Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.0% → 81.9%

Time: 33.8s

Alternatives: 25

Speedup: 0.5×

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

Specification

Math

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

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: 73.0% 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: 81.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	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 * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * ((t * j) - (z * b))
	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(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.0%

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

   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 c around inf 57.9%

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

4. Final simplification 84.4%

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

Alternative 2: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t_3 + t_1\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;t_3 + t_2\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-179}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;t_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (+ t_3 t_1)))
   (if (<= x -1.25e-16)
     (+ t_3 t_2)
     (if (<= x -2.4e-78)
       (* a (- (* b i) (* x t)))
       (if (<= x -5.2e-114)
         (* y (- (* x z) (* i j)))
         (if (<= x 1.05e-179)
           t_4
           (if (<= x 9.8e-98)
             (- t_1 (* a (* x t)))
             (if (<= x 1.85e+27) t_4 (- t_2 (* c (* z b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_1;
	double tmp;
	if (x <= -1.25e-16) {
		tmp = t_3 + t_2;
	} else if (x <= -2.4e-78) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -5.2e-114) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.05e-179) {
		tmp = t_4;
	} else if (x <= 9.8e-98) {
		tmp = t_1 - (a * (x * t));
	} else if (x <= 1.85e+27) {
		tmp = t_4;
	} else {
		tmp = t_2 - (c * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    t_4 = t_3 + t_1
    if (x <= (-1.25d-16)) then
        tmp = t_3 + t_2
    else if (x <= (-2.4d-78)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= (-5.2d-114)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 1.05d-179) then
        tmp = t_4
    else if (x <= 9.8d-98) then
        tmp = t_1 - (a * (x * t))
    else if (x <= 1.85d+27) then
        tmp = t_4
    else
        tmp = t_2 - (c * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_1;
	double tmp;
	if (x <= -1.25e-16) {
		tmp = t_3 + t_2;
	} else if (x <= -2.4e-78) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -5.2e-114) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.05e-179) {
		tmp = t_4;
	} else if (x <= 9.8e-98) {
		tmp = t_1 - (a * (x * t));
	} else if (x <= 1.85e+27) {
		tmp = t_4;
	} else {
		tmp = t_2 - (c * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((t * c) - (y * i))
	t_4 = t_3 + t_1
	tmp = 0
	if x <= -1.25e-16:
		tmp = t_3 + t_2
	elif x <= -2.4e-78:
		tmp = a * ((b * i) - (x * t))
	elif x <= -5.2e-114:
		tmp = y * ((x * z) - (i * j))
	elif x <= 1.05e-179:
		tmp = t_4
	elif x <= 9.8e-98:
		tmp = t_1 - (a * (x * t))
	elif x <= 1.85e+27:
		tmp = t_4
	else:
		tmp = t_2 - (c * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(t_3 + t_1)
	tmp = 0.0
	if (x <= -1.25e-16)
		tmp = Float64(t_3 + t_2);
	elseif (x <= -2.4e-78)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= -5.2e-114)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 1.05e-179)
		tmp = t_4;
	elseif (x <= 9.8e-98)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (x <= 1.85e+27)
		tmp = t_4;
	else
		tmp = Float64(t_2 - Float64(c * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((t * c) - (y * i));
	t_4 = t_3 + t_1;
	tmp = 0.0;
	if (x <= -1.25e-16)
		tmp = t_3 + t_2;
	elseif (x <= -2.4e-78)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= -5.2e-114)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 1.05e-179)
		tmp = t_4;
	elseif (x <= 9.8e-98)
		tmp = t_1 - (a * (x * t));
	elseif (x <= 1.85e+27)
		tmp = t_4;
	else
		tmp = t_2 - (c * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, If[LessEqual[x, -1.25e-16], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[x, -2.4e-78], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-114], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-179], t$95$4, If[LessEqual[x, 9.8e-98], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+27], t$95$4, N[(t$95$2 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.2500000000000001e-16

   1. Initial program 80.8%

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

   2. Taylor expanded in b around 0 78.4%

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

   if -1.2500000000000001e-16 < x < -2.4e-78

   1. Initial program 48.4%

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

   2. Taylor expanded in a around inf 69.5%

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

      1. distribute-lft-out-- 69.5%

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

      2. *-commutative 69.5%

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

   4. Simplified 69.5%

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

   if -2.4e-78 < x < -5.20000000000000026e-114

   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 y around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

      4. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   if -5.20000000000000026e-114 < x < 1.0499999999999999e-179 or 9.80000000000000028e-98 < x < 1.85000000000000001e27

   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 x around 0 76.6%

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

   if 1.0499999999999999e-179 < x < 9.80000000000000028e-98

   1. Initial program 58.4%

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

   2. Taylor expanded in j around 0 69.3%

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

      1. fma-neg 69.3%

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

      2. *-commutative 69.3%

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

      3. *-commutative 69.3%

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

      4. fma-neg 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in y around 0 74.4%

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

      1. associate-*r* 74.4%

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

      2. neg-mul-1 74.4%

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

      3. *-commutative 74.4%

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

   7. Simplified 74.4%

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

   if 1.85000000000000001e27 < x

   1. Initial program 75.5%

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

   2. Taylor expanded in j around 0 78.7%

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

      1. fma-neg 80.2%

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

      2. *-commutative 80.2%

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

      3. *-commutative 80.2%

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

      4. fma-neg 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in c around inf 75.7%

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

      1. *-commutative 74.0%

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

      2. associate-*l* 75.5%

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

      3. *-commutative 75.5%

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

   7. Simplified 77.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 3: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(t_1 - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* t c) (* y i))) (- t_1 (* c (* z b))))))
   (if (<= j -1.25e-50)
     t_2
     (if (<= j 1.4e+58)
       (+ t_1 (* b (- (* a i) (* z c))))
       (if (<= j 2.2e+250) t_2 (* c (- (* t j) (* z b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (j * ((t * c) - (y * i))) + (t_1 - (c * (z * b)));
	double tmp;
	if (j <= -1.25e-50) {
		tmp = t_2;
	} else if (j <= 1.4e+58) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (j <= 2.2e+250) {
		tmp = t_2;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (j * ((t * c) - (y * i))) + (t_1 - (c * (z * b)))
    if (j <= (-1.25d-50)) then
        tmp = t_2
    else if (j <= 1.4d+58) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else if (j <= 2.2d+250) then
        tmp = t_2
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (j * ((t * c) - (y * i))) + (t_1 - (c * (z * b)));
	double tmp;
	if (j <= -1.25e-50) {
		tmp = t_2;
	} else if (j <= 1.4e+58) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (j <= 2.2e+250) {
		tmp = t_2;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (j * ((t * c) - (y * i))) + (t_1 - (c * (z * b)))
	tmp = 0
	if j <= -1.25e-50:
		tmp = t_2
	elif j <= 1.4e+58:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	elif j <= 2.2e+250:
		tmp = t_2
	else:
		tmp = c * ((t * j) - (z * b))
	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(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_1 - Float64(c * Float64(z * b))))
	tmp = 0.0
	if (j <= -1.25e-50)
		tmp = t_2;
	elseif (j <= 1.4e+58)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 2.2e+250)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (j * ((t * c) - (y * i))) + (t_1 - (c * (z * b)));
	tmp = 0.0;
	if (j <= -1.25e-50)
		tmp = t_2;
	elseif (j <= 1.4e+58)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	elseif (j <= 2.2e+250)
		tmp = t_2;
	else
		tmp = c * ((t * j) - (z * b));
	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[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e-50], t$95$2, If[LessEqual[j, 1.4e+58], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+250], t$95$2, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.24999999999999992e-50 or 1.3999999999999999e58 < j < 2.20000000000000014e250

   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 c around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*l* 76.0%

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

      3. *-commutative 76.0%

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

   4. Simplified 76.0%

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

   if -1.24999999999999992e-50 < j < 1.3999999999999999e58

   1. Initial program 76.9%

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

   2. Taylor expanded in j around 0 81.4%

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

      1. fma-neg 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

      4. fma-neg 81.4%

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

   4. Simplified 81.4%

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

   if 2.20000000000000014e250 < j

   1. Initial program 55.1%

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

   2. Taylor expanded in c around inf 93.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+250}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 4: 29.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -3.4 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 10^{+21}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+243}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* i (* y (- j)))))
   (if (<= j -3.4e+134)
     t_2
     (if (<= j -5e-67)
       t_1
       (if (<= j -1.05e-304)
         (* x (* y z))
         (if (<= j 1.45e-213)
           (* i (* a b))
           (if (<= j 7.5e-146)
             (* z (* x y))
             (if (<= j 1.95e-50)
               t_1
               (if (<= j 1e+21)
                 (* c (- (* z b)))
                 (if (<= j 6.8e+41)
                   t_1
                   (if (<= j 1.16e+114)
                     (* j (- (* y i)))
                     (if (<= j 3.6e+198)
                       (* t (* c j))
                       (if (<= j 1.05e+243) t_2 (* 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 t_1 = x * (t * -a);
	double t_2 = i * (y * -j);
	double tmp;
	if (j <= -3.4e+134) {
		tmp = t_2;
	} else if (j <= -5e-67) {
		tmp = t_1;
	} else if (j <= -1.05e-304) {
		tmp = x * (y * z);
	} else if (j <= 1.45e-213) {
		tmp = i * (a * b);
	} else if (j <= 7.5e-146) {
		tmp = z * (x * y);
	} else if (j <= 1.95e-50) {
		tmp = t_1;
	} else if (j <= 1e+21) {
		tmp = c * -(z * b);
	} else if (j <= 6.8e+41) {
		tmp = t_1;
	} else if (j <= 1.16e+114) {
		tmp = j * -(y * i);
	} else if (j <= 3.6e+198) {
		tmp = t * (c * j);
	} else if (j <= 1.05e+243) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t * -a)
    t_2 = i * (y * -j)
    if (j <= (-3.4d+134)) then
        tmp = t_2
    else if (j <= (-5d-67)) then
        tmp = t_1
    else if (j <= (-1.05d-304)) then
        tmp = x * (y * z)
    else if (j <= 1.45d-213) then
        tmp = i * (a * b)
    else if (j <= 7.5d-146) then
        tmp = z * (x * y)
    else if (j <= 1.95d-50) then
        tmp = t_1
    else if (j <= 1d+21) then
        tmp = c * -(z * b)
    else if (j <= 6.8d+41) then
        tmp = t_1
    else if (j <= 1.16d+114) then
        tmp = j * -(y * i)
    else if (j <= 3.6d+198) then
        tmp = t * (c * j)
    else if (j <= 1.05d+243) then
        tmp = t_2
    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 t_1 = x * (t * -a);
	double t_2 = i * (y * -j);
	double tmp;
	if (j <= -3.4e+134) {
		tmp = t_2;
	} else if (j <= -5e-67) {
		tmp = t_1;
	} else if (j <= -1.05e-304) {
		tmp = x * (y * z);
	} else if (j <= 1.45e-213) {
		tmp = i * (a * b);
	} else if (j <= 7.5e-146) {
		tmp = z * (x * y);
	} else if (j <= 1.95e-50) {
		tmp = t_1;
	} else if (j <= 1e+21) {
		tmp = c * -(z * b);
	} else if (j <= 6.8e+41) {
		tmp = t_1;
	} else if (j <= 1.16e+114) {
		tmp = j * -(y * i);
	} else if (j <= 3.6e+198) {
		tmp = t * (c * j);
	} else if (j <= 1.05e+243) {
		tmp = t_2;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = i * (y * -j)
	tmp = 0
	if j <= -3.4e+134:
		tmp = t_2
	elif j <= -5e-67:
		tmp = t_1
	elif j <= -1.05e-304:
		tmp = x * (y * z)
	elif j <= 1.45e-213:
		tmp = i * (a * b)
	elif j <= 7.5e-146:
		tmp = z * (x * y)
	elif j <= 1.95e-50:
		tmp = t_1
	elif j <= 1e+21:
		tmp = c * -(z * b)
	elif j <= 6.8e+41:
		tmp = t_1
	elif j <= 1.16e+114:
		tmp = j * -(y * i)
	elif j <= 3.6e+198:
		tmp = t * (c * j)
	elif j <= 1.05e+243:
		tmp = t_2
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (j <= -3.4e+134)
		tmp = t_2;
	elseif (j <= -5e-67)
		tmp = t_1;
	elseif (j <= -1.05e-304)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.45e-213)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 7.5e-146)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 1.95e-50)
		tmp = t_1;
	elseif (j <= 1e+21)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (j <= 6.8e+41)
		tmp = t_1;
	elseif (j <= 1.16e+114)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (j <= 3.6e+198)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 1.05e+243)
		tmp = t_2;
	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)
	t_1 = x * (t * -a);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (j <= -3.4e+134)
		tmp = t_2;
	elseif (j <= -5e-67)
		tmp = t_1;
	elseif (j <= -1.05e-304)
		tmp = x * (y * z);
	elseif (j <= 1.45e-213)
		tmp = i * (a * b);
	elseif (j <= 7.5e-146)
		tmp = z * (x * y);
	elseif (j <= 1.95e-50)
		tmp = t_1;
	elseif (j <= 1e+21)
		tmp = c * -(z * b);
	elseif (j <= 6.8e+41)
		tmp = t_1;
	elseif (j <= 1.16e+114)
		tmp = j * -(y * i);
	elseif (j <= 3.6e+198)
		tmp = t * (c * j);
	elseif (j <= 1.05e+243)
		tmp = t_2;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.4e+134], t$95$2, If[LessEqual[j, -5e-67], t$95$1, If[LessEqual[j, -1.05e-304], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e-213], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-146], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.95e-50], t$95$1, If[LessEqual[j, 1e+21], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 6.8e+41], t$95$1, If[LessEqual[j, 1.16e+114], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 3.6e+198], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e+243], t$95$2, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -3.40000000000000018e134 or 3.6000000000000002e198 < j < 1.05e243

   1. Initial program 66.7%

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

   2. Taylor expanded in c around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*l* 72.0%

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

      3. *-commutative 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in i around inf 65.0%

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

      1. associate-*r* 65.0%

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

      2. neg-mul-1 65.0%

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

   7. Simplified 65.0%

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

   if -3.40000000000000018e134 < j < -4.9999999999999999e-67 or 7.49999999999999981e-146 < j < 1.9500000000000001e-50 or 1e21 < j < 6.79999999999999996e41

   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 j around 0 72.1%

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

      1. fma-neg 73.7%

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

      2. *-commutative 73.7%

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

      3. *-commutative 73.7%

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

      4. fma-neg 72.1%

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

   4. Simplified 72.1%

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

      1. *-commutative 72.1%

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

      2. prod-diff 67.7%

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

      3. fma-neg 67.7%

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

      4. cancel-sign-sub-inv 67.7%

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

      5. fma-def 67.7%

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

      6. *-commutative 67.7%

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

   6. Applied egg-rr 67.7%

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

   7. Taylor expanded in t around inf 41.7%

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

      1. associate-*r* 41.7%

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

      2. *-commutative 41.7%

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

      3. neg-mul-1 41.7%

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

      4. *-commutative 41.7%

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

      5. associate-*l* 44.5%

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

   9. Simplified 44.5%

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

   if -4.9999999999999999e-67 < j < -1.05000000000000004e-304

   1. Initial program 70.3%

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

   2. Taylor expanded in y around inf 39.2%

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

      1. +-commutative 39.2%

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

      2. mul-1-neg 39.2%

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

      3. unsub-neg 39.2%

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

      4. *-commutative 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in z around inf 39.0%

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

   if -1.05000000000000004e-304 < j < 1.45e-213

   1. Initial program 82.3%

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

   2. Taylor expanded in j around 0 86.6%

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

      1. fma-neg 86.6%

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

      2. *-commutative 86.6%

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

      3. *-commutative 86.6%

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

      4. fma-neg 86.6%

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

   4. Simplified 86.6%

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

      1. *-commutative 86.6%

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

      2. prod-diff 75.7%

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

      3. fma-neg 75.6%

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

      4. cancel-sign-sub-inv 75.6%

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

      5. fma-def 75.7%

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

      6. *-commutative 75.7%

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

   6. Applied egg-rr 75.7%

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

   7. Taylor expanded in i around inf 38.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \color{blue}{-b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)} \]

      2. *-commutative 38.7%

         \[\leadsto -\color{blue}{\left(i \cdot \left(a + -2 \cdot a\right)\right) \cdot b} \]

      3. distribute-rgt-in 27.8%

         \[\leadsto -\color{blue}{\left(a \cdot i + \left(-2 \cdot a\right) \cdot i\right)} \cdot b \]

      4. associate-*r* 27.8%

         \[\leadsto -\left(a \cdot i + \color{blue}{-2 \cdot \left(a \cdot i\right)}\right) \cdot b \]

      5. +-commutative 27.8%

         \[\leadsto -\color{blue}{\left(-2 \cdot \left(a \cdot i\right) + a \cdot i\right)} \cdot b \]

      6. distribute-lft1-in 38.7%

         \[\leadsto -\color{blue}{\left(\left(-2 + 1\right) \cdot \left(a \cdot i\right)\right)} \cdot b \]

      7. metadata-eval 38.7%

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

      8. neg-mul-1 38.7%

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

      9. distribute-lft-neg-in 38.7%

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

      10. associate-*r* 42.0%

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

      11. remove-double-neg 42.0%

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

      12. *-commutative 42.0%

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

      13. associate-*l* 43.8%

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

      14. *-commutative 43.8%

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

   9. Simplified 43.8%

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

   if 1.45e-213 < j < 7.49999999999999981e-146

   1. Initial program 74.0%

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

   2. Taylor expanded in y around inf 41.9%

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

      1. +-commutative 41.9%

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

      2. mul-1-neg 41.9%

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

      3. unsub-neg 41.9%

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

      4. *-commutative 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in z around inf 48.4%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   if 1.9500000000000001e-50 < j < 1e21

   1. Initial program 86.4%

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

   2. Taylor expanded in c around inf 48.2%

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

   3. Taylor expanded in j around 0 42.0%

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

      1. neg-mul-1 42.0%

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

      2. distribute-lft-neg-in 42.0%

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

      3. *-commutative 42.0%

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

   5. Simplified 42.0%

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

   if 6.79999999999999996e41 < j < 1.15999999999999994e114

   1. Initial program 90.8%

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

   2. Taylor expanded in c around inf 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-*l* 82.6%

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

      3. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in i around inf 73.4%

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

      1. associate-*r* 73.4%

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

      2. neg-mul-1 73.4%

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

      3. associate-*r* 73.4%

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

      4. *-commutative 73.4%

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

      5. associate-*l* 73.4%

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

      6. *-commutative 73.4%

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

   7. Simplified 73.4%

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

   if 1.15999999999999994e114 < j < 3.6000000000000002e198

   1. Initial program 64.5%

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

   2. Taylor expanded in t around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. *-commutative 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in j around inf 53.8%

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

   if 1.05e243 < j

   1. Initial program 61.1%

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

   2. Taylor expanded in c around inf 87.7%

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

   3. Taylor expanded in j around inf 81.4%

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

      1. *-commutative 81.4%

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

   5. Simplified 81.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{+134}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 10^{+21}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+243}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 5: 41.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -130000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2.65 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-179}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.7 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 210:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* a (* x (- t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -130000.0)
     t_3
     (if (<= c -2.65e-79)
       t_1
       (if (<= c -7.8e-83)
         t_3
         (if (<= c -1.55e-179)
           (* i (* y (- j)))
           (if (<= c -2.3e-208)
             t_2
             (if (<= c -5.7e-223)
               (* y (* i (- j)))
               (if (<= c -1e-274)
                 t_1
                 (if (<= c 2.5e-30)
                   (* x (* y z))
                   (if (<= c 210.0) 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 = z * (x * y);
	double t_2 = a * (x * -t);
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -130000.0) {
		tmp = t_3;
	} else if (c <= -2.65e-79) {
		tmp = t_1;
	} else if (c <= -7.8e-83) {
		tmp = t_3;
	} else if (c <= -1.55e-179) {
		tmp = i * (y * -j);
	} else if (c <= -2.3e-208) {
		tmp = t_2;
	} else if (c <= -5.7e-223) {
		tmp = y * (i * -j);
	} else if (c <= -1e-274) {
		tmp = t_1;
	} else if (c <= 2.5e-30) {
		tmp = x * (y * z);
	} else if (c <= 210.0) {
		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 = z * (x * y)
    t_2 = a * (x * -t)
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-130000.0d0)) then
        tmp = t_3
    else if (c <= (-2.65d-79)) then
        tmp = t_1
    else if (c <= (-7.8d-83)) then
        tmp = t_3
    else if (c <= (-1.55d-179)) then
        tmp = i * (y * -j)
    else if (c <= (-2.3d-208)) then
        tmp = t_2
    else if (c <= (-5.7d-223)) then
        tmp = y * (i * -j)
    else if (c <= (-1d-274)) then
        tmp = t_1
    else if (c <= 2.5d-30) then
        tmp = x * (y * z)
    else if (c <= 210.0d0) 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 = z * (x * y);
	double t_2 = a * (x * -t);
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -130000.0) {
		tmp = t_3;
	} else if (c <= -2.65e-79) {
		tmp = t_1;
	} else if (c <= -7.8e-83) {
		tmp = t_3;
	} else if (c <= -1.55e-179) {
		tmp = i * (y * -j);
	} else if (c <= -2.3e-208) {
		tmp = t_2;
	} else if (c <= -5.7e-223) {
		tmp = y * (i * -j);
	} else if (c <= -1e-274) {
		tmp = t_1;
	} else if (c <= 2.5e-30) {
		tmp = x * (y * z);
	} else if (c <= 210.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * (x * -t)
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -130000.0:
		tmp = t_3
	elif c <= -2.65e-79:
		tmp = t_1
	elif c <= -7.8e-83:
		tmp = t_3
	elif c <= -1.55e-179:
		tmp = i * (y * -j)
	elif c <= -2.3e-208:
		tmp = t_2
	elif c <= -5.7e-223:
		tmp = y * (i * -j)
	elif c <= -1e-274:
		tmp = t_1
	elif c <= 2.5e-30:
		tmp = x * (y * z)
	elif c <= 210.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(x * Float64(-t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -130000.0)
		tmp = t_3;
	elseif (c <= -2.65e-79)
		tmp = t_1;
	elseif (c <= -7.8e-83)
		tmp = t_3;
	elseif (c <= -1.55e-179)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= -2.3e-208)
		tmp = t_2;
	elseif (c <= -5.7e-223)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= -1e-274)
		tmp = t_1;
	elseif (c <= 2.5e-30)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 210.0)
		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 = z * (x * y);
	t_2 = a * (x * -t);
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -130000.0)
		tmp = t_3;
	elseif (c <= -2.65e-79)
		tmp = t_1;
	elseif (c <= -7.8e-83)
		tmp = t_3;
	elseif (c <= -1.55e-179)
		tmp = i * (y * -j);
	elseif (c <= -2.3e-208)
		tmp = t_2;
	elseif (c <= -5.7e-223)
		tmp = y * (i * -j);
	elseif (c <= -1e-274)
		tmp = t_1;
	elseif (c <= 2.5e-30)
		tmp = x * (y * z);
	elseif (c <= 210.0)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -130000.0], t$95$3, If[LessEqual[c, -2.65e-79], t$95$1, If[LessEqual[c, -7.8e-83], t$95$3, If[LessEqual[c, -1.55e-179], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.3e-208], t$95$2, If[LessEqual[c, -5.7e-223], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1e-274], t$95$1, If[LessEqual[c, 2.5e-30], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 210.0], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.3e5 or -2.6499999999999999e-79 < c < -7.800000000000001e-83 or 210 < c

   1. Initial program 65.2%

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

   2. Taylor expanded in c around inf 66.0%

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

   if -1.3e5 < c < -2.6499999999999999e-79 or -5.6999999999999998e-223 < c < -9.99999999999999966e-275

   1. Initial program 86.6%

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

   2. Taylor expanded in y around inf 45.3%

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

      1. +-commutative 45.3%

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

      2. mul-1-neg 45.3%

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

      3. unsub-neg 45.3%

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

      4. *-commutative 45.3%

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

   4. Simplified 45.3%

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

   5. Taylor expanded in z around inf 42.0%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if -7.800000000000001e-83 < c < -1.5500000000000001e-179

   1. Initial program 80.8%

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

   2. Taylor expanded in c around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*l* 62.6%

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

      3. *-commutative 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in i around inf 45.8%

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

      1. associate-*r* 45.8%

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

      2. neg-mul-1 45.8%

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

   7. Simplified 45.8%

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

   if -1.5500000000000001e-179 < c < -2.29999999999999997e-208 or 2.49999999999999986e-30 < c < 210

   1. Initial program 78.8%

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

   2. Taylor expanded in c around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 78.5%

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

      3. *-commutative 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in a around inf 72.0%

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

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

   7. Simplified 72.0%

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

   if -2.29999999999999997e-208 < c < -5.6999999999999998e-223

   1. Initial program 66.2%

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

   2. Taylor expanded in y around inf 68.1%

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

      1. +-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in z around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-lft-neg-out 68.1%

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

      3. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   if -9.99999999999999966e-275 < c < 2.49999999999999986e-30

   1. Initial program 85.8%

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

   2. Taylor expanded in y around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. unsub-neg 51.4%

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

      4. *-commutative 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in z around inf 39.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -130000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.65 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-179}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -5.7 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 210:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 56.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-87} \lor \neg \left(x \leq 5.1 \cdot 10^{+22}\right):\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.15e+19)
     t_1
     (if (<= x -2.4e-77)
       (* a (- (* b i) (* x t)))
       (if (<= x 8.5e-197)
         (- (* j (- (* t c) (* y i))) (* b (* z c)))
         (if (or (<= x 3.6e-87) (not (<= x 5.1e+22)))
           (- t_1 (* c (* z b)))
           (* 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+19) {
		tmp = t_1;
	} else if (x <= -2.4e-77) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 8.5e-197) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if ((x <= 3.6e-87) || !(x <= 5.1e+22)) {
		tmp = t_1 - (c * (z * b));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.15d+19)) then
        tmp = t_1
    else if (x <= (-2.4d-77)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 8.5d-197) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if ((x <= 3.6d-87) .or. (.not. (x <= 5.1d+22))) then
        tmp = t_1 - (c * (z * b))
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+19) {
		tmp = t_1;
	} else if (x <= -2.4e-77) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 8.5e-197) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if ((x <= 3.6e-87) || !(x <= 5.1e+22)) {
		tmp = t_1 - (c * (z * b));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	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 <= -1.15e+19:
		tmp = t_1
	elif x <= -2.4e-77:
		tmp = a * ((b * i) - (x * t))
	elif x <= 8.5e-197:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif (x <= 3.6e-87) or not (x <= 5.1e+22):
		tmp = t_1 - (c * (z * b))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.15e+19)
		tmp = t_1;
	elseif (x <= -2.4e-77)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 8.5e-197)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif ((x <= 3.6e-87) || !(x <= 5.1e+22))
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.15e+19)
		tmp = t_1;
	elseif (x <= -2.4e-77)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 8.5e-197)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif ((x <= 3.6e-87) || ~((x <= 5.1e+22)))
		tmp = t_1 - (c * (z * b));
	else
		tmp = 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+19], t$95$1, If[LessEqual[x, -2.4e-77], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-197], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.6e-87], N[Not[LessEqual[x, 5.1e+22]], $MachinePrecision]], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.15e19

   1. Initial program 80.3%

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

   2. Taylor expanded in c around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*l* 82.2%

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

      3. *-commutative 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in x around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. *-commutative 74.5%

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

   7. Simplified 74.5%

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

   if -1.15e19 < x < -2.3999999999999999e-77

   1. Initial program 61.4%

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

   2. Taylor expanded in a around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

      2. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -2.3999999999999999e-77 < x < 8.5e-197

   1. Initial program 69.8%

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

   2. Taylor expanded in c around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*l* 66.0%

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

      3. *-commutative 66.0%

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

   4. Simplified 66.0%

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

   5. Taylor expanded in x around 0 69.0%

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

   if 8.5e-197 < x < 3.59999999999999993e-87 or 5.1000000000000002e22 < x

   1. Initial program 72.7%

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

   2. Taylor expanded in j around 0 76.2%

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

      1. fma-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. fma-neg 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 69.5%

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

      2. associate-*l* 70.6%

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

      3. *-commutative 70.6%

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

   7. Simplified 73.1%

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

   if 3.59999999999999993e-87 < x < 5.1000000000000002e22

   1. Initial program 90.1%

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

   2. Taylor expanded in b around inf 57.6%

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

      1. *-commutative 57.6%

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

   4. Simplified 57.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-87} \lor \neg \left(x \leq 5.1 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 7: 65.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -6.6 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;j \leq 9.8 \cdot 10^{+41}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+252}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= j -6.6e+195)
     (* i (- (* a b) (* y j)))
     (if (<= j -1.1e-26)
       (+ t_1 t_2)
       (if (<= j 9.8e+41)
         (+ t_2 (* b (- (* a i) (* z c))))
         (if (<= j 3e+252)
           (- t_1 (* b (* z c)))
           (* c (- (* t j) (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -6.6e+195) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= -1.1e-26) {
		tmp = t_1 + t_2;
	} else if (j <= 9.8e+41) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (j <= 3e+252) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (j <= (-6.6d+195)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= (-1.1d-26)) then
        tmp = t_1 + t_2
    else if (j <= 9.8d+41) then
        tmp = t_2 + (b * ((a * i) - (z * c)))
    else if (j <= 3d+252) then
        tmp = t_1 - (b * (z * c))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -6.6e+195) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= -1.1e-26) {
		tmp = t_1 + t_2;
	} else if (j <= 9.8e+41) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (j <= 3e+252) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -6.6e+195:
		tmp = i * ((a * b) - (y * j))
	elif j <= -1.1e-26:
		tmp = t_1 + t_2
	elif j <= 9.8e+41:
		tmp = t_2 + (b * ((a * i) - (z * c)))
	elif j <= 3e+252:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = c * ((t * j) - (z * b))
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -6.6e+195)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= -1.1e-26)
		tmp = Float64(t_1 + t_2);
	elseif (j <= 9.8e+41)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 3e+252)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -6.6e+195)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= -1.1e-26)
		tmp = t_1 + t_2;
	elseif (j <= 9.8e+41)
		tmp = t_2 + (b * ((a * i) - (z * c)));
	elseif (j <= 3e+252)
		tmp = t_1 - (b * (z * c));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.6e+195], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1e-26], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[j, 9.8e+41], N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e+252], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.5999999999999999e195

   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 i around inf 73.9%

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

      1. distribute-lft-out-- 73.9%

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

      2. *-commutative 73.9%

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

   4. Simplified 73.9%

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

   if -6.5999999999999999e195 < j < -1.1e-26

   1. Initial program 75.5%

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

   2. Taylor expanded in b around 0 71.9%

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

   if -1.1e-26 < j < 9.7999999999999998e41

   1. Initial program 78.3%

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

   2. Taylor expanded in j around 0 82.0%

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

      1. fma-neg 82.7%

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

      2. *-commutative 82.7%

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

      3. *-commutative 82.7%

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

      4. fma-neg 82.0%

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

   4. Simplified 82.0%

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

   if 9.7999999999999998e41 < j < 2.99999999999999989e252

   1. Initial program 75.5%

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

   2. Taylor expanded in c around inf 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-*l* 81.2%

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

      3. *-commutative 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in x around 0 76.5%

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

   if 2.99999999999999989e252 < j

   1. Initial program 55.1%

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

   2. Taylor expanded in c around inf 93.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 8: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -9e+18)
     t_1
     (if (<= x -1.3e-76)
       (* a (- (* b i) (* x t)))
       (if (<= x 1.65e-177)
         (- (* j (- (* t c) (* y i))) (* b (* z c)))
         (if (<= x 1.85e+27)
           (- (* b (- (* a i) (* z c))) (* a (* x t)))
           (- t_1 (* c (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9e+18) {
		tmp = t_1;
	} else if (x <= -1.3e-76) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 1.65e-177) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 1.85e+27) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_1 - (c * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-9d+18)) then
        tmp = t_1
    else if (x <= (-1.3d-76)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 1.65d-177) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if (x <= 1.85d+27) then
        tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
    else
        tmp = t_1 - (c * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9e+18) {
		tmp = t_1;
	} else if (x <= -1.3e-76) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 1.65e-177) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 1.85e+27) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_1 - (c * (z * b));
	}
	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 <= -9e+18:
		tmp = t_1
	elif x <= -1.3e-76:
		tmp = a * ((b * i) - (x * t))
	elif x <= 1.65e-177:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif x <= 1.85e+27:
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
	else:
		tmp = t_1 - (c * (z * b))
	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 <= -9e+18)
		tmp = t_1;
	elseif (x <= -1.3e-76)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 1.65e-177)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 1.85e+27)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	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 <= -9e+18)
		tmp = t_1;
	elseif (x <= -1.3e-76)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 1.65e-177)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif (x <= 1.85e+27)
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	else
		tmp = t_1 - (c * (z * b));
	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, -9e+18], t$95$1, If[LessEqual[x, -1.3e-76], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-177], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+27], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9e18

   1. Initial program 80.3%

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

   2. Taylor expanded in c around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*l* 82.2%

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

      3. *-commutative 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in x around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. *-commutative 74.5%

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

   7. Simplified 74.5%

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

   if -9e18 < x < -1.3e-76

   1. Initial program 61.4%

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

   2. Taylor expanded in a around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

      2. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -1.3e-76 < x < 1.65e-177

   1. Initial program 68.8%

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

   2. Taylor expanded in c around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l* 65.2%

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

      3. *-commutative 65.2%

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

   4. Simplified 65.2%

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

   5. Taylor expanded in x around 0 66.6%

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

   if 1.65e-177 < x < 1.85000000000000001e27

   1. Initial program 78.4%

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

   2. Taylor expanded in j around 0 70.9%

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

      1. fma-neg 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. fma-neg 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in y around 0 66.3%

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

      1. associate-*r* 66.3%

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

      2. neg-mul-1 66.3%

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

      3. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if 1.85000000000000001e27 < x

   1. Initial program 75.5%

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

   2. Taylor expanded in j around 0 78.7%

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

      1. fma-neg 80.2%

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

      2. *-commutative 80.2%

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

      3. *-commutative 80.2%

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

      4. fma-neg 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in c around inf 75.7%

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

      1. *-commutative 74.0%

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

      2. associate-*l* 75.5%

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

      3. *-commutative 75.5%

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

   7. Simplified 77.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 9: 67.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.42 \cdot 10^{+101} \lor \neg \left(b \leq 2.8 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.42e+101) (not (<= b 2.8e+37)))
   (- (* b (- (* a i) (* z c))) (* a (* x t)))
   (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t 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 ((b <= -2.42e+101) || !(b <= 2.8e+37)) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * 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 ((b <= (-2.42d+101)) .or. (.not. (b <= 2.8d+37))) then
        tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
    else
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * 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 ((b <= -2.42e+101) || !(b <= 2.8e+37)) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.42e+101) or not (b <= 2.8e+37):
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.42e+101) || !(b <= 2.8e+37))
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.42e+101) || ~((b <= 2.8e+37)))
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	else
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.42e+101], N[Not[LessEqual[b, 2.8e+37]], $MachinePrecision]], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4200000000000001e101 or 2.7999999999999998e37 < b

   1. Initial program 76.6%

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

   2. Taylor expanded in j around 0 78.1%

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

      1. fma-neg 80.4%

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

      2. *-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. fma-neg 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in y around 0 76.1%

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

      1. associate-*r* 76.1%

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

      2. neg-mul-1 76.1%

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

      3. *-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -2.4200000000000001e101 < b < 2.7999999999999998e37

   1. Initial program 72.9%

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

   2. Taylor expanded in b around 0 71.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.42 \cdot 10^{+101} \lor \neg \left(b \leq 2.8 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 10: 30.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))) (t_2 (* z (* x y))))
   (if (<= x -4e+174)
     t_2
     (if (<= x -5.8e+163)
       (* x (* t (- a)))
       (if (<= x -1.5e+19)
         t_2
         (if (<= x -7.8e-141)
           (* y (* i (- j)))
           (if (<= x -1.9e-229)
             t_1
             (if (<= x -3.8e-275)
               (* j (- (* y i)))
               (if (<= x 1.08e-179)
                 (* c (* t j))
                 (if (<= x 3.4e+41) 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 = c * -(z * b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -4e+174) {
		tmp = t_2;
	} else if (x <= -5.8e+163) {
		tmp = x * (t * -a);
	} else if (x <= -1.5e+19) {
		tmp = t_2;
	} else if (x <= -7.8e-141) {
		tmp = y * (i * -j);
	} else if (x <= -1.9e-229) {
		tmp = t_1;
	} else if (x <= -3.8e-275) {
		tmp = j * -(y * i);
	} else if (x <= 1.08e-179) {
		tmp = c * (t * j);
	} else if (x <= 3.4e+41) {
		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 = c * -(z * b)
    t_2 = z * (x * y)
    if (x <= (-4d+174)) then
        tmp = t_2
    else if (x <= (-5.8d+163)) then
        tmp = x * (t * -a)
    else if (x <= (-1.5d+19)) then
        tmp = t_2
    else if (x <= (-7.8d-141)) then
        tmp = y * (i * -j)
    else if (x <= (-1.9d-229)) then
        tmp = t_1
    else if (x <= (-3.8d-275)) then
        tmp = j * -(y * i)
    else if (x <= 1.08d-179) then
        tmp = c * (t * j)
    else if (x <= 3.4d+41) 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 = c * -(z * b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -4e+174) {
		tmp = t_2;
	} else if (x <= -5.8e+163) {
		tmp = x * (t * -a);
	} else if (x <= -1.5e+19) {
		tmp = t_2;
	} else if (x <= -7.8e-141) {
		tmp = y * (i * -j);
	} else if (x <= -1.9e-229) {
		tmp = t_1;
	} else if (x <= -3.8e-275) {
		tmp = j * -(y * i);
	} else if (x <= 1.08e-179) {
		tmp = c * (t * j);
	} else if (x <= 3.4e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -4e+174:
		tmp = t_2
	elif x <= -5.8e+163:
		tmp = x * (t * -a)
	elif x <= -1.5e+19:
		tmp = t_2
	elif x <= -7.8e-141:
		tmp = y * (i * -j)
	elif x <= -1.9e-229:
		tmp = t_1
	elif x <= -3.8e-275:
		tmp = j * -(y * i)
	elif x <= 1.08e-179:
		tmp = c * (t * j)
	elif x <= 3.4e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -4e+174)
		tmp = t_2;
	elseif (x <= -5.8e+163)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -1.5e+19)
		tmp = t_2;
	elseif (x <= -7.8e-141)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (x <= -1.9e-229)
		tmp = t_1;
	elseif (x <= -3.8e-275)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (x <= 1.08e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 3.4e+41)
		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 = c * -(z * b);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -4e+174)
		tmp = t_2;
	elseif (x <= -5.8e+163)
		tmp = x * (t * -a);
	elseif (x <= -1.5e+19)
		tmp = t_2;
	elseif (x <= -7.8e-141)
		tmp = y * (i * -j);
	elseif (x <= -1.9e-229)
		tmp = t_1;
	elseif (x <= -3.8e-275)
		tmp = j * -(y * i);
	elseif (x <= 1.08e-179)
		tmp = c * (t * j);
	elseif (x <= 3.4e+41)
		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[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+174], t$95$2, If[LessEqual[x, -5.8e+163], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+19], t$95$2, If[LessEqual[x, -7.8e-141], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-229], t$95$1, If[LessEqual[x, -3.8e-275], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.08e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+41], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.00000000000000028e174 or -5.79999999999999996e163 < x < -1.5e19 or 3.39999999999999998e41 < x

   1. Initial program 80.7%

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

   2. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in z around inf 47.4%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

   7. Simplified 49.7%

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

   if -4.00000000000000028e174 < x < -5.79999999999999996e163

   1. Initial program 50.0%

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

   2. Taylor expanded in j around 0 50.0%

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

      1. fma-neg 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-neg 50.0%

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

   4. Simplified 50.0%

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

      1. *-commutative 50.0%

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

      2. prod-diff 33.3%

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

      3. fma-neg 33.3%

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

      4. cancel-sign-sub-inv 33.3%

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

      5. fma-def 33.3%

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

      6. *-commutative 33.3%

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

   6. Applied egg-rr 33.3%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

   if -1.5e19 < x < -7.7999999999999994e-141

   1. Initial program 63.1%

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

   2. Taylor expanded in y around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

      4. *-commutative 44.7%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in z around 0 32.8%

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

      1. mul-1-neg 32.8%

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

      2. distribute-lft-neg-out 32.8%

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

      3. *-commutative 32.8%

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

   7. Simplified 32.8%

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

   if -7.7999999999999994e-141 < x < -1.9000000000000001e-229 or 1.08000000000000006e-179 < x < 3.39999999999999998e41

   1. Initial program 72.1%

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

   2. Taylor expanded in c around inf 56.6%

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

   3. Taylor expanded in j around 0 40.5%

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

      1. neg-mul-1 40.5%

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

      2. distribute-lft-neg-in 40.5%

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

      3. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   if -1.9000000000000001e-229 < x < -3.79999999999999972e-275

   1. Initial program 89.8%

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

   2. Taylor expanded in c around inf 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 71.7%

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

      3. *-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in i around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. associate-*r* 50.8%

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

      4. *-commutative 50.8%

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

      5. associate-*l* 60.4%

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

      6. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if -3.79999999999999972e-275 < x < 1.08000000000000006e-179

   1. Initial program 66.8%

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

   2. Taylor expanded in c around inf 57.0%

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

   3. Taylor expanded in j around inf 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 11: 30.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-274}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))) (t_2 (* z (* x y))))
   (if (<= x -1.65e+174)
     t_2
     (if (<= x -3e+159)
       (* x (* t (- a)))
       (if (<= x -1.3e+19)
         t_2
         (if (<= x -8.5e-116)
           (* i (* y (- j)))
           (if (<= x -3.5e-230)
             t_1
             (if (<= x -1.05e-274)
               (* j (- (* y i)))
               (if (<= x 1.28e-179)
                 (* c (* t j))
                 (if (<= x 3e+41) 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 * c) * -b;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.65e+174) {
		tmp = t_2;
	} else if (x <= -3e+159) {
		tmp = x * (t * -a);
	} else if (x <= -1.3e+19) {
		tmp = t_2;
	} else if (x <= -8.5e-116) {
		tmp = i * (y * -j);
	} else if (x <= -3.5e-230) {
		tmp = t_1;
	} else if (x <= -1.05e-274) {
		tmp = j * -(y * i);
	} else if (x <= 1.28e-179) {
		tmp = c * (t * j);
	} else if (x <= 3e+41) {
		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 * c) * -b
    t_2 = z * (x * y)
    if (x <= (-1.65d+174)) then
        tmp = t_2
    else if (x <= (-3d+159)) then
        tmp = x * (t * -a)
    else if (x <= (-1.3d+19)) then
        tmp = t_2
    else if (x <= (-8.5d-116)) then
        tmp = i * (y * -j)
    else if (x <= (-3.5d-230)) then
        tmp = t_1
    else if (x <= (-1.05d-274)) then
        tmp = j * -(y * i)
    else if (x <= 1.28d-179) then
        tmp = c * (t * j)
    else if (x <= 3d+41) 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 * c) * -b;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.65e+174) {
		tmp = t_2;
	} else if (x <= -3e+159) {
		tmp = x * (t * -a);
	} else if (x <= -1.3e+19) {
		tmp = t_2;
	} else if (x <= -8.5e-116) {
		tmp = i * (y * -j);
	} else if (x <= -3.5e-230) {
		tmp = t_1;
	} else if (x <= -1.05e-274) {
		tmp = j * -(y * i);
	} else if (x <= 1.28e-179) {
		tmp = c * (t * j);
	} else if (x <= 3e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	t_2 = z * (x * y)
	tmp = 0
	if x <= -1.65e+174:
		tmp = t_2
	elif x <= -3e+159:
		tmp = x * (t * -a)
	elif x <= -1.3e+19:
		tmp = t_2
	elif x <= -8.5e-116:
		tmp = i * (y * -j)
	elif x <= -3.5e-230:
		tmp = t_1
	elif x <= -1.05e-274:
		tmp = j * -(y * i)
	elif x <= 1.28e-179:
		tmp = c * (t * j)
	elif x <= 3e+41:
		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 * c) * Float64(-b))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.65e+174)
		tmp = t_2;
	elseif (x <= -3e+159)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -1.3e+19)
		tmp = t_2;
	elseif (x <= -8.5e-116)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (x <= -3.5e-230)
		tmp = t_1;
	elseif (x <= -1.05e-274)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (x <= 1.28e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 3e+41)
		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 * c) * -b;
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.65e+174)
		tmp = t_2;
	elseif (x <= -3e+159)
		tmp = x * (t * -a);
	elseif (x <= -1.3e+19)
		tmp = t_2;
	elseif (x <= -8.5e-116)
		tmp = i * (y * -j);
	elseif (x <= -3.5e-230)
		tmp = t_1;
	elseif (x <= -1.05e-274)
		tmp = j * -(y * i);
	elseif (x <= 1.28e-179)
		tmp = c * (t * j);
	elseif (x <= 3e+41)
		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 * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+174], t$95$2, If[LessEqual[x, -3e+159], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+19], t$95$2, If[LessEqual[x, -8.5e-116], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-230], t$95$1, If[LessEqual[x, -1.05e-274], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.28e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+41], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.65e174 or -3.0000000000000002e159 < x < -1.3e19 or 2.9999999999999998e41 < x

   1. Initial program 80.7%

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

   2. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in z around inf 47.4%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

   7. Simplified 49.7%

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

   if -1.65e174 < x < -3.0000000000000002e159

   1. Initial program 50.0%

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

   2. Taylor expanded in j around 0 50.0%

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

      1. fma-neg 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-neg 50.0%

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

   4. Simplified 50.0%

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

      1. *-commutative 50.0%

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

      2. prod-diff 33.3%

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

      3. fma-neg 33.3%

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

      4. cancel-sign-sub-inv 33.3%

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

      5. fma-def 33.3%

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

      6. *-commutative 33.3%

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

   6. Applied egg-rr 33.3%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

   if -1.3e19 < x < -8.4999999999999995e-116

   1. Initial program 61.5%

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

   2. Taylor expanded in c around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-*l* 55.9%

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

      3. *-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in i around inf 34.5%

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

      1. associate-*r* 34.5%

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

      2. neg-mul-1 34.5%

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

   7. Simplified 34.5%

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

   if -8.4999999999999995e-116 < x < -3.49999999999999988e-230 or 1.28000000000000006e-179 < x < 2.9999999999999998e41

   1. Initial program 72.3%

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

   2. Taylor expanded in c around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l* 61.4%

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

      3. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   5. Taylor expanded in b around inf 42.6%

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

      1. mul-1-neg 42.6%

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

      2. *-commutative 42.6%

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

      3. distribute-rgt-neg-in 42.6%

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

   7. Simplified 42.6%

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

   if -3.49999999999999988e-230 < x < -1.04999999999999997e-274

   1. Initial program 89.8%

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

   2. Taylor expanded in c around inf 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 71.7%

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

      3. *-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in i around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. associate-*r* 50.8%

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

      4. *-commutative 50.8%

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

      5. associate-*l* 60.4%

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

      6. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if -1.04999999999999997e-274 < x < 1.28000000000000006e-179

   1. Initial program 66.8%

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

   2. Taylor expanded in c around inf 57.0%

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

   3. Taylor expanded in j around inf 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-230}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-274}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+41}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 39.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= x -9.5e+172)
     t_1
     (if (<= x -1.9e+163)
       (* x (* t (- a)))
       (if (<= x -400000000.0)
         t_1
         (if (<= x 7.5e-251)
           t_2
           (if (<= x 1.08e-179)
             (* c (* t j))
             (if (<= x 3.2e+44) t_2 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);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -9.5e+172) {
		tmp = t_1;
	} else if (x <= -1.9e+163) {
		tmp = x * (t * -a);
	} else if (x <= -400000000.0) {
		tmp = t_1;
	} else if (x <= 7.5e-251) {
		tmp = t_2;
	} else if (x <= 1.08e-179) {
		tmp = c * (t * j);
	} else if (x <= 3.2e+44) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = b * ((a * i) - (z * c))
    if (x <= (-9.5d+172)) then
        tmp = t_1
    else if (x <= (-1.9d+163)) then
        tmp = x * (t * -a)
    else if (x <= (-400000000.0d0)) then
        tmp = t_1
    else if (x <= 7.5d-251) then
        tmp = t_2
    else if (x <= 1.08d-179) then
        tmp = c * (t * j)
    else if (x <= 3.2d+44) then
        tmp = t_2
    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);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -9.5e+172) {
		tmp = t_1;
	} else if (x <= -1.9e+163) {
		tmp = x * (t * -a);
	} else if (x <= -400000000.0) {
		tmp = t_1;
	} else if (x <= 7.5e-251) {
		tmp = t_2;
	} else if (x <= 1.08e-179) {
		tmp = c * (t * j);
	} else if (x <= 3.2e+44) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if x <= -9.5e+172:
		tmp = t_1
	elif x <= -1.9e+163:
		tmp = x * (t * -a)
	elif x <= -400000000.0:
		tmp = t_1
	elif x <= 7.5e-251:
		tmp = t_2
	elif x <= 1.08e-179:
		tmp = c * (t * j)
	elif x <= 3.2e+44:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -9.5e+172)
		tmp = t_1;
	elseif (x <= -1.9e+163)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -400000000.0)
		tmp = t_1;
	elseif (x <= 7.5e-251)
		tmp = t_2;
	elseif (x <= 1.08e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 3.2e+44)
		tmp = t_2;
	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);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (x <= -9.5e+172)
		tmp = t_1;
	elseif (x <= -1.9e+163)
		tmp = x * (t * -a);
	elseif (x <= -400000000.0)
		tmp = t_1;
	elseif (x <= 7.5e-251)
		tmp = t_2;
	elseif (x <= 1.08e-179)
		tmp = c * (t * j);
	elseif (x <= 3.2e+44)
		tmp = t_2;
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+172], t$95$1, If[LessEqual[x, -1.9e+163], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -400000000.0], t$95$1, If[LessEqual[x, 7.5e-251], t$95$2, If[LessEqual[x, 1.08e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+44], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.50000000000000027e172 or -1.90000000000000004e163 < x < -4e8 or 3.20000000000000004e44 < x

   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 y around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in z around inf 47.0%

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

      1. associate-*r* 49.3%

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

      2. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   if -9.50000000000000027e172 < x < -1.90000000000000004e163

   1. Initial program 50.0%

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

   2. Taylor expanded in j around 0 50.0%

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

      1. fma-neg 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-neg 50.0%

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

   4. Simplified 50.0%

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

      1. *-commutative 50.0%

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

      2. prod-diff 33.3%

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

      3. fma-neg 33.3%

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

      4. cancel-sign-sub-inv 33.3%

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

      5. fma-def 33.3%

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

      6. *-commutative 33.3%

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

   6. Applied egg-rr 33.3%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

   if -4e8 < x < 7.5000000000000004e-251 or 1.08000000000000006e-179 < x < 3.20000000000000004e44

   1. Initial program 69.2%

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

   2. Taylor expanded in b around inf 46.2%

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

      1. *-commutative 46.2%

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

   4. Simplified 46.2%

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

   if 7.5000000000000004e-251 < x < 1.08000000000000006e-179

   1. Initial program 64.3%

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

   2. Taylor expanded in c around inf 64.1%

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

   3. Taylor expanded in j around inf 63.5%

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

      1. *-commutative 63.5%

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

   5. Simplified 63.5%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+172}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -400000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-251}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 52.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.24 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -9e+18)
     t_2
     (if (<= x -1.24e-86)
       t_1
       (if (<= x -5.4e-114)
         (* i (* y (- j)))
         (if (<= x 6e-25)
           (* c (- (* t j) (* z b)))
           (if (<= x 3.5e+43)
             (* b (- (* a i) (* z c)))
             (if (<= x 8.8e+66) 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 = t * ((c * j) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9e+18) {
		tmp = t_2;
	} else if (x <= -1.24e-86) {
		tmp = t_1;
	} else if (x <= -5.4e-114) {
		tmp = i * (y * -j);
	} else if (x <= 6e-25) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 3.5e+43) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 8.8e+66) {
		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 = t * ((c * j) - (x * a))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-9d+18)) then
        tmp = t_2
    else if (x <= (-1.24d-86)) then
        tmp = t_1
    else if (x <= (-5.4d-114)) then
        tmp = i * (y * -j)
    else if (x <= 6d-25) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 3.5d+43) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 8.8d+66) 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 = t * ((c * j) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9e+18) {
		tmp = t_2;
	} else if (x <= -1.24e-86) {
		tmp = t_1;
	} else if (x <= -5.4e-114) {
		tmp = i * (y * -j);
	} else if (x <= 6e-25) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 3.5e+43) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 8.8e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -9e+18:
		tmp = t_2
	elif x <= -1.24e-86:
		tmp = t_1
	elif x <= -5.4e-114:
		tmp = i * (y * -j)
	elif x <= 6e-25:
		tmp = c * ((t * j) - (z * b))
	elif x <= 3.5e+43:
		tmp = b * ((a * i) - (z * c))
	elif x <= 8.8e+66:
		tmp = t_1
	else:
		tmp = t_2
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -9e+18)
		tmp = t_2;
	elseif (x <= -1.24e-86)
		tmp = t_1;
	elseif (x <= -5.4e-114)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (x <= 6e-25)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 3.5e+43)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 8.8e+66)
		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 = t * ((c * j) - (x * a));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -9e+18)
		tmp = t_2;
	elseif (x <= -1.24e-86)
		tmp = t_1;
	elseif (x <= -5.4e-114)
		tmp = i * (y * -j);
	elseif (x <= 6e-25)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 3.5e+43)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 8.8e+66)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+18], t$95$2, If[LessEqual[x, -1.24e-86], t$95$1, If[LessEqual[x, -5.4e-114], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-25], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+43], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e+66], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9e18 or 8.7999999999999994e66 < x

   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 c around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*l* 80.3%

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

      3. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

   7. Simplified 75.7%

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

   if -9e18 < x < -1.23999999999999999e-86 or 3.5000000000000001e43 < x < 8.7999999999999994e66

   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 inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

   4. Simplified 58.3%

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

   if -1.23999999999999999e-86 < x < -5.3999999999999999e-114

   1. Initial program 58.5%

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

   2. Taylor expanded in c around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*l* 66.8%

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

      3. *-commutative 66.8%

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

   4. Simplified 66.8%

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

   5. Taylor expanded in i around inf 59.3%

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

      1. associate-*r* 59.3%

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

      2. neg-mul-1 59.3%

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

   7. Simplified 59.3%

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

   if -5.3999999999999999e-114 < x < 5.9999999999999995e-25

   1. Initial program 71.6%

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

   2. Taylor expanded in c around inf 54.8%

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

   if 5.9999999999999995e-25 < x < 3.5000000000000001e43

   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 inf 67.6%

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

      1. *-commutative 67.6%

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

   4. Simplified 67.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.24 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 14: 52.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.3e+19)
     t_2
     (if (<= x -5.9e-86)
       t_1
       (if (<= x -2.65e-138)
         (* y (- (* x z) (* i j)))
         (if (<= x 1.25e-23)
           (* c (- (* t j) (* z b)))
           (if (<= x 2.9e+44)
             (* b (- (* a i) (* z c)))
             (if (<= x 5.4e+65) 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 = t * ((c * j) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.3e+19) {
		tmp = t_2;
	} else if (x <= -5.9e-86) {
		tmp = t_1;
	} else if (x <= -2.65e-138) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.25e-23) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 2.9e+44) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.4e+65) {
		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 = t * ((c * j) - (x * a))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.3d+19)) then
        tmp = t_2
    else if (x <= (-5.9d-86)) then
        tmp = t_1
    else if (x <= (-2.65d-138)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 1.25d-23) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 2.9d+44) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 5.4d+65) 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 = t * ((c * j) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.3e+19) {
		tmp = t_2;
	} else if (x <= -5.9e-86) {
		tmp = t_1;
	} else if (x <= -2.65e-138) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.25e-23) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 2.9e+44) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.4e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.3e+19:
		tmp = t_2
	elif x <= -5.9e-86:
		tmp = t_1
	elif x <= -2.65e-138:
		tmp = y * ((x * z) - (i * j))
	elif x <= 1.25e-23:
		tmp = c * ((t * j) - (z * b))
	elif x <= 2.9e+44:
		tmp = b * ((a * i) - (z * c))
	elif x <= 5.4e+65:
		tmp = t_1
	else:
		tmp = t_2
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.3e+19)
		tmp = t_2;
	elseif (x <= -5.9e-86)
		tmp = t_1;
	elseif (x <= -2.65e-138)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 1.25e-23)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 2.9e+44)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 5.4e+65)
		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 = t * ((c * j) - (x * a));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.3e+19)
		tmp = t_2;
	elseif (x <= -5.9e-86)
		tmp = t_1;
	elseif (x <= -2.65e-138)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 1.25e-23)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 2.9e+44)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 5.4e+65)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+19], t$95$2, If[LessEqual[x, -5.9e-86], t$95$1, If[LessEqual[x, -2.65e-138], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-23], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+44], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e+65], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.3e19 or 5.40000000000000038e65 < x

   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 c around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*l* 80.3%

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

      3. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

   7. Simplified 75.7%

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

   if -1.3e19 < x < -5.89999999999999998e-86 or 2.9000000000000002e44 < x < 5.40000000000000038e65

   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 inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

   4. Simplified 58.3%

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

   if -5.89999999999999998e-86 < x < -2.65000000000000013e-138

   1. Initial program 62.9%

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

   2. Taylor expanded in y around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

      4. *-commutative 69.8%

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

   4. Simplified 69.8%

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

   if -2.65000000000000013e-138 < x < 1.2500000000000001e-23

   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 c around inf 56.1%

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

   if 1.2500000000000001e-23 < x < 2.9000000000000002e44

   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 inf 67.6%

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

      1. *-commutative 67.6%

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

   4. Simplified 67.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 15: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.6e+19)
     t_1
     (if (<= x -6e-86)
       (* a (- (* b i) (* x t)))
       (if (<= x -4.8e-139)
         (* y (- (* x z) (* i j)))
         (if (<= x 4.2e-33)
           (* c (- (* t j) (* z b)))
           (if (<= x 9e+43)
             (* b (- (* a i) (* z c)))
             (if (<= x 5.2e+65) (* t (- (* c j) (* x a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.6e+19) {
		tmp = t_1;
	} else if (x <= -6e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -4.8e-139) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 4.2e-33) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 9e+43) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.2e+65) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.6d+19)) then
        tmp = t_1
    else if (x <= (-6d-86)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= (-4.8d-139)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 4.2d-33) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 9d+43) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 5.2d+65) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.6e+19) {
		tmp = t_1;
	} else if (x <= -6e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -4.8e-139) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 4.2e-33) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 9e+43) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.2e+65) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.6e+19:
		tmp = t_1
	elif x <= -6e-86:
		tmp = a * ((b * i) - (x * t))
	elif x <= -4.8e-139:
		tmp = y * ((x * z) - (i * j))
	elif x <= 4.2e-33:
		tmp = c * ((t * j) - (z * b))
	elif x <= 9e+43:
		tmp = b * ((a * i) - (z * c))
	elif x <= 5.2e+65:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.6e+19)
		tmp = t_1;
	elseif (x <= -6e-86)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= -4.8e-139)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 4.2e-33)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 9e+43)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 5.2e+65)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.6e+19)
		tmp = t_1;
	elseif (x <= -6e-86)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= -4.8e-139)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 4.2e-33)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 9e+43)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 5.2e+65)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+19], t$95$1, If[LessEqual[x, -6e-86], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-139], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-33], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+43], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+65], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.6e19 or 5.20000000000000005e65 < x

   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 c around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*l* 80.3%

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

      3. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

   7. Simplified 75.7%

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

   if -2.6e19 < x < -6.0000000000000002e-86

   1. Initial program 63.3%

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

   2. Taylor expanded in a around inf 57.8%

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

      1. distribute-lft-out-- 57.8%

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

      2. *-commutative 57.8%

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

   4. Simplified 57.8%

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

   if -6.0000000000000002e-86 < x < -4.80000000000000029e-139

   1. Initial program 62.9%

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

   2. Taylor expanded in y around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

      4. *-commutative 69.8%

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

   4. Simplified 69.8%

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

   if -4.80000000000000029e-139 < x < 4.2e-33

   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 c around inf 56.1%

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

   if 4.2e-33 < x < 9e43

   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 inf 67.6%

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

      1. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   if 9e43 < x < 5.20000000000000005e65

   1. Initial program 75.0%

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

   2. Taylor expanded in t around inf 75.3%

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

      1. +-commutative 75.3%

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

      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. *-commutative 75.3%

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

   4. Simplified 75.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 16: 51.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -300000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-179}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 330:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.5e+133)
     t_2
     (if (<= c -2e+110)
       t_1
       (if (<= c -300000.0)
         (* b (- (* a i) (* z c)))
         (if (<= c -1.55e-39)
           t_1
           (if (<= c -1.25e-179)
             (* i (- (* a b) (* y j)))
             (if (<= c 330.0) 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));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.5e+133) {
		tmp = t_2;
	} else if (c <= -2e+110) {
		tmp = t_1;
	} else if (c <= -300000.0) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -1.55e-39) {
		tmp = t_1;
	} else if (c <= -1.25e-179) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 330.0) {
		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))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.5d+133)) then
        tmp = t_2
    else if (c <= (-2d+110)) then
        tmp = t_1
    else if (c <= (-300000.0d0)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= (-1.55d-39)) then
        tmp = t_1
    else if (c <= (-1.25d-179)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 330.0d0) 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));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.5e+133) {
		tmp = t_2;
	} else if (c <= -2e+110) {
		tmp = t_1;
	} else if (c <= -300000.0) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -1.55e-39) {
		tmp = t_1;
	} else if (c <= -1.25e-179) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 330.0) {
		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))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.5e+133:
		tmp = t_2
	elif c <= -2e+110:
		tmp = t_1
	elif c <= -300000.0:
		tmp = b * ((a * i) - (z * c))
	elif c <= -1.55e-39:
		tmp = t_1
	elif c <= -1.25e-179:
		tmp = i * ((a * b) - (y * j))
	elif c <= 330.0:
		tmp = t_1
	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(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.5e+133)
		tmp = t_2;
	elseif (c <= -2e+110)
		tmp = t_1;
	elseif (c <= -300000.0)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= -1.55e-39)
		tmp = t_1;
	elseif (c <= -1.25e-179)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 330.0)
		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));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.5e+133)
		tmp = t_2;
	elseif (c <= -2e+110)
		tmp = t_1;
	elseif (c <= -300000.0)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= -1.55e-39)
		tmp = t_1;
	elseif (c <= -1.25e-179)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 330.0)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+133], t$95$2, If[LessEqual[c, -2e+110], t$95$1, If[LessEqual[c, -300000.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.55e-39], t$95$1, If[LessEqual[c, -1.25e-179], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 330.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.50000000000000003e133 or 330 < c

   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 c around inf 68.3%

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

   if -1.50000000000000003e133 < c < -2e110 or -3e5 < c < -1.54999999999999985e-39 or -1.2499999999999999e-179 < c < 330

   1. Initial program 82.3%

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

   2. Taylor expanded in c around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*l* 78.7%

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

      3. *-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in x around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if -2e110 < c < -3e5

   1. Initial program 94.0%

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

   2. Taylor expanded in b around inf 77.1%

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

      1. *-commutative 77.1%

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

   4. Simplified 77.1%

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

   if -1.54999999999999985e-39 < c < -1.2499999999999999e-179

   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 i around inf 64.2%

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

      1. distribute-lft-out-- 64.2%

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

      2. *-commutative 64.2%

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

   4. Simplified 64.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -300000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-179}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 330:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 17: 56.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-187}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -9e+18)
     t_1
     (if (<= x -2.1e-76)
       (* a (- (* b i) (* x t)))
       (if (<= x 3e-187)
         (- (* j (- (* t c) (* y i))) (* b (* z c)))
         (if (<= x 2.5e+41) (* 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9e+18) {
		tmp = t_1;
	} else if (x <= -2.1e-76) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 3e-187) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 2.5e+41) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-9d+18)) then
        tmp = t_1
    else if (x <= (-2.1d-76)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 3d-187) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if (x <= 2.5d+41) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9e+18) {
		tmp = t_1;
	} else if (x <= -2.1e-76) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 3e-187) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 2.5e+41) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -9e+18:
		tmp = t_1
	elif x <= -2.1e-76:
		tmp = a * ((b * i) - (x * t))
	elif x <= 3e-187:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif x <= 2.5e+41:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -9e+18)
		tmp = t_1;
	elseif (x <= -2.1e-76)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 3e-187)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 2.5e+41)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -9e+18)
		tmp = t_1;
	elseif (x <= -2.1e-76)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 3e-187)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif (x <= 2.5e+41)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+18], t$95$1, If[LessEqual[x, -2.1e-76], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-187], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+41], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9e18 or 2.50000000000000011e41 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in c around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 80.1%

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

      3. *-commutative 80.1%

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

   4. Simplified 80.1%

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

   5. Taylor expanded in x around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   if -9e18 < x < -2.09999999999999992e-76

   1. Initial program 61.4%

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

   2. Taylor expanded in a around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

      2. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -2.09999999999999992e-76 < x < 3.00000000000000004e-187

   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 c around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*l* 66.9%

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

      3. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in x around 0 68.5%

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

   if 3.00000000000000004e-187 < x < 2.50000000000000011e41

   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 b around inf 58.1%

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

      1. *-commutative 58.1%

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

   4. Simplified 58.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-187}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 18: 29.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -3.7e+174)
     t_1
     (if (<= x -3.4e+164)
       (* x (* t (- a)))
       (if (<= x -1.6e+19)
         t_1
         (if (<= x 1.5e-179)
           (* c (* t j))
           (if (<= x 5.6e+41) (* c (- (* z b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -3.7e+174) {
		tmp = t_1;
	} else if (x <= -3.4e+164) {
		tmp = x * (t * -a);
	} else if (x <= -1.6e+19) {
		tmp = t_1;
	} else if (x <= 1.5e-179) {
		tmp = c * (t * j);
	} else if (x <= 5.6e+41) {
		tmp = c * -(z * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-3.7d+174)) then
        tmp = t_1
    else if (x <= (-3.4d+164)) then
        tmp = x * (t * -a)
    else if (x <= (-1.6d+19)) then
        tmp = t_1
    else if (x <= 1.5d-179) then
        tmp = c * (t * j)
    else if (x <= 5.6d+41) then
        tmp = c * -(z * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -3.7e+174) {
		tmp = t_1;
	} else if (x <= -3.4e+164) {
		tmp = x * (t * -a);
	} else if (x <= -1.6e+19) {
		tmp = t_1;
	} else if (x <= 1.5e-179) {
		tmp = c * (t * j);
	} else if (x <= 5.6e+41) {
		tmp = c * -(z * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -3.7e+174:
		tmp = t_1
	elif x <= -3.4e+164:
		tmp = x * (t * -a)
	elif x <= -1.6e+19:
		tmp = t_1
	elif x <= 1.5e-179:
		tmp = c * (t * j)
	elif x <= 5.6e+41:
		tmp = c * -(z * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -3.7e+174)
		tmp = t_1;
	elseif (x <= -3.4e+164)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -1.6e+19)
		tmp = t_1;
	elseif (x <= 1.5e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 5.6e+41)
		tmp = Float64(c * Float64(-Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -3.7e+174)
		tmp = t_1;
	elseif (x <= -3.4e+164)
		tmp = x * (t * -a);
	elseif (x <= -1.6e+19)
		tmp = t_1;
	elseif (x <= 1.5e-179)
		tmp = c * (t * j);
	elseif (x <= 5.6e+41)
		tmp = c * -(z * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+174], t$95$1, If[LessEqual[x, -3.4e+164], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e+19], t$95$1, If[LessEqual[x, 1.5e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+41], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.7000000000000002e174 or -3.4000000000000001e164 < x < -1.6e19 or 5.5999999999999999e41 < x

   1. Initial program 80.7%

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

   2. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in z around inf 47.4%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

   7. Simplified 49.7%

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

   if -3.7000000000000002e174 < x < -3.4000000000000001e164

   1. Initial program 50.0%

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

   2. Taylor expanded in j around 0 50.0%

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

      1. fma-neg 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-neg 50.0%

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

   4. Simplified 50.0%

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

      1. *-commutative 50.0%

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

      2. prod-diff 33.3%

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

      3. fma-neg 33.3%

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

      4. cancel-sign-sub-inv 33.3%

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

      5. fma-def 33.3%

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

      6. *-commutative 33.3%

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

   6. Applied egg-rr 33.3%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

   if -1.6e19 < x < 1.50000000000000003e-179

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 45.3%

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

   3. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

   if 1.50000000000000003e-179 < x < 5.5999999999999999e41

   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 c around inf 53.8%

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

   3. Taylor expanded in j around 0 39.8%

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

      1. neg-mul-1 39.8%

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

      2. distribute-lft-neg-in 39.8%

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

      3. *-commutative 39.8%

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

   5. Simplified 39.8%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 19: 50.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+114} \lor \neg \left(b \leq 6.8 \cdot 10^{-34}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.2e+114) (not (<= b 6.8e-34)))
   (* b (- (* a i) (* z c)))
   (* 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 ((b <= -4.2e+114) || !(b <= 6.8e-34)) {
		tmp = b * ((a * i) - (z * c));
	} 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 ((b <= (-4.2d+114)) .or. (.not. (b <= 6.8d-34))) then
        tmp = b * ((a * i) - (z * c))
    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 ((b <= -4.2e+114) || !(b <= 6.8e-34)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.2e+114) or not (b <= 6.8e-34):
		tmp = b * ((a * i) - (z * c))
	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 ((b <= -4.2e+114) || !(b <= 6.8e-34))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	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 ((b <= -4.2e+114) || ~((b <= 6.8e-34)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -4.2e+114], N[Not[LessEqual[b, 6.8e-34]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2000000000000001e114 or 6.8000000000000001e-34 < b

   1. Initial program 79.2%

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

   2. Taylor expanded in b around inf 60.4%

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

      1. *-commutative 60.4%

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

   4. Simplified 60.4%

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

   if -4.2000000000000001e114 < b < 6.8000000000000001e-34

   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 t around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

      4. *-commutative 49.2%

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

   4. Simplified 49.2%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+114} \lor \neg \left(b \leq 6.8 \cdot 10^{-34}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 20: 29.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -1.1e+19)
     t_1
     (if (<= x 1.15e-179)
       (* c (* t j))
       (if (<= x 2.65e+41) (* c (- (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -1.1e+19) {
		tmp = t_1;
	} else if (x <= 1.15e-179) {
		tmp = c * (t * j);
	} else if (x <= 2.65e+41) {
		tmp = c * -(z * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-1.1d+19)) then
        tmp = t_1
    else if (x <= 1.15d-179) then
        tmp = c * (t * j)
    else if (x <= 2.65d+41) then
        tmp = c * -(z * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -1.1e+19) {
		tmp = t_1;
	} else if (x <= 1.15e-179) {
		tmp = c * (t * j);
	} else if (x <= 2.65e+41) {
		tmp = c * -(z * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -1.1e+19:
		tmp = t_1
	elif x <= 1.15e-179:
		tmp = c * (t * j)
	elif x <= 2.65e+41:
		tmp = c * -(z * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.1e+19)
		tmp = t_1;
	elseif (x <= 1.15e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 2.65e+41)
		tmp = Float64(c * Float64(-Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.1e+19)
		tmp = t_1;
	elseif (x <= 1.15e-179)
		tmp = c * (t * j);
	elseif (x <= 2.65e+41)
		tmp = c * -(z * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+19], t$95$1, If[LessEqual[x, 1.15e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.65e+41], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e19 or 2.6499999999999998e41 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

   4. Simplified 52.5%

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

   5. Taylor expanded in z around inf 46.0%

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

      1. associate-*r* 48.1%

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

      2. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   if -1.1e19 < x < 1.14999999999999994e-179

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 45.3%

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

   3. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

   if 1.14999999999999994e-179 < x < 2.6499999999999998e41

   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 c around inf 53.8%

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

   3. Taylor expanded in j around 0 39.8%

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

      1. neg-mul-1 39.8%

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

      2. distribute-lft-neg-in 39.8%

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

      3. *-commutative 39.8%

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

   5. Simplified 39.8%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 21: 29.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= x -2.8e+19)
     t_1
     (if (<= x 1.45e-179)
       (* c (* t j))
       (if (<= x 2.7e+44) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (x <= -2.8e+19) {
		tmp = t_1;
	} else if (x <= 1.45e-179) {
		tmp = c * (t * j);
	} else if (x <= 2.7e+44) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (x <= (-2.8d+19)) then
        tmp = t_1
    else if (x <= 1.45d-179) then
        tmp = c * (t * j)
    else if (x <= 2.7d+44) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (x <= -2.8e+19) {
		tmp = t_1;
	} else if (x <= 1.45e-179) {
		tmp = c * (t * j);
	} else if (x <= 2.7e+44) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if x <= -2.8e+19:
		tmp = t_1
	elif x <= 1.45e-179:
		tmp = c * (t * j)
	elif x <= 2.7e+44:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (x <= -2.8e+19)
		tmp = t_1;
	elseif (x <= 1.45e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 2.7e+44)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (x <= -2.8e+19)
		tmp = t_1;
	elseif (x <= 1.45e-179)
		tmp = c * (t * j);
	elseif (x <= 2.7e+44)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+19], t$95$1, If[LessEqual[x, 1.45e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+44], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e19 or 2.7e44 < x

   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 y around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in z around inf 46.3%

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

   if -2.8e19 < x < 1.4499999999999999e-179

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 45.3%

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

   3. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

   if 1.4499999999999999e-179 < x < 2.7e44

   1. Initial program 71.8%

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

   2. Taylor expanded in j around 0 71.6%

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

      1. fma-neg 71.6%

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

      2. *-commutative 71.6%

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

      3. *-commutative 71.6%

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

      4. fma-neg 71.6%

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

   4. Simplified 71.6%

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

      1. *-commutative 71.6%

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

      2. prod-diff 59.3%

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

      3. fma-neg 59.3%

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

      4. cancel-sign-sub-inv 59.3%

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

      5. fma-def 59.3%

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

      6. *-commutative 59.3%

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

   6. Applied egg-rr 59.3%

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

   7. Taylor expanded in i around inf 28.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 28.7%

         \[\leadsto \color{blue}{-b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)} \]

      2. *-commutative 28.7%

         \[\leadsto -\color{blue}{\left(i \cdot \left(a + -2 \cdot a\right)\right) \cdot b} \]

      3. distribute-rgt-in 14.4%

         \[\leadsto -\color{blue}{\left(a \cdot i + \left(-2 \cdot a\right) \cdot i\right)} \cdot b \]

      4. associate-*r* 14.4%

         \[\leadsto -\left(a \cdot i + \color{blue}{-2 \cdot \left(a \cdot i\right)}\right) \cdot b \]

      5. +-commutative 14.4%

         \[\leadsto -\color{blue}{\left(-2 \cdot \left(a \cdot i\right) + a \cdot i\right)} \cdot b \]

      6. distribute-lft1-in 28.7%

         \[\leadsto -\color{blue}{\left(\left(-2 + 1\right) \cdot \left(a \cdot i\right)\right)} \cdot b \]

      7. metadata-eval 28.7%

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

      8. neg-mul-1 28.7%

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

      9. distribute-lft-neg-in 28.7%

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

      10. associate-*r* 26.8%

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

      11. remove-double-neg 26.8%

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

      12. *-commutative 26.8%

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

      13. associate-*l* 30.7%

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

      14. *-commutative 30.7%

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

   9. Simplified 30.7%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 22: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -9.2e+18)
     t_1
     (if (<= x 1.1e-179)
       (* c (* t j))
       (if (<= x 1.25e+44) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -9.2e+18) {
		tmp = t_1;
	} else if (x <= 1.1e-179) {
		tmp = c * (t * j);
	} else if (x <= 1.25e+44) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-9.2d+18)) then
        tmp = t_1
    else if (x <= 1.1d-179) then
        tmp = c * (t * j)
    else if (x <= 1.25d+44) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -9.2e+18) {
		tmp = t_1;
	} else if (x <= 1.1e-179) {
		tmp = c * (t * j);
	} else if (x <= 1.25e+44) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -9.2e+18:
		tmp = t_1
	elif x <= 1.1e-179:
		tmp = c * (t * j)
	elif x <= 1.25e+44:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -9.2e+18)
		tmp = t_1;
	elseif (x <= 1.1e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 1.25e+44)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -9.2e+18)
		tmp = t_1;
	elseif (x <= 1.1e-179)
		tmp = c * (t * j);
	elseif (x <= 1.25e+44)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+18], t$95$1, If[LessEqual[x, 1.1e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+44], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.2e18 or 1.2499999999999999e44 < x

   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 y around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in z around inf 46.3%

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

      1. associate-*r* 48.5%

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

      2. *-commutative 48.5%

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

   7. Simplified 48.5%

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

   if -9.2e18 < x < 1.10000000000000002e-179

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 45.3%

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

   3. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

   if 1.10000000000000002e-179 < x < 1.2499999999999999e44

   1. Initial program 71.8%

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

   2. Taylor expanded in j around 0 71.6%

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

      1. fma-neg 71.6%

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

      2. *-commutative 71.6%

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

      3. *-commutative 71.6%

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

      4. fma-neg 71.6%

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

   4. Simplified 71.6%

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

      1. *-commutative 71.6%

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

      2. prod-diff 59.3%

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

      3. fma-neg 59.3%

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

      4. cancel-sign-sub-inv 59.3%

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

      5. fma-def 59.3%

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

      6. *-commutative 59.3%

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

   6. Applied egg-rr 59.3%

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

   7. Taylor expanded in i around inf 28.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 28.7%

         \[\leadsto \color{blue}{-b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)} \]

      2. *-commutative 28.7%

         \[\leadsto -\color{blue}{\left(i \cdot \left(a + -2 \cdot a\right)\right) \cdot b} \]

      3. distribute-rgt-in 14.4%

         \[\leadsto -\color{blue}{\left(a \cdot i + \left(-2 \cdot a\right) \cdot i\right)} \cdot b \]

      4. associate-*r* 14.4%

         \[\leadsto -\left(a \cdot i + \color{blue}{-2 \cdot \left(a \cdot i\right)}\right) \cdot b \]

      5. +-commutative 14.4%

         \[\leadsto -\color{blue}{\left(-2 \cdot \left(a \cdot i\right) + a \cdot i\right)} \cdot b \]

      6. distribute-lft1-in 28.7%

         \[\leadsto -\color{blue}{\left(\left(-2 + 1\right) \cdot \left(a \cdot i\right)\right)} \cdot b \]

      7. metadata-eval 28.7%

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

      8. neg-mul-1 28.7%

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

      9. distribute-lft-neg-in 28.7%

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

      10. associate-*r* 26.8%

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

      11. remove-double-neg 26.8%

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

      12. *-commutative 26.8%

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

      13. associate-*l* 30.7%

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

      14. *-commutative 30.7%

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

   9. Simplified 30.7%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 23: 29.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.3e+118)
   (* b (* a i))
   (if (<= b 1.5e+40) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.3e+118) {
		tmp = b * (a * i);
	} else if (b <= 1.5e+40) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3.3d+118)) then
        tmp = b * (a * i)
    else if (b <= 1.5d+40) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.3e+118) {
		tmp = b * (a * i);
	} else if (b <= 1.5e+40) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.3e+118:
		tmp = b * (a * i)
	elif b <= 1.5e+40:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.3e+118)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 1.5e+40)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.3e+118)
		tmp = b * (a * i);
	elseif (b <= 1.5e+40)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.3e+118], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+40], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3e118

   1. Initial program 76.2%

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

   2. Taylor expanded in b around inf 71.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 71.3%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 71.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 33.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.5%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. associate-*l* 38.5%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} \]

   7. Simplified 38.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} \]

   if -3.3e118 < b < 1.5000000000000001e40

   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 c around inf 36.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 28.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 28.5%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   5. Simplified 28.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 1.5000000000000001e40 < b

   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 b around inf 61.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 61.2%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 61.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 24: 29.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.22e+100)
   (* i (* a b))
   (if (<= b 7.5e+41) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.22e+100) {
		tmp = i * (a * b);
	} else if (b <= 7.5e+41) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.22d+100)) then
        tmp = i * (a * b)
    else if (b <= 7.5d+41) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.22e+100) {
		tmp = i * (a * b);
	} else if (b <= 7.5e+41) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.22e+100:
		tmp = i * (a * b)
	elif b <= 7.5e+41:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.22e+100)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= 7.5e+41)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.22e+100)
		tmp = i * (a * b);
	elseif (b <= 7.5e+41)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.22e+100], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+41], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.21999999999999995e100

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around 0 73.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. fma-neg 78.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      2. *-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - \color{blue}{t \cdot a}, -b \cdot \left(c \cdot z - a \cdot i\right)\right) \]

      3. *-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) \]

      4. fma-neg 73.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   4. Simplified 73.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]
   5. Step-by-step derivation

      1. *-commutative 73.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right) \]

      2. prod-diff 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{fma}\left(c, z, -i \cdot a\right) + \mathsf{fma}\left(-i, a, i \cdot a\right)\right)} \]

      3. fma-neg 63.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{\left(c \cdot z - i \cdot a\right)} + \mathsf{fma}\left(-i, a, i \cdot a\right)\right) \]

      4. cancel-sign-sub-inv 63.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{\left(c \cdot z + \left(-i\right) \cdot a\right)} + \mathsf{fma}\left(-i, a, i \cdot a\right)\right) \]

      5. fma-def 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{\mathsf{fma}\left(c, z, \left(-i\right) \cdot a\right)} + \mathsf{fma}\left(-i, a, i \cdot a\right)\right) \]

      6. *-commutative 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\mathsf{fma}\left(c, z, \left(-i\right) \cdot a\right) + \mathsf{fma}\left(-i, a, \color{blue}{a \cdot i}\right)\right) \]

   6. Applied egg-rr 63.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\mathsf{fma}\left(c, z, \left(-i\right) \cdot a\right) + \mathsf{fma}\left(-i, a, a \cdot i\right)\right)} \]

   7. Taylor expanded in i around inf 38.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto \color{blue}{-b \cdot \left(i \cdot \left(a + -2 \cdot a\right)\right)} \]

      2. *-commutative 38.3%

         \[\leadsto -\color{blue}{\left(i \cdot \left(a + -2 \cdot a\right)\right) \cdot b} \]

      3. distribute-rgt-in 23.7%

         \[\leadsto -\color{blue}{\left(a \cdot i + \left(-2 \cdot a\right) \cdot i\right)} \cdot b \]

      4. associate-*r* 23.7%

         \[\leadsto -\left(a \cdot i + \color{blue}{-2 \cdot \left(a \cdot i\right)}\right) \cdot b \]

      5. +-commutative 23.7%

         \[\leadsto -\color{blue}{\left(-2 \cdot \left(a \cdot i\right) + a \cdot i\right)} \cdot b \]

      6. distribute-lft1-in 38.3%

         \[\leadsto -\color{blue}{\left(\left(-2 + 1\right) \cdot \left(a \cdot i\right)\right)} \cdot b \]

      7. metadata-eval 38.3%

         \[\leadsto -\left(\color{blue}{-1} \cdot \left(a \cdot i\right)\right) \cdot b \]

      8. neg-mul-1 38.3%

         \[\leadsto -\color{blue}{\left(-a \cdot i\right)} \cdot b \]

      9. distribute-lft-neg-in 38.3%

         \[\leadsto -\color{blue}{\left(-\left(a \cdot i\right) \cdot b\right)} \]

      10. associate-*r* 36.1%

          \[\leadsto -\left(-\color{blue}{a \cdot \left(i \cdot b\right)}\right) \]

      11. remove-double-neg 36.1%

          \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

      12. *-commutative 36.1%

          \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} \]

      13. associate-*l* 40.7%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

      14. *-commutative 40.7%

          \[\leadsto i \cdot \color{blue}{\left(a \cdot b\right)} \]

   9. Simplified 40.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -1.21999999999999995e100 < b < 7.50000000000000072e41

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 36.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 27.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 27.8%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   5. Simplified 27.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 7.50000000000000072e41 < b

   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 b around inf 61.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 61.2%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 61.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 35.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 25: 21.8% 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 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 b around inf 35.4%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Step-by-step derivation

   1. *-commutative 35.4%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

4. Simplified 35.4%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

5. Taylor expanded in i around inf 17.4%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

6. Final simplification 17.4%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024024 
(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)))))