N[Not[LessEqual[a, 2.95e-6]], $MachinePrecision]], t$95$1, N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6e14 or -1.22e-95 < a < -2.0000000000000001e-133 or 2.95000000000000013e-6 < a

   1. Initial program 59.4%

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

   2. Taylor expanded in a around inf 68.5%

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

      1. associate-*r* 68.5%

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

      2. neg-mul-1 68.5%

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

      3. cancel-sign-sub 68.5%

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

      4. +-commutative 68.5%

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

      5. mul-1-neg 68.5%

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

      6. unsub-neg 68.5%

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

   4. Simplified 68.5%

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

   if -3.6e14 < a < -1.22e-95

   1. Initial program 86.8%

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

   2. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

   4. Simplified 47.6%

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

   5. Taylor expanded in z around inf 34.0%

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

   if -2.0000000000000001e-133 < a < 2.95000000000000013e-6

   1. Initial program 78.7%

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

   2. Taylor expanded in y around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in z around 0 31.0%

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

      1. mul-1-neg 31.0%

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

      2. associate-*r* 31.0%

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

      3. *-commutative 31.0%

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

      4. associate-*r* 34.5%

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

      5. distribute-rgt-neg-in 34.5%

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

      6. *-commutative 34.5%

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

      7. distribute-rgt-neg-in 34.5%

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

   7. Simplified 34.5%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-133} \lor \neg \left(a \leq 2.95 \cdot 10^{-6}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]

Alternative 18: 52.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -8.2e+16)
     t_2
     (if (<= a 2.3e-126)
       t_1
       (if (<= a 1.7e-32)
         (* t (- (* c j) (* x a)))
         (if (<= a 3e+51) 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 = y * ((x * z) - (i * j));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.2e+16) {
		tmp = t_2;
	} else if (a <= 2.3e-126) {
		tmp = t_1;
	} else if (a <= 1.7e-32) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= 3e+51) {
		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 = y * ((x * z) - (i * j))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-8.2d+16)) then
        tmp = t_2
    else if (a <= 2.3d-126) then
        tmp = t_1
    else if (a <= 1.7d-32) then
        tmp = t * ((c * j) - (x * a))
    else if (a <= 3d+51) 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 = y * ((x * z) - (i * j));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.2e+16) {
		tmp = t_2;
	} else if (a <= 2.3e-126) {
		tmp = t_1;
	} else if (a <= 1.7e-32) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= 3e+51) {
		tmp = t_1;
	} 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 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -8.2e+16:
		tmp = t_2
	elif a <= 2.3e-126:
		tmp = t_1
	elif a <= 1.7e-32:
		tmp = t * ((c * j) - (x * a))
	elif a <= 3e+51:
		tmp = t_1
	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(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.2e+16)
		tmp = t_2;
	elseif (a <= 2.3e-126)
		tmp = t_1;
	elseif (a <= 1.7e-32)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (a <= 3e+51)
		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 = y * ((x * z) - (i * j));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -8.2e+16)
		tmp = t_2;
	elseif (a <= 2.3e-126)
		tmp = t_1;
	elseif (a <= 1.7e-32)
		tmp = t * ((c * j) - (x * a));
	elseif (a <= 3e+51)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+16], t$95$2, If[LessEqual[a, 2.3e-126], t$95$1, If[LessEqual[a, 1.7e-32], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.2e16 or 3e51 < a

   1. Initial program 54.7%

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

   2. Taylor expanded in a around inf 71.6%

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

      1. associate-*r* 71.6%

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

      2. neg-mul-1 71.6%

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

      3. cancel-sign-sub 71.6%

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

      4. +-commutative 71.6%

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

      5. mul-1-neg 71.6%

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

      6. unsub-neg 71.6%

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

   4. Simplified 71.6%

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

   if -8.2e16 < a < 2.30000000000000011e-126 or 1.69999999999999989e-32 < a < 3e51

   1. Initial program 81.2%

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

   2. Taylor expanded in y around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

   4. Simplified 52.1%

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

   if 2.30000000000000011e-126 < a < 1.69999999999999989e-32

   1. Initial program 71.4%

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

   2. Taylor expanded in t around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

   4. Simplified 76.4%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 19: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{-34}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))) (t_2 (* c (* t j))) (t_3 (* y (* x z))))
   (if (<= z -2.75e-34)
     t_3
     (if (<= z -3.55e-183)
       t_1
       (if (<= z 5.2e-286)
         t_2
         (if (<= z 1.3e-231) t_1 (if (<= z 7.6e-31) t_2 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 = i * (a * b);
	double t_2 = c * (t * j);
	double t_3 = y * (x * z);
	double tmp;
	if (z <= -2.75e-34) {
		tmp = t_3;
	} else if (z <= -3.55e-183) {
		tmp = t_1;
	} else if (z <= 5.2e-286) {
		tmp = t_2;
	} else if (z <= 1.3e-231) {
		tmp = t_1;
	} else if (z <= 7.6e-31) {
		tmp = t_2;
	} 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 = i * (a * b)
    t_2 = c * (t * j)
    t_3 = y * (x * z)
    if (z <= (-2.75d-34)) then
        tmp = t_3
    else if (z <= (-3.55d-183)) then
        tmp = t_1
    else if (z <= 5.2d-286) then
        tmp = t_2
    else if (z <= 1.3d-231) then
        tmp = t_1
    else if (z <= 7.6d-31) then
        tmp = t_2
    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 = i * (a * b);
	double t_2 = c * (t * j);
	double t_3 = y * (x * z);
	double tmp;
	if (z <= -2.75e-34) {
		tmp = t_3;
	} else if (z <= -3.55e-183) {
		tmp = t_1;
	} else if (z <= 5.2e-286) {
		tmp = t_2;
	} else if (z <= 1.3e-231) {
		tmp = t_1;
	} else if (z <= 7.6e-31) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	t_2 = c * (t * j)
	t_3 = y * (x * z)
	tmp = 0
	if z <= -2.75e-34:
		tmp = t_3
	elif z <= -3.55e-183:
		tmp = t_1
	elif z <= 5.2e-286:
		tmp = t_2
	elif z <= 1.3e-231:
		tmp = t_1
	elif z <= 7.6e-31:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	t_2 = Float64(c * Float64(t * j))
	t_3 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -2.75e-34)
		tmp = t_3;
	elseif (z <= -3.55e-183)
		tmp = t_1;
	elseif (z <= 5.2e-286)
		tmp = t_2;
	elseif (z <= 1.3e-231)
		tmp = t_1;
	elseif (z <= 7.6e-31)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (a * b);
	t_2 = c * (t * j);
	t_3 = y * (x * z);
	tmp = 0.0;
	if (z <= -2.75e-34)
		tmp = t_3;
	elseif (z <= -3.55e-183)
		tmp = t_1;
	elseif (z <= 5.2e-286)
		tmp = t_2;
	elseif (z <= 1.3e-231)
		tmp = t_1;
	elseif (z <= 7.6e-31)
		tmp = t_2;
	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[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e-34], t$95$3, If[LessEqual[z, -3.55e-183], t$95$1, If[LessEqual[z, 5.2e-286], t$95$2, If[LessEqual[z, 1.3e-231], t$95$1, If[LessEqual[z, 7.6e-31], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.75000000000000007e-34 or 7.5999999999999999e-31 < z

   1. Initial program 63.2%

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

   2. Taylor expanded in y around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

   4. Simplified 52.8%

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

   5. Taylor expanded in z around inf 42.5%

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

   if -2.75000000000000007e-34 < z < -3.5499999999999998e-183 or 5.1999999999999999e-286 < z < 1.30000000000000001e-231

   1. Initial program 73.3%

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

   2. Taylor expanded in a around inf 57.4%

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

      1. associate-*r* 57.4%

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

      2. neg-mul-1 57.4%

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

      3. cancel-sign-sub 57.4%

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

      4. +-commutative 57.4%

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

      5. mul-1-neg 57.4%

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

      6. unsub-neg 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in i around inf 36.4%

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

   6. Taylor expanded in a around 0 43.4%

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

      1. *-commutative 43.4%

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

   8. Simplified 43.4%

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

   if -3.5499999999999998e-183 < z < 5.1999999999999999e-286 or 1.30000000000000001e-231 < z < 7.5999999999999999e-31

   1. Initial program 80.0%

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

   2. Taylor expanded in t around -inf 67.8%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in c around -inf 52.6%

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

   6. Taylor expanded in j around inf 31.4%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-183}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-286}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 20: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))) (t_2 (* c (* t j))))
   (if (<= z -5.6e-34)
     (* z (* x y))
     (if (<= z -3.1e-187)
       t_1
       (if (<= z 2.2e-280)
         t_2
         (if (<= z 6.6e-230) t_1 (if (<= z 2.4e-44) t_2 (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double t_2 = c * (t * j);
	double tmp;
	if (z <= -5.6e-34) {
		tmp = z * (x * y);
	} else if (z <= -3.1e-187) {
		tmp = t_1;
	} else if (z <= 2.2e-280) {
		tmp = t_2;
	} else if (z <= 6.6e-230) {
		tmp = t_1;
	} else if (z <= 2.4e-44) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (a * b)
    t_2 = c * (t * j)
    if (z <= (-5.6d-34)) then
        tmp = z * (x * y)
    else if (z <= (-3.1d-187)) then
        tmp = t_1
    else if (z <= 2.2d-280) then
        tmp = t_2
    else if (z <= 6.6d-230) then
        tmp = t_1
    else if (z <= 2.4d-44) then
        tmp = t_2
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double t_2 = c * (t * j);
	double tmp;
	if (z <= -5.6e-34) {
		tmp = z * (x * y);
	} else if (z <= -3.1e-187) {
		tmp = t_1;
	} else if (z <= 2.2e-280) {
		tmp = t_2;
	} else if (z <= 6.6e-230) {
		tmp = t_1;
	} else if (z <= 2.4e-44) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	t_2 = c * (t * j)
	tmp = 0
	if z <= -5.6e-34:
		tmp = z * (x * y)
	elif z <= -3.1e-187:
		tmp = t_1
	elif z <= 2.2e-280:
		tmp = t_2
	elif z <= 6.6e-230:
		tmp = t_1
	elif z <= 2.4e-44:
		tmp = t_2
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (z <= -5.6e-34)
		tmp = Float64(z * Float64(x * y));
	elseif (z <= -3.1e-187)
		tmp = t_1;
	elseif (z <= 2.2e-280)
		tmp = t_2;
	elseif (z <= 6.6e-230)
		tmp = t_1;
	elseif (z <= 2.4e-44)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (a * b);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (z <= -5.6e-34)
		tmp = z * (x * y);
	elseif (z <= -3.1e-187)
		tmp = t_1;
	elseif (z <= 2.2e-280)
		tmp = t_2;
	elseif (z <= 6.6e-230)
		tmp = t_1;
	elseif (z <= 2.4e-44)
		tmp = t_2;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-34], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-187], t$95$1, If[LessEqual[z, 2.2e-280], t$95$2, If[LessEqual[z, 6.6e-230], t$95$1, If[LessEqual[z, 2.4e-44], t$95$2, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.59999999999999994e-34

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in z around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-*l* 39.4%

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

   7. Simplified 39.4%

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

   if -5.59999999999999994e-34 < z < -3.10000000000000019e-187 or 2.2000000000000001e-280 < z < 6.59999999999999987e-230

   1. Initial program 73.3%

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

   2. Taylor expanded in a around inf 57.4%

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

      1. associate-*r* 57.4%

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

      2. neg-mul-1 57.4%

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

      3. cancel-sign-sub 57.4%

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

      4. +-commutative 57.4%

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

      5. mul-1-neg 57.4%

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

      6. unsub-neg 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in i around inf 36.4%

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

   6. Taylor expanded in a around 0 43.4%

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

      1. *-commutative 43.4%

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

   8. Simplified 43.4%

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

   if -3.10000000000000019e-187 < z < 2.2000000000000001e-280 or 6.59999999999999987e-230 < z < 2.40000000000000009e-44

   1. Initial program 80.0%

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

   2. Taylor expanded in t around -inf 67.8%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in c around -inf 52.6%

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

   6. Taylor expanded in j around inf 31.4%

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

   if 2.40000000000000009e-44 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in z around inf 46.2%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-280}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 21: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-184}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= z -2.8e-34)
     (* z (* x y))
     (if (<= z -2.1e-184)
       (* i (* a b))
       (if (<= z 1.8e-287)
         t_1
         (if (<= z 5.8e-229)
           (* b (* a i))
           (if (<= z 3.7e-44) t_1 (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (z <= -2.8e-34) {
		tmp = z * (x * y);
	} else if (z <= -2.1e-184) {
		tmp = i * (a * b);
	} else if (z <= 1.8e-287) {
		tmp = t_1;
	} else if (z <= 5.8e-229) {
		tmp = b * (a * i);
	} else if (z <= 3.7e-44) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (z <= (-2.8d-34)) then
        tmp = z * (x * y)
    else if (z <= (-2.1d-184)) then
        tmp = i * (a * b)
    else if (z <= 1.8d-287) then
        tmp = t_1
    else if (z <= 5.8d-229) then
        tmp = b * (a * i)
    else if (z <= 3.7d-44) then
        tmp = t_1
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (z <= -2.8e-34) {
		tmp = z * (x * y);
	} else if (z <= -2.1e-184) {
		tmp = i * (a * b);
	} else if (z <= 1.8e-287) {
		tmp = t_1;
	} else if (z <= 5.8e-229) {
		tmp = b * (a * i);
	} else if (z <= 3.7e-44) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if z <= -2.8e-34:
		tmp = z * (x * y)
	elif z <= -2.1e-184:
		tmp = i * (a * b)
	elif z <= 1.8e-287:
		tmp = t_1
	elif z <= 5.8e-229:
		tmp = b * (a * i)
	elif z <= 3.7e-44:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (z <= -2.8e-34)
		tmp = Float64(z * Float64(x * y));
	elseif (z <= -2.1e-184)
		tmp = Float64(i * Float64(a * b));
	elseif (z <= 1.8e-287)
		tmp = t_1;
	elseif (z <= 5.8e-229)
		tmp = Float64(b * Float64(a * i));
	elseif (z <= 3.7e-44)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (z <= -2.8e-34)
		tmp = z * (x * y);
	elseif (z <= -2.1e-184)
		tmp = i * (a * b);
	elseif (z <= 1.8e-287)
		tmp = t_1;
	elseif (z <= 5.8e-229)
		tmp = b * (a * i);
	elseif (z <= 3.7e-44)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-34], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-184], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-287], t$95$1, If[LessEqual[z, 5.8e-229], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-44], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.79999999999999997e-34

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in z around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-*l* 39.4%

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

   7. Simplified 39.4%

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

   if -2.79999999999999997e-34 < z < -2.0999999999999999e-184

   1. Initial program 78.7%

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

   2. Taylor expanded in a around inf 54.9%

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

      1. associate-*r* 54.9%

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

      2. neg-mul-1 54.9%

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

      3. cancel-sign-sub 54.9%

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

      4. +-commutative 54.9%

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

      5. mul-1-neg 54.9%

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

      6. unsub-neg 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in i around inf 38.1%

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

   6. Taylor expanded in a around 0 44.9%

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

      1. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -2.0999999999999999e-184 < z < 1.8000000000000001e-287 or 5.7999999999999999e-229 < z < 3.7e-44

   1. Initial program 80.0%

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

   2. Taylor expanded in t around -inf 67.8%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in c around -inf 52.6%

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

   6. Taylor expanded in j around inf 31.4%

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

   if 1.8000000000000001e-287 < z < 5.7999999999999999e-229

   1. Initial program 61.8%

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

      1. associate-+l- 61.8%

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

      2. sub-neg 61.8%

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

      3. sub-neg 61.8%

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

      4. *-commutative 61.8%

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

      5. fma-neg 61.8%

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

      6. *-commutative 61.8%

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

      7. *-commutative 61.8%

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

      8. fma-neg 77.2%

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

      9. distribute-lft-neg-out 77.2%

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

      10. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in b around inf 40.3%

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

   5. Taylor expanded in a around inf 40.1%

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

   if 3.7e-44 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in z around inf 46.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-184}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-287}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 22: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= z -3.4e-34)
     (* x (* y z))
     (if (<= z -7.4e-186)
       (* i (* a b))
       (if (<= z 4.6e-289)
         t_1
         (if (<= z 8.8e-231)
           (* b (* a i))
           (if (<= z 4.6e-44) t_1 (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (z <= -3.4e-34) {
		tmp = x * (y * z);
	} else if (z <= -7.4e-186) {
		tmp = i * (a * b);
	} else if (z <= 4.6e-289) {
		tmp = t_1;
	} else if (z <= 8.8e-231) {
		tmp = b * (a * i);
	} else if (z <= 4.6e-44) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (z <= (-3.4d-34)) then
        tmp = x * (y * z)
    else if (z <= (-7.4d-186)) then
        tmp = i * (a * b)
    else if (z <= 4.6d-289) then
        tmp = t_1
    else if (z <= 8.8d-231) then
        tmp = b * (a * i)
    else if (z <= 4.6d-44) then
        tmp = t_1
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (z <= -3.4e-34) {
		tmp = x * (y * z);
	} else if (z <= -7.4e-186) {
		tmp = i * (a * b);
	} else if (z <= 4.6e-289) {
		tmp = t_1;
	} else if (z <= 8.8e-231) {
		tmp = b * (a * i);
	} else if (z <= 4.6e-44) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if z <= -3.4e-34:
		tmp = x * (y * z)
	elif z <= -7.4e-186:
		tmp = i * (a * b)
	elif z <= 4.6e-289:
		tmp = t_1
	elif z <= 8.8e-231:
		tmp = b * (a * i)
	elif z <= 4.6e-44:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (z <= -3.4e-34)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -7.4e-186)
		tmp = Float64(i * Float64(a * b));
	elseif (z <= 4.6e-289)
		tmp = t_1;
	elseif (z <= 8.8e-231)
		tmp = Float64(b * Float64(a * i));
	elseif (z <= 4.6e-44)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (z <= -3.4e-34)
		tmp = x * (y * z);
	elseif (z <= -7.4e-186)
		tmp = i * (a * b);
	elseif (z <= 4.6e-289)
		tmp = t_1;
	elseif (z <= 8.8e-231)
		tmp = b * (a * i);
	elseif (z <= 4.6e-44)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-34], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-186], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-289], t$95$1, If[LessEqual[z, 8.8e-231], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-44], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.4000000000000001e-34

   1. Initial program 60.9%

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

   2. Taylor expanded in t around -inf 60.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in x around inf 53.2%

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

   6. Taylor expanded in y around inf 41.0%

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

   if -3.4000000000000001e-34 < z < -7.4000000000000004e-186

   1. Initial program 78.7%

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

   2. Taylor expanded in a around inf 54.9%

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

      1. associate-*r* 54.9%

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

      2. neg-mul-1 54.9%

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

      3. cancel-sign-sub 54.9%

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

      4. +-commutative 54.9%

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

      5. mul-1-neg 54.9%

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

      6. unsub-neg 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in i around inf 38.1%

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

   6. Taylor expanded in a around 0 44.9%

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

      1. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -7.4000000000000004e-186 < z < 4.6000000000000004e-289 or 8.80000000000000036e-231 < z < 4.59999999999999996e-44

   1. Initial program 80.0%

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

   2. Taylor expanded in t around -inf 67.8%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in c around -inf 52.6%

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

   6. Taylor expanded in j around inf 31.4%

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

   if 4.6000000000000004e-289 < z < 8.80000000000000036e-231

   1. Initial program 61.8%

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

      1. associate-+l- 61.8%

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

      2. sub-neg 61.8%

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

      3. sub-neg 61.8%

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

      4. *-commutative 61.8%

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

      5. fma-neg 61.8%

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

      6. *-commutative 61.8%

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

      7. *-commutative 61.8%

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

      8. fma-neg 77.2%

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

      9. distribute-lft-neg-out 77.2%

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

      10. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in b around inf 40.3%

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

   5. Taylor expanded in a around inf 40.1%

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

   if 4.59999999999999996e-44 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in z around inf 46.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 23: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+277}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.4e+277)
   (* (* z c) (- b))
   (if (<= z -4.6e-34)
     (* x (* y z))
     (if (<= z -6.5e-164)
       (* i (* a b))
       (if (<= z 5.1e-197)
         (* a (* t (- x)))
         (if (<= z 9e-42) (* c (* t j)) (* y (* x z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.4e+277) {
		tmp = (z * c) * -b;
	} else if (z <= -4.6e-34) {
		tmp = x * (y * z);
	} else if (z <= -6.5e-164) {
		tmp = i * (a * b);
	} else if (z <= 5.1e-197) {
		tmp = a * (t * -x);
	} else if (z <= 9e-42) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.4d+277)) then
        tmp = (z * c) * -b
    else if (z <= (-4.6d-34)) then
        tmp = x * (y * z)
    else if (z <= (-6.5d-164)) then
        tmp = i * (a * b)
    else if (z <= 5.1d-197) then
        tmp = a * (t * -x)
    else if (z <= 9d-42) then
        tmp = c * (t * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.4e+277) {
		tmp = (z * c) * -b;
	} else if (z <= -4.6e-34) {
		tmp = x * (y * z);
	} else if (z <= -6.5e-164) {
		tmp = i * (a * b);
	} else if (z <= 5.1e-197) {
		tmp = a * (t * -x);
	} else if (z <= 9e-42) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.4e+277:
		tmp = (z * c) * -b
	elif z <= -4.6e-34:
		tmp = x * (y * z)
	elif z <= -6.5e-164:
		tmp = i * (a * b)
	elif z <= 5.1e-197:
		tmp = a * (t * -x)
	elif z <= 9e-42:
		tmp = c * (t * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.4e+277)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (z <= -4.6e-34)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -6.5e-164)
		tmp = Float64(i * Float64(a * b));
	elseif (z <= 5.1e-197)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (z <= 9e-42)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.4e+277)
		tmp = (z * c) * -b;
	elseif (z <= -4.6e-34)
		tmp = x * (y * z);
	elseif (z <= -6.5e-164)
		tmp = i * (a * b);
	elseif (z <= 5.1e-197)
		tmp = a * (t * -x);
	elseif (z <= 9e-42)
		tmp = c * (t * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.4e+277], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[z, -4.6e-34], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-164], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-197], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-42], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.4000000000000001e277

   1. Initial program 55.6%

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

      1. associate-+l- 55.6%

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

      2. sub-neg 55.6%

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

      3. sub-neg 55.6%

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

      4. *-commutative 55.6%

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

      5. fma-neg 55.6%

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

      6. *-commutative 55.6%

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

      7. *-commutative 55.6%

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

      8. fma-neg 55.6%

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

      9. distribute-lft-neg-out 55.6%

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

      10. *-commutative 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in b around inf 67.6%

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

   5. Taylor expanded in a around 0 67.6%

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

      1. neg-mul-1 67.6%

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

      2. distribute-rgt-neg-in 67.6%

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

   7. Simplified 67.6%

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

   if -3.4000000000000001e277 < z < -4.60000000000000022e-34

   1. Initial program 61.7%

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

   2. Taylor expanded in t around -inf 63.3%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in x around inf 56.2%

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

   6. Taylor expanded in y around inf 43.8%

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

   if -4.60000000000000022e-34 < z < -6.50000000000000004e-164

   1. Initial program 81.9%

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

   2. Taylor expanded in a around inf 51.5%

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

      1. associate-*r* 51.5%

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

      2. neg-mul-1 51.5%

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

      3. cancel-sign-sub 51.5%

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

      4. +-commutative 51.5%

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

      5. mul-1-neg 51.5%

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

      6. unsub-neg 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in i around inf 39.0%

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

   6. Taylor expanded in a around 0 47.7%

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

      1. *-commutative 47.7%

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

   8. Simplified 47.7%

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

   if -6.50000000000000004e-164 < z < 5.1000000000000003e-197

   1. Initial program 76.0%

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

   2. Taylor expanded in a around inf 55.8%

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

      1. associate-*r* 55.8%

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

      2. neg-mul-1 55.8%

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

      3. cancel-sign-sub 55.8%

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

      4. +-commutative 55.8%

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

      5. mul-1-neg 55.8%

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

      6. unsub-neg 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in i around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. distribute-lft-neg-out 41.6%

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

      3. *-commutative 41.6%

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

   7. Simplified 41.6%

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

   if 5.1000000000000003e-197 < z < 9e-42

   1. Initial program 79.5%

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

   2. Taylor expanded in t around -inf 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in c around -inf 53.8%

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

   6. Taylor expanded in j around inf 39.9%

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

   if 9e-42 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in z around inf 46.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+277}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 24: 30.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.95e-34)
   (* x (* y z))
   (if (<= z -1.9e-167)
     (* i (* a b))
     (if (<= z 1.55e-198)
       (* a (* t (- x)))
       (if (<= z 1.2e-35) (* c (* t j)) (* y (* x z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.95e-34) {
		tmp = x * (y * z);
	} else if (z <= -1.9e-167) {
		tmp = i * (a * b);
	} else if (z <= 1.55e-198) {
		tmp = a * (t * -x);
	} else if (z <= 1.2e-35) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.95d-34)) then
        tmp = x * (y * z)
    else if (z <= (-1.9d-167)) then
        tmp = i * (a * b)
    else if (z <= 1.55d-198) then
        tmp = a * (t * -x)
    else if (z <= 1.2d-35) then
        tmp = c * (t * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.95e-34) {
		tmp = x * (y * z);
	} else if (z <= -1.9e-167) {
		tmp = i * (a * b);
	} else if (z <= 1.55e-198) {
		tmp = a * (t * -x);
	} else if (z <= 1.2e-35) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.95e-34:
		tmp = x * (y * z)
	elif z <= -1.9e-167:
		tmp = i * (a * b)
	elif z <= 1.55e-198:
		tmp = a * (t * -x)
	elif z <= 1.2e-35:
		tmp = c * (t * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.95e-34)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -1.9e-167)
		tmp = Float64(i * Float64(a * b));
	elseif (z <= 1.55e-198)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (z <= 1.2e-35)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.95e-34)
		tmp = x * (y * z);
	elseif (z <= -1.9e-167)
		tmp = i * (a * b);
	elseif (z <= 1.55e-198)
		tmp = a * (t * -x);
	elseif (z <= 1.2e-35)
		tmp = c * (t * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.95e-34], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-167], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-198], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-35], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.9500000000000001e-34

   1. Initial program 60.9%

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

   2. Taylor expanded in t around -inf 60.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in x around inf 53.2%

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

   6. Taylor expanded in y around inf 41.0%

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

   if -2.9500000000000001e-34 < z < -1.89999999999999984e-167

   1. Initial program 81.9%

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

   2. Taylor expanded in a around inf 51.5%

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

      1. associate-*r* 51.5%

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

      2. neg-mul-1 51.5%

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

      3. cancel-sign-sub 51.5%

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

      4. +-commutative 51.5%

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

      5. mul-1-neg 51.5%

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

      6. unsub-neg 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in i around inf 39.0%

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

   6. Taylor expanded in a around 0 47.7%

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

      1. *-commutative 47.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot a\right)} \]

   8. Simplified 47.7%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   if -1.89999999999999984e-167 < z < 1.5499999999999999e-198

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 55.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 55.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 55.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 55.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 55.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 55.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 55.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 55.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around 0 41.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 41.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 41.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   7. Simplified 41.6%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 1.5499999999999999e-198 < z < 1.2000000000000001e-35

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around -inf 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   4. Simplified 68.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot a - c \cdot z\right)\right) - t \cdot \left(a \cdot x - c \cdot j\right)} \]

   5. Taylor expanded in c around -inf 53.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} - t \cdot \left(a \cdot x - c \cdot j\right) \]

   6. Taylor expanded in j around inf 39.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 1.2000000000000001e-35 < z

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around inf 57.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   3. Step-by-step derivation

      1. +-commutative 57.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 57.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 57.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   4. Simplified 57.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around inf 46.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 25: 52.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+40} \lor \neg \left(c \leq 0.00043\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.95e+40) (not (<= c 0.00043)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* 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 ((c <= -1.95e+40) || !(c <= 0.00043)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (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 ((c <= (-1.95d+40)) .or. (.not. (c <= 0.00043d0))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (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 ((c <= -1.95e+40) || !(c <= 0.00043)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.95e+40) or not (c <= 0.00043):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.95e+40) || !(c <= 0.00043))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - 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 ((c <= -1.95e+40) || ~((c <= 0.00043)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.95e+40], N[Not[LessEqual[c, 0.00043]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.95e40 or 4.29999999999999989e-4 < c

   1. Initial program 61.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 60.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 60.7%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 60.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -1.95e40 < c < 4.29999999999999989e-4

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 42.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 42.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 42.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 42.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 42.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 42.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 42.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+40} \lor \neg \left(c \leq 0.00043\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 26: 51.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+40} \lor \neg \left(c \leq 49000000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.15e+40) (not (<= c 49000000000000.0)))
   (* c (- (* t j) (* z b)))
   (* i (- (* a b) (* y 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 <= -1.15e+40) || !(c <= 49000000000000.0)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = i * ((a * b) - (y * 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 <= (-1.15d+40)) .or. (.not. (c <= 49000000000000.0d0))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = i * ((a * b) - (y * 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 <= -1.15e+40) || !(c <= 49000000000000.0)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.15e+40) or not (c <= 49000000000000.0):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.15e+40) || !(c <= 49000000000000.0))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.15e+40) || ~((c <= 49000000000000.0)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.15e+40], N[Not[LessEqual[c, 49000000000000.0]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.14999999999999997e40 or 4.9e13 < c

   1. Initial program 60.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 61.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 61.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -1.14999999999999997e40 < c < 4.9e13

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in i around inf 42.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   3. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. associate-*r* 42.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot a\right) \cdot b}\right) \]

      3. neg-mul-1 42.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-a\right)} \cdot b\right) \]

      4. cancel-sign-sub 42.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + a \cdot b\right)} \]

      5. +-commutative 42.5%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 42.5%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 42.5%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

   4. Simplified 42.5%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+40} \lor \neg \left(c \leq 49000000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 27: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.28 \cdot 10^{-23} \lor \neg \left(i \leq 7.2 \cdot 10^{-96}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.28e-23) (not (<= i 7.2e-96))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.28e-23) || !(i <= 7.2e-96)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.28d-23)) .or. (.not. (i <= 7.2d-96))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.28e-23) || !(i <= 7.2e-96)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.28e-23) or not (i <= 7.2e-96):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.28e-23) || !(i <= 7.2e-96))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.28e-23) || ~((i <= 7.2e-96)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.28e-23], N[Not[LessEqual[i, 7.2e-96]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.28000000000000005e-23 or 7.20000000000000016e-96 < i

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 47.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 47.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 47.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 47.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 47.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 30.1%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   if -1.28000000000000005e-23 < i < 7.20000000000000016e-96

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around -inf 75.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   4. Simplified 83.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot a - c \cdot z\right)\right) - t \cdot \left(a \cdot x - c \cdot j\right)} \]

   5. Taylor expanded in c around -inf 60.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} - t \cdot \left(a \cdot x - c \cdot j\right) \]

   6. Taylor expanded in j around inf 27.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.28 \cdot 10^{-23} \lor \neg \left(i \leq 7.2 \cdot 10^{-96}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 28: 30.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6500000 \lor \neg \left(j \leq 1.75 \cdot 10^{+45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6500000.0) (not (<= j 1.75e+45))) (* c (* t j)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6500000.0) || !(j <= 1.75e+45)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-6500000.0d0)) .or. (.not. (j <= 1.75d+45))) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6500000.0) || !(j <= 1.75e+45)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6500000.0) or not (j <= 1.75e+45):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6500000.0) || !(j <= 1.75e+45))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6500000.0) || ~((j <= 1.75e+45)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6500000.0], N[Not[LessEqual[j, 1.75e+45]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.5e6 or 1.75000000000000011e45 < j

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around -inf 56.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot j\right)\right) + \left(-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   4. Simplified 62.3%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot a - c \cdot z\right)\right) - t \cdot \left(a \cdot x - c \cdot j\right)} \]

   5. Taylor expanded in c around -inf 50.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} - t \cdot \left(a \cdot x - c \cdot j\right) \]

   6. Taylor expanded in j around inf 36.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -6.5e6 < j < 1.75000000000000011e45

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 44.4%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 44.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 44.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 44.4%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 44.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 22.9%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Taylor expanded in a around 0 23.5%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. *-commutative 23.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot a\right)} \]

   8. Simplified 23.5%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6500000 \lor \neg \left(j \leq 1.75 \cdot 10^{+45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 29: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in a around inf 38.4%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
3. Step-by-step derivation

   1. associate-*r* 38.4%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

   2. neg-mul-1 38.4%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

   3. cancel-sign-sub 38.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   4. +-commutative 38.4%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg 38.4%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   6. unsub-neg 38.4%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

4. Simplified 38.4%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

5. Taylor expanded in i around inf 18.9%

   \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

6. Final simplification 18.9%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))