Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 80.8%

Time: 20.4s

Alternatives: 20

Speedup: 0.5×

• 57.0% 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: 73.1% 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: 80.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := \left(t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (+ t_1 (* x (- (* y z) (* t a)))) (* j (- (* t c) (* y i))))))
   (if (<= t_2 INFINITY) 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 = b * ((a * i) - (z * c));
	double t_2 = (t_1 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (t_1 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (t_1 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	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(Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		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 = b * ((a * i) - (z * c));
	t_2 = (t_1 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= Inf)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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 93.3%

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

   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 b around inf 57.1%

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

4. Final simplification 88.8%

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

Alternative 2: 29.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := \left(t \cdot a\right) \cdot \left(-x\right)\\ t_3 := \left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 10^{-241}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* (* t a) (- x))) (t_3 (* (* b c) (- z))))
   (if (<= b -2.8e+134)
     t_3
     (if (<= b -6e+48)
       t_1
       (if (<= b -8e+28)
         t_3
         (if (<= b -6.8e-168)
           (* y (* x z))
           (if (<= b 1e-241)
             (* t (* c j))
             (if (<= b 1.4e-172)
               t_2
               (if (<= b 3e-59)
                 (* c (* t j))
                 (if (<= b 7.8e+31)
                   t_1
                   (if (<= b 1.06e+89)
                     t_2
                     (if (<= b 1.8e+160) (* a (* b i)) t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = (t * a) * -x;
	double t_3 = (b * c) * -z;
	double tmp;
	if (b <= -2.8e+134) {
		tmp = t_3;
	} else if (b <= -6e+48) {
		tmp = t_1;
	} else if (b <= -8e+28) {
		tmp = t_3;
	} else if (b <= -6.8e-168) {
		tmp = y * (x * z);
	} else if (b <= 1e-241) {
		tmp = t * (c * j);
	} else if (b <= 1.4e-172) {
		tmp = t_2;
	} else if (b <= 3e-59) {
		tmp = c * (t * j);
	} else if (b <= 7.8e+31) {
		tmp = t_1;
	} else if (b <= 1.06e+89) {
		tmp = t_2;
	} else if (b <= 1.8e+160) {
		tmp = a * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = (t * a) * -x
    t_3 = (b * c) * -z
    if (b <= (-2.8d+134)) then
        tmp = t_3
    else if (b <= (-6d+48)) then
        tmp = t_1
    else if (b <= (-8d+28)) then
        tmp = t_3
    else if (b <= (-6.8d-168)) then
        tmp = y * (x * z)
    else if (b <= 1d-241) then
        tmp = t * (c * j)
    else if (b <= 1.4d-172) then
        tmp = t_2
    else if (b <= 3d-59) then
        tmp = c * (t * j)
    else if (b <= 7.8d+31) then
        tmp = t_1
    else if (b <= 1.06d+89) then
        tmp = t_2
    else if (b <= 1.8d+160) then
        tmp = a * (b * i)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = (t * a) * -x;
	double t_3 = (b * c) * -z;
	double tmp;
	if (b <= -2.8e+134) {
		tmp = t_3;
	} else if (b <= -6e+48) {
		tmp = t_1;
	} else if (b <= -8e+28) {
		tmp = t_3;
	} else if (b <= -6.8e-168) {
		tmp = y * (x * z);
	} else if (b <= 1e-241) {
		tmp = t * (c * j);
	} else if (b <= 1.4e-172) {
		tmp = t_2;
	} else if (b <= 3e-59) {
		tmp = c * (t * j);
	} else if (b <= 7.8e+31) {
		tmp = t_1;
	} else if (b <= 1.06e+89) {
		tmp = t_2;
	} else if (b <= 1.8e+160) {
		tmp = a * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = (t * a) * -x
	t_3 = (b * c) * -z
	tmp = 0
	if b <= -2.8e+134:
		tmp = t_3
	elif b <= -6e+48:
		tmp = t_1
	elif b <= -8e+28:
		tmp = t_3
	elif b <= -6.8e-168:
		tmp = y * (x * z)
	elif b <= 1e-241:
		tmp = t * (c * j)
	elif b <= 1.4e-172:
		tmp = t_2
	elif b <= 3e-59:
		tmp = c * (t * j)
	elif b <= 7.8e+31:
		tmp = t_1
	elif b <= 1.06e+89:
		tmp = t_2
	elif b <= 1.8e+160:
		tmp = a * (b * i)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(Float64(t * a) * Float64(-x))
	t_3 = Float64(Float64(b * c) * Float64(-z))
	tmp = 0.0
	if (b <= -2.8e+134)
		tmp = t_3;
	elseif (b <= -6e+48)
		tmp = t_1;
	elseif (b <= -8e+28)
		tmp = t_3;
	elseif (b <= -6.8e-168)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1e-241)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 1.4e-172)
		tmp = t_2;
	elseif (b <= 3e-59)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 7.8e+31)
		tmp = t_1;
	elseif (b <= 1.06e+89)
		tmp = t_2;
	elseif (b <= 1.8e+160)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = (t * a) * -x;
	t_3 = (b * c) * -z;
	tmp = 0.0;
	if (b <= -2.8e+134)
		tmp = t_3;
	elseif (b <= -6e+48)
		tmp = t_1;
	elseif (b <= -8e+28)
		tmp = t_3;
	elseif (b <= -6.8e-168)
		tmp = y * (x * z);
	elseif (b <= 1e-241)
		tmp = t * (c * j);
	elseif (b <= 1.4e-172)
		tmp = t_2;
	elseif (b <= 3e-59)
		tmp = c * (t * j);
	elseif (b <= 7.8e+31)
		tmp = t_1;
	elseif (b <= 1.06e+89)
		tmp = t_2;
	elseif (b <= 1.8e+160)
		tmp = a * (b * i);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[b, -2.8e+134], t$95$3, If[LessEqual[b, -6e+48], t$95$1, If[LessEqual[b, -8e+28], t$95$3, If[LessEqual[b, -6.8e-168], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-241], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-172], t$95$2, If[LessEqual[b, 3e-59], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+31], t$95$1, If[LessEqual[b, 1.06e+89], t$95$2, If[LessEqual[b, 1.8e+160], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.7999999999999999e134 or -5.9999999999999999e48 < b < -7.99999999999999967e28 or 1.80000000000000011e160 < b

   1. Initial program 82.2%

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

   2. Taylor expanded in t around 0 80.0%

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

      1. *-commutative 80.0%

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

      2. cancel-sign-sub-inv 80.0%

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

      3. *-commutative 80.0%

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

      4. associate-*r* 80.1%

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

      5. associate-*r* 77.7%

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

      6. associate-*r* 77.7%

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

      7. distribute-rgt-in 77.7%

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

      8. +-commutative 77.7%

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

      9. mul-1-neg 77.7%

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

      10. unsub-neg 77.7%

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

      11. *-commutative 77.7%

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

      12. distribute-lft-neg-in 77.7%

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

      13. distribute-rgt-neg-in 77.7%

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

      14. neg-sub0 77.7%

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

      15. *-commutative 77.7%

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

      16. associate--r- 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in z around inf 77.8%

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

   6. Taylor expanded in c around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. associate-*r* 59.5%

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

      3. *-commutative 59.5%

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

      4. distribute-rgt-neg-in 59.5%

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

      5. *-commutative 59.5%

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

      6. distribute-rgt-neg-in 59.5%

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

   8. Simplified 59.5%

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

   if -2.7999999999999999e134 < b < -5.9999999999999999e48 or 3.0000000000000001e-59 < b < 7.79999999999999999e31

   1. Initial program 69.3%

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

   2. Taylor expanded in t around 0 62.2%

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

      1. *-commutative 62.2%

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

      2. cancel-sign-sub-inv 62.2%

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

      3. *-commutative 62.2%

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

      4. associate-*r* 62.2%

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

      5. associate-*r* 65.9%

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

      6. associate-*r* 65.9%

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

      7. distribute-rgt-in 72.8%

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

      8. +-commutative 72.8%

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

      9. mul-1-neg 72.8%

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

      10. unsub-neg 72.8%

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

      11. *-commutative 72.8%

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

      12. distribute-lft-neg-in 72.8%

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

      13. distribute-rgt-neg-in 72.8%

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

      14. neg-sub0 72.8%

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

      15. *-commutative 72.8%

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

      16. associate--r- 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in x around inf 49.6%

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

      1. *-commutative 49.6%

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

   7. Simplified 49.6%

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

   if -7.99999999999999967e28 < b < -6.80000000000000043e-168

   1. Initial program 90.0%

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

   2. Taylor expanded in y around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

   4. Simplified 55.3%

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

   5. Taylor expanded in z around inf 41.9%

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

   if -6.80000000000000043e-168 < b < 9.9999999999999997e-242

   1. Initial program 83.8%

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

   2. Taylor expanded in j around inf 66.2%

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

   3. Taylor expanded in c around inf 43.5%

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

      1. associate-*r* 43.5%

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

   5. Simplified 43.5%

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

   if 9.9999999999999997e-242 < b < 1.40000000000000006e-172 or 7.79999999999999999e31 < b < 1.05999999999999997e89

   1. Initial program 75.4%

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

   2. Taylor expanded in x around inf 57.2%

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

      1. *-commutative 57.2%

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

   4. Simplified 57.2%

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

   5. Taylor expanded in z around 0 48.0%

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

      1. associate-*r* 48.0%

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

      2. neg-mul-1 48.0%

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

      3. *-commutative 48.0%

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

   7. Simplified 48.0%

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

   if 1.40000000000000006e-172 < b < 3.0000000000000001e-59

   1. Initial program 87.8%

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

   2. Taylor expanded in j around inf 60.1%

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

   3. Taylor expanded in c around inf 52.2%

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

   if 1.05999999999999997e89 < b < 1.80000000000000011e160

   1. Initial program 77.8%

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

   2. Taylor expanded in t around 0 88.9%

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

      1. *-commutative 88.9%

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

      2. cancel-sign-sub-inv 88.9%

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

      3. *-commutative 88.9%

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

      4. associate-*r* 88.9%

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

      5. associate-*r* 88.9%

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

      6. associate-*r* 88.9%

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

      7. distribute-rgt-in 88.9%

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

      8. +-commutative 88.9%

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

      9. mul-1-neg 88.9%

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

      10. unsub-neg 88.9%

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

      11. *-commutative 88.9%

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

      12. distribute-lft-neg-in 88.9%

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

      13. distribute-rgt-neg-in 88.9%

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

      14. neg-sub0 88.9%

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

      15. *-commutative 88.9%

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

      16. associate--r- 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in a around inf 67.2%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+134}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{+28}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 10^{-241}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-172}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+89}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -3.1e+209)
     t_3
     (if (<= b -6.5e+154)
       t_2
       (if (<= b -2.5e+61)
         (* y (- (* x z) (* i j)))
         (if (<= b -2.55e-76)
           t_2
           (if (<= b 1.08e-240)
             (* j (- (* t c) (* y i)))
             (if (<= b 3.1e-183)
               t_1
               (if (<= b 2.7e-79)
                 (* c (- (* t j) (* z b)))
                 (if (<= b 2.05e+80) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+209) {
		tmp = t_3;
	} else if (b <= -6.5e+154) {
		tmp = t_2;
	} else if (b <= -2.5e+61) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -2.55e-76) {
		tmp = t_2;
	} else if (b <= 1.08e-240) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 3.1e-183) {
		tmp = t_1;
	} else if (b <= 2.7e-79) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 2.05e+80) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-3.1d+209)) then
        tmp = t_3
    else if (b <= (-6.5d+154)) then
        tmp = t_2
    else if (b <= (-2.5d+61)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= (-2.55d-76)) then
        tmp = t_2
    else if (b <= 1.08d-240) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 3.1d-183) then
        tmp = t_1
    else if (b <= 2.7d-79) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 2.05d+80) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+209) {
		tmp = t_3;
	} else if (b <= -6.5e+154) {
		tmp = t_2;
	} else if (b <= -2.5e+61) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -2.55e-76) {
		tmp = t_2;
	} else if (b <= 1.08e-240) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 3.1e-183) {
		tmp = t_1;
	} else if (b <= 2.7e-79) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 2.05e+80) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.1e+209:
		tmp = t_3
	elif b <= -6.5e+154:
		tmp = t_2
	elif b <= -2.5e+61:
		tmp = y * ((x * z) - (i * j))
	elif b <= -2.55e-76:
		tmp = t_2
	elif b <= 1.08e-240:
		tmp = j * ((t * c) - (y * i))
	elif b <= 3.1e-183:
		tmp = t_1
	elif b <= 2.7e-79:
		tmp = c * ((t * j) - (z * b))
	elif b <= 2.05e+80:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.1e+209)
		tmp = t_3;
	elseif (b <= -6.5e+154)
		tmp = t_2;
	elseif (b <= -2.5e+61)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= -2.55e-76)
		tmp = t_2;
	elseif (b <= 1.08e-240)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 3.1e-183)
		tmp = t_1;
	elseif (b <= 2.7e-79)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 2.05e+80)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = z * ((x * y) - (b * c));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.1e+209)
		tmp = t_3;
	elseif (b <= -6.5e+154)
		tmp = t_2;
	elseif (b <= -2.5e+61)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= -2.55e-76)
		tmp = t_2;
	elseif (b <= 1.08e-240)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 3.1e-183)
		tmp = t_1;
	elseif (b <= 2.7e-79)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 2.05e+80)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+209], t$95$3, If[LessEqual[b, -6.5e+154], t$95$2, If[LessEqual[b, -2.5e+61], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.55e-76], t$95$2, If[LessEqual[b, 1.08e-240], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-183], t$95$1, If[LessEqual[b, 2.7e-79], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+80], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.1000000000000001e209 or 2.05000000000000001e80 < b

   1. Initial program 82.8%

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

   2. Taylor expanded in b around inf 82.4%

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

   if -3.1000000000000001e209 < b < -6.5000000000000005e154 or -2.50000000000000009e61 < b < -2.54999999999999993e-76

   1. Initial program 77.3%

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

   2. Taylor expanded in z around inf 81.3%

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

   if -6.5000000000000005e154 < b < -2.50000000000000009e61

   1. Initial program 71.2%

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

   2. Taylor expanded in y around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

   4. Simplified 65.2%

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

   if -2.54999999999999993e-76 < b < 1.08e-240

   1. Initial program 87.5%

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

   2. Taylor expanded in j around inf 59.8%

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

   if 1.08e-240 < b < 3.1e-183 or 2.7000000000000002e-79 < b < 2.05000000000000001e80

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 62.5%

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

      1. *-commutative 62.5%

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

   4. Simplified 62.5%

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

   if 3.1e-183 < b < 2.7000000000000002e-79

   1. Initial program 84.5%

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

   2. Taylor expanded in c around inf 61.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 49.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-238}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -4.1e+210)
     t_3
     (if (<= b -7.5e+140)
       t_2
       (if (<= b -9.5e+65)
         (* i (- (* a b) (* y j)))
         (if (<= b -5.2e-74)
           t_2
           (if (<= b 1.45e-238)
             (* j (- (* t c) (* y i)))
             (if (<= b 2.1e-179)
               t_1
               (if (<= b 6.2e-75)
                 (* c (- (* t j) (* z b)))
                 (if (<= b 5.6e+81) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.1e+210) {
		tmp = t_3;
	} else if (b <= -7.5e+140) {
		tmp = t_2;
	} else if (b <= -9.5e+65) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -5.2e-74) {
		tmp = t_2;
	} else if (b <= 1.45e-238) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.1e-179) {
		tmp = t_1;
	} else if (b <= 6.2e-75) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 5.6e+81) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-4.1d+210)) then
        tmp = t_3
    else if (b <= (-7.5d+140)) then
        tmp = t_2
    else if (b <= (-9.5d+65)) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= (-5.2d-74)) then
        tmp = t_2
    else if (b <= 1.45d-238) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 2.1d-179) then
        tmp = t_1
    else if (b <= 6.2d-75) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 5.6d+81) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.1e+210) {
		tmp = t_3;
	} else if (b <= -7.5e+140) {
		tmp = t_2;
	} else if (b <= -9.5e+65) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -5.2e-74) {
		tmp = t_2;
	} else if (b <= 1.45e-238) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.1e-179) {
		tmp = t_1;
	} else if (b <= 6.2e-75) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 5.6e+81) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.1e+210:
		tmp = t_3
	elif b <= -7.5e+140:
		tmp = t_2
	elif b <= -9.5e+65:
		tmp = i * ((a * b) - (y * j))
	elif b <= -5.2e-74:
		tmp = t_2
	elif b <= 1.45e-238:
		tmp = j * ((t * c) - (y * i))
	elif b <= 2.1e-179:
		tmp = t_1
	elif b <= 6.2e-75:
		tmp = c * ((t * j) - (z * b))
	elif b <= 5.6e+81:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.1e+210)
		tmp = t_3;
	elseif (b <= -7.5e+140)
		tmp = t_2;
	elseif (b <= -9.5e+65)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= -5.2e-74)
		tmp = t_2;
	elseif (b <= 1.45e-238)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 2.1e-179)
		tmp = t_1;
	elseif (b <= 6.2e-75)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 5.6e+81)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = z * ((x * y) - (b * c));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.1e+210)
		tmp = t_3;
	elseif (b <= -7.5e+140)
		tmp = t_2;
	elseif (b <= -9.5e+65)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= -5.2e-74)
		tmp = t_2;
	elseif (b <= 1.45e-238)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 2.1e-179)
		tmp = t_1;
	elseif (b <= 6.2e-75)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 5.6e+81)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+210], t$95$3, If[LessEqual[b, -7.5e+140], t$95$2, If[LessEqual[b, -9.5e+65], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-74], t$95$2, If[LessEqual[b, 1.45e-238], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-179], t$95$1, If[LessEqual[b, 6.2e-75], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+81], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.10000000000000001e210 or 5.5999999999999999e81 < b

   1. Initial program 82.8%

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

   2. Taylor expanded in b around inf 82.4%

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

   if -4.10000000000000001e210 < b < -7.4999999999999997e140 or -9.5000000000000005e65 < b < -5.2000000000000002e-74

   1. Initial program 79.0%

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

   2. Taylor expanded in z around inf 80.2%

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

   if -7.4999999999999997e140 < b < -9.5000000000000005e65

   1. Initial program 65.0%

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

   2. Taylor expanded in i around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

   4. Simplified 65.0%

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

   if -5.2000000000000002e-74 < b < 1.4499999999999999e-238

   1. Initial program 87.5%

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

   2. Taylor expanded in j around inf 59.8%

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

   if 1.4499999999999999e-238 < b < 2.0999999999999999e-179 or 6.20000000000000013e-75 < b < 5.5999999999999999e81

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 62.5%

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

      1. *-commutative 62.5%

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

   4. Simplified 62.5%

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

   if 2.0999999999999999e-179 < b < 6.20000000000000013e-75

   1. Initial program 84.5%

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

   2. Taylor expanded in c around inf 61.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+210}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-238}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5: 62.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-37} \lor \neg \left(c \leq 4.1 \cdot 10^{+99}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.9e-37) (not (<= c 4.1e+99)))
   (* c (- (* t j) (* z b)))
   (+ (* b (- (* a i) (* z c))) (* y (- (* x z) (* i j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.9e-37) || !(c <= 4.1e+99)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = (b * ((a * i) - (z * c))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.9d-37)) .or. (.not. (c <= 4.1d+99))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = (b * ((a * i) - (z * c))) + (y * ((x * z) - (i * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.9e-37) || !(c <= 4.1e+99)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = (b * ((a * i) - (z * c))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.9e-37) or not (c <= 4.1e+99):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = (b * ((a * i) - (z * c))) + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.9e-37) || !(c <= 4.1e+99))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.9e-37) || ~((c <= 4.1e+99)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = (b * ((a * i) - (z * c))) + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.9e-37], N[Not[LessEqual[c, 4.1e+99]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.9000000000000002e-37 or 4.09999999999999979e99 < c

   1. Initial program 77.9%

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

   2. Taylor expanded in c around inf 75.5%

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

   if -1.9000000000000002e-37 < c < 4.09999999999999979e99

   1. Initial program 84.6%

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

   2. Taylor expanded in t around 0 66.2%

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

      1. *-commutative 66.2%

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

      2. cancel-sign-sub-inv 66.2%

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

      3. *-commutative 66.2%

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

      4. associate-*r* 66.2%

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

      5. associate-*r* 66.2%

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

      6. associate-*r* 66.2%

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

      7. distribute-rgt-in 67.6%

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

      8. +-commutative 67.6%

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

      9. mul-1-neg 67.6%

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

      10. unsub-neg 67.6%

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

      11. *-commutative 67.6%

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

      12. distribute-lft-neg-in 67.6%

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

      13. distribute-rgt-neg-in 67.6%

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

      14. neg-sub0 67.6%

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

      15. *-commutative 67.6%

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

      16. associate--r- 67.6%

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

   4. Simplified 67.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-37} \lor \neg \left(c \leq 4.1 \cdot 10^{+99}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 6: 49.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.8e+134)
     t_2
     (if (<= b -2e-172)
       t_1
       (if (<= b 8.5e-244)
         (* j (- (* t c) (* y i)))
         (if (<= b 4.3e-182)
           t_1
           (if (<= b 2.4e-81)
             (* c (- (* t j) (* z b)))
             (if (<= b 4.5e+80) 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.8e+134) {
		tmp = t_2;
	} else if (b <= -2e-172) {
		tmp = t_1;
	} else if (b <= 8.5e-244) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 4.3e-182) {
		tmp = t_1;
	} else if (b <= 2.4e-81) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 4.5e+80) {
		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 = b * ((a * i) - (z * c))
    if (b <= (-2.8d+134)) then
        tmp = t_2
    else if (b <= (-2d-172)) then
        tmp = t_1
    else if (b <= 8.5d-244) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 4.3d-182) then
        tmp = t_1
    else if (b <= 2.4d-81) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 4.5d+80) 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.8e+134) {
		tmp = t_2;
	} else if (b <= -2e-172) {
		tmp = t_1;
	} else if (b <= 8.5e-244) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 4.3e-182) {
		tmp = t_1;
	} else if (b <= 2.4e-81) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 4.5e+80) {
		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 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.8e+134:
		tmp = t_2
	elif b <= -2e-172:
		tmp = t_1
	elif b <= 8.5e-244:
		tmp = j * ((t * c) - (y * i))
	elif b <= 4.3e-182:
		tmp = t_1
	elif b <= 2.4e-81:
		tmp = c * ((t * j) - (z * b))
	elif b <= 4.5e+80:
		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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.8e+134)
		tmp = t_2;
	elseif (b <= -2e-172)
		tmp = t_1;
	elseif (b <= 8.5e-244)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 4.3e-182)
		tmp = t_1;
	elseif (b <= 2.4e-81)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 4.5e+80)
		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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.8e+134)
		tmp = t_2;
	elseif (b <= -2e-172)
		tmp = t_1;
	elseif (b <= 8.5e-244)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 4.3e-182)
		tmp = t_1;
	elseif (b <= 2.4e-81)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 4.5e+80)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+134], t$95$2, If[LessEqual[b, -2e-172], t$95$1, If[LessEqual[b, 8.5e-244], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e-182], t$95$1, If[LessEqual[b, 2.4e-81], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+80], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.7999999999999999e134 or 4.50000000000000007e80 < b

   1. Initial program 84.5%

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

   2. Taylor expanded in b around inf 76.3%

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

   if -2.7999999999999999e134 < b < -2.0000000000000001e-172 or 8.4999999999999999e-244 < b < 4.3e-182 or 2.3999999999999999e-81 < b < 4.50000000000000007e80

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   if -2.0000000000000001e-172 < b < 8.4999999999999999e-244

   1. Initial program 83.8%

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

   2. Taylor expanded in j around inf 66.2%

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

   if 4.3e-182 < b < 2.3999999999999999e-81

   1. Initial program 84.5%

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

   2. Taylor expanded in c around inf 61.5%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 7: 49.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.9 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+39} \lor \neg \left(b \leq 4 \cdot 10^{+88}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4.9e-60)
     t_1
     (if (<= b 1.85e-58)
       (* j (- (* t c) (* y i)))
       (if (<= b 2.1e-32)
         (* x (* y z))
         (if (or (<= b 3e+39) (not (<= b 4e+88))) t_1 (* (* t a) (- x))))))))

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 tmp;
	if (b <= -4.9e-60) {
		tmp = t_1;
	} else if (b <= 1.85e-58) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.1e-32) {
		tmp = x * (y * z);
	} else if ((b <= 3e+39) || !(b <= 4e+88)) {
		tmp = t_1;
	} else {
		tmp = (t * a) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-4.9d-60)) then
        tmp = t_1
    else if (b <= 1.85d-58) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 2.1d-32) then
        tmp = x * (y * z)
    else if ((b <= 3d+39) .or. (.not. (b <= 4d+88))) then
        tmp = t_1
    else
        tmp = (t * a) * -x
    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 tmp;
	if (b <= -4.9e-60) {
		tmp = t_1;
	} else if (b <= 1.85e-58) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.1e-32) {
		tmp = x * (y * z);
	} else if ((b <= 3e+39) || !(b <= 4e+88)) {
		tmp = t_1;
	} else {
		tmp = (t * a) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.9e-60:
		tmp = t_1
	elif b <= 1.85e-58:
		tmp = j * ((t * c) - (y * i))
	elif b <= 2.1e-32:
		tmp = x * (y * z)
	elif (b <= 3e+39) or not (b <= 4e+88):
		tmp = t_1
	else:
		tmp = (t * a) * -x
	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)))
	tmp = 0.0
	if (b <= -4.9e-60)
		tmp = t_1;
	elseif (b <= 1.85e-58)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 2.1e-32)
		tmp = Float64(x * Float64(y * z));
	elseif ((b <= 3e+39) || !(b <= 4e+88))
		tmp = t_1;
	else
		tmp = Float64(Float64(t * a) * Float64(-x));
	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));
	tmp = 0.0;
	if (b <= -4.9e-60)
		tmp = t_1;
	elseif (b <= 1.85e-58)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 2.1e-32)
		tmp = x * (y * z);
	elseif ((b <= 3e+39) || ~((b <= 4e+88)))
		tmp = t_1;
	else
		tmp = (t * a) * -x;
	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]}, If[LessEqual[b, -4.9e-60], t$95$1, If[LessEqual[b, 1.85e-58], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-32], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3e+39], N[Not[LessEqual[b, 4e+88]], $MachinePrecision]], t$95$1, N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.89999999999999988e-60 or 2.0999999999999999e-32 < b < 3e39 or 3.99999999999999984e88 < b

   1. Initial program 78.1%

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

   2. Taylor expanded in b around inf 66.3%

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

   if -4.89999999999999988e-60 < b < 1.8500000000000001e-58

   1. Initial program 84.6%

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

   2. Taylor expanded in j around inf 53.7%

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

   if 1.8500000000000001e-58 < b < 2.0999999999999999e-32

   1. Initial program 83.3%

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

   2. Taylor expanded in t around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. cancel-sign-sub-inv 50.0%

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

      3. *-commutative 50.0%

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

      4. associate-*r* 49.7%

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

      5. associate-*r* 83.1%

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

      6. associate-*r* 83.1%

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

      7. distribute-rgt-in 83.1%

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

      8. +-commutative 83.1%

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

      9. mul-1-neg 83.1%

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

      10. unsub-neg 83.1%

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

      11. *-commutative 83.1%

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

      12. distribute-lft-neg-in 83.1%

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

      13. distribute-rgt-neg-in 83.1%

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

      14. neg-sub0 83.1%

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

      15. *-commutative 83.1%

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

      16. associate--r- 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in x around inf 84.0%

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

      1. *-commutative 84.0%

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

   7. Simplified 84.0%

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

   if 3e39 < b < 3.99999999999999984e88

   1. Initial program 92.1%

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

   2. Taylor expanded in x around inf 66.9%

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

      1. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in z around 0 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. *-commutative 58.7%

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

   7. Simplified 58.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+39} \lor \neg \left(b \leq 4 \cdot 10^{+88}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \end{array} \]

Alternative 8: 44.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-211}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -4.8e-48)
     t_2
     (if (<= c -8.5e-127)
       t_1
       (if (<= c -4.9e-254)
         (* y (* x z))
         (if (<= c 1.25e-211)
           (* i (* j (- y)))
           (if (<= c 6.5e-60) 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 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.8e-48) {
		tmp = t_2;
	} else if (c <= -8.5e-127) {
		tmp = t_1;
	} else if (c <= -4.9e-254) {
		tmp = y * (x * z);
	} else if (c <= 1.25e-211) {
		tmp = i * (j * -y);
	} else if (c <= 6.5e-60) {
		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 = b * ((a * i) - (z * c))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-4.8d-48)) then
        tmp = t_2
    else if (c <= (-8.5d-127)) then
        tmp = t_1
    else if (c <= (-4.9d-254)) then
        tmp = y * (x * z)
    else if (c <= 1.25d-211) then
        tmp = i * (j * -y)
    else if (c <= 6.5d-60) 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 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.8e-48) {
		tmp = t_2;
	} else if (c <= -8.5e-127) {
		tmp = t_1;
	} else if (c <= -4.9e-254) {
		tmp = y * (x * z);
	} else if (c <= 1.25e-211) {
		tmp = i * (j * -y);
	} else if (c <= 6.5e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.8e-48:
		tmp = t_2
	elif c <= -8.5e-127:
		tmp = t_1
	elif c <= -4.9e-254:
		tmp = y * (x * z)
	elif c <= 1.25e-211:
		tmp = i * (j * -y)
	elif c <= 6.5e-60:
		tmp = t_1
	else:
		tmp = t_2
	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(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.8e-48)
		tmp = t_2;
	elseif (c <= -8.5e-127)
		tmp = t_1;
	elseif (c <= -4.9e-254)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 1.25e-211)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (c <= 6.5e-60)
		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 = b * ((a * i) - (z * c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.8e-48)
		tmp = t_2;
	elseif (c <= -8.5e-127)
		tmp = t_1;
	elseif (c <= -4.9e-254)
		tmp = y * (x * z);
	elseif (c <= 1.25e-211)
		tmp = i * (j * -y);
	elseif (c <= 6.5e-60)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.8e-48], t$95$2, If[LessEqual[c, -8.5e-127], t$95$1, If[LessEqual[c, -4.9e-254], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-211], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-60], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.8e-48 or 6.49999999999999995e-60 < c

   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 c around inf 69.3%

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

   if -4.8e-48 < c < -8.5e-127 or 1.2500000000000001e-211 < c < 6.49999999999999995e-60

   1. Initial program 89.2%

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

   2. Taylor expanded in b around inf 49.1%

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

   if -8.5e-127 < c < -4.8999999999999998e-254

   1. Initial program 82.9%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

      4. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in z around inf 44.4%

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

   if -4.8999999999999998e-254 < c < 1.2500000000000001e-211

   1. Initial program 76.3%

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

   2. Taylor expanded in y around inf 49.1%

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

      1. +-commutative 49.1%

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

      2. mul-1-neg 49.1%

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

      3. unsub-neg 49.1%

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

      4. *-commutative 49.1%

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

   4. Simplified 49.1%

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

   5. Taylor expanded in z around 0 43.3%

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

      1. associate-*r* 43.3%

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

      2. neg-mul-1 43.3%

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

   7. Simplified 43.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-211}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 9: 57.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{+151} \lor \neg \left(j \leq 3 \cdot 10^{+48}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.6e+151) (not (<= j 3e+48)))
   (* j (- (* t c) (* y i)))
   (+ (* b (- (* a i) (* z c))) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.6e+151) || !(j <= 3e+48)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-6.6d+151)) .or. (.not. (j <= 3d+48))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (b * ((a * i) - (z * c))) + (y * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.6e+151) || !(j <= 3e+48)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.6e+151) or not (j <= 3e+48):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.6e+151) || !(j <= 3e+48))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(y * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6.6e+151) || ~((j <= 3e+48)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.6e+151], N[Not[LessEqual[j, 3e+48]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.60000000000000049e151 or 3e48 < j

   1. Initial program 82.6%

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

   2. Taylor expanded in j around inf 69.5%

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

   if -6.60000000000000049e151 < j < 3e48

   1. Initial program 81.1%

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

   2. Taylor expanded in t around 0 66.7%

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

      1. *-commutative 66.7%

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

      2. cancel-sign-sub-inv 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-*r* 68.4%

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

      5. associate-*r* 69.5%

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

      6. associate-*r* 69.5%

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

      7. distribute-rgt-in 70.7%

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

      8. +-commutative 70.7%

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

      9. mul-1-neg 70.7%

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

      10. unsub-neg 70.7%

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

      11. *-commutative 70.7%

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

      12. distribute-lft-neg-in 70.7%

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

      13. distribute-rgt-neg-in 70.7%

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

      14. neg-sub0 70.7%

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

      15. *-commutative 70.7%

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

      16. associate--r- 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in z around inf 65.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{+151} \lor \neg \left(j \leq 3 \cdot 10^{+48}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 10: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.3e-44)
     t_1
     (if (<= c 4e-139)
       (* y (- (* x z) (* i j)))
       (if (<= c 1.3e-58)
         (* b (- (* a i) (* z c)))
         (if (<= c 7.5e+26) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.3e-44) {
		tmp = t_1;
	} else if (c <= 4e-139) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.3e-58) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 7.5e+26) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-1.3d-44)) then
        tmp = t_1
    else if (c <= 4d-139) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.3d-58) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 7.5d+26) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.3e-44) {
		tmp = t_1;
	} else if (c <= 4e-139) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.3e-58) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 7.5e+26) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.3e-44:
		tmp = t_1
	elif c <= 4e-139:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.3e-58:
		tmp = b * ((a * i) - (z * c))
	elif c <= 7.5e+26:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.3e-44)
		tmp = t_1;
	elseif (c <= 4e-139)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.3e-58)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 7.5e+26)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.3e-44)
		tmp = t_1;
	elseif (c <= 4e-139)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.3e-58)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 7.5e+26)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e-44], t$95$1, If[LessEqual[c, 4e-139], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-58], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+26], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.2999999999999999e-44 or 7.49999999999999941e26 < c

   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 c around inf 74.0%

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

   if -1.2999999999999999e-44 < c < 4.00000000000000012e-139

   1. Initial program 82.5%

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

   2. Taylor expanded in y around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   if 4.00000000000000012e-139 < c < 1.30000000000000003e-58

   1. Initial program 90.7%

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

   2. Taylor expanded in b around inf 60.2%

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

   if 1.30000000000000003e-58 < c < 7.49999999999999941e26

   1. Initial program 92.8%

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

   2. Taylor expanded in x around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 11: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 10^{-211}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* j (* t c))))
   (if (<= c -2.3e-26)
     t_2
     (if (<= c -8.5e-254)
       t_1
       (if (<= c 1e-211)
         (* (* y i) (- j))
         (if (<= c 1.16e-59) (* a (* b i)) (if (<= c 1.8e+102) 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);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -2.3e-26) {
		tmp = t_2;
	} else if (c <= -8.5e-254) {
		tmp = t_1;
	} else if (c <= 1e-211) {
		tmp = (y * i) * -j;
	} else if (c <= 1.16e-59) {
		tmp = a * (b * i);
	} else if (c <= 1.8e+102) {
		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_2 = j * (t * c)
    if (c <= (-2.3d-26)) then
        tmp = t_2
    else if (c <= (-8.5d-254)) then
        tmp = t_1
    else if (c <= 1d-211) then
        tmp = (y * i) * -j
    else if (c <= 1.16d-59) then
        tmp = a * (b * i)
    else if (c <= 1.8d+102) 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);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -2.3e-26) {
		tmp = t_2;
	} else if (c <= -8.5e-254) {
		tmp = t_1;
	} else if (c <= 1e-211) {
		tmp = (y * i) * -j;
	} else if (c <= 1.16e-59) {
		tmp = a * (b * i);
	} else if (c <= 1.8e+102) {
		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_2 = j * (t * c)
	tmp = 0
	if c <= -2.3e-26:
		tmp = t_2
	elif c <= -8.5e-254:
		tmp = t_1
	elif c <= 1e-211:
		tmp = (y * i) * -j
	elif c <= 1.16e-59:
		tmp = a * (b * i)
	elif c <= 1.8e+102:
		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(y * z))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -2.3e-26)
		tmp = t_2;
	elseif (c <= -8.5e-254)
		tmp = t_1;
	elseif (c <= 1e-211)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (c <= 1.16e-59)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 1.8e+102)
		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_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -2.3e-26)
		tmp = t_2;
	elseif (c <= -8.5e-254)
		tmp = t_1;
	elseif (c <= 1e-211)
		tmp = (y * i) * -j;
	elseif (c <= 1.16e-59)
		tmp = a * (b * i);
	elseif (c <= 1.8e+102)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.3e-26], t$95$2, If[LessEqual[c, -8.5e-254], t$95$1, If[LessEqual[c, 1e-211], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, 1.16e-59], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+102], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.30000000000000009e-26 or 1.8000000000000001e102 < c

   1. Initial program 77.3%

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

   2. Taylor expanded in j around inf 57.8%

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

   3. Taylor expanded in c around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   if -2.30000000000000009e-26 < c < -8.49999999999999963e-254 or 1.16e-59 < c < 1.8000000000000001e102

   1. Initial program 87.2%

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

   2. Taylor expanded in t around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. cancel-sign-sub-inv 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*r* 69.9%

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

      5. associate-*r* 72.5%

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

      6. associate-*r* 72.5%

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

      7. distribute-rgt-in 72.5%

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

      8. +-commutative 72.5%

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

      9. mul-1-neg 72.5%

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

      10. unsub-neg 72.5%

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

      11. *-commutative 72.5%

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

      12. distribute-lft-neg-in 72.5%

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

      13. distribute-rgt-neg-in 72.5%

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

      14. neg-sub0 72.5%

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

      15. *-commutative 72.5%

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

      16. associate--r- 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in x around inf 35.2%

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

      1. *-commutative 35.2%

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

   7. Simplified 35.2%

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

   if -8.49999999999999963e-254 < c < 1.00000000000000009e-211

   1. Initial program 76.3%

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

   2. Taylor expanded in j around inf 46.2%

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

   3. Taylor expanded in c around 0 40.7%

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

      1. neg-mul-1 40.7%

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

      2. distribute-lft-neg-in 40.7%

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

      3. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   if 1.00000000000000009e-211 < c < 1.16e-59

   1. Initial program 88.7%

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

   2. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. cancel-sign-sub-inv 72.5%

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

      3. *-commutative 72.5%

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

      4. associate-*r* 70.0%

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

      5. associate-*r* 67.4%

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

      6. associate-*r* 67.4%

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

      7. distribute-rgt-in 70.1%

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

      8. +-commutative 70.1%

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

      9. mul-1-neg 70.1%

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

      10. unsub-neg 70.1%

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

      11. *-commutative 70.1%

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

      12. distribute-lft-neg-in 70.1%

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

      13. distribute-rgt-neg-in 70.1%

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

      14. neg-sub0 70.1%

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

      15. *-commutative 70.1%

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

      16. associate--r- 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in a around inf 35.4%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 10^{-211}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 12: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-243}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.4e+34)
   (* (- a) (* x t))
   (if (<= x -4.5e-243)
     (* (* b c) (- z))
     (if (<= x 9e-189)
       (* t (* c j))
       (if (<= x 3.1e-9)
         (* b (* a i))
         (if (<= x 7.8e+83) (* c (* t j)) (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.4e+34) {
		tmp = -a * (x * t);
	} else if (x <= -4.5e-243) {
		tmp = (b * c) * -z;
	} else if (x <= 9e-189) {
		tmp = t * (c * j);
	} else if (x <= 3.1e-9) {
		tmp = b * (a * i);
	} else if (x <= 7.8e+83) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-3.4d+34)) then
        tmp = -a * (x * t)
    else if (x <= (-4.5d-243)) then
        tmp = (b * c) * -z
    else if (x <= 9d-189) then
        tmp = t * (c * j)
    else if (x <= 3.1d-9) then
        tmp = b * (a * i)
    else if (x <= 7.8d+83) then
        tmp = c * (t * j)
    else
        tmp = z * (x * y)
    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 (x <= -3.4e+34) {
		tmp = -a * (x * t);
	} else if (x <= -4.5e-243) {
		tmp = (b * c) * -z;
	} else if (x <= 9e-189) {
		tmp = t * (c * j);
	} else if (x <= 3.1e-9) {
		tmp = b * (a * i);
	} else if (x <= 7.8e+83) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3.4e+34:
		tmp = -a * (x * t)
	elif x <= -4.5e-243:
		tmp = (b * c) * -z
	elif x <= 9e-189:
		tmp = t * (c * j)
	elif x <= 3.1e-9:
		tmp = b * (a * i)
	elif x <= 7.8e+83:
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.4e+34)
		tmp = Float64(Float64(-a) * Float64(x * t));
	elseif (x <= -4.5e-243)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (x <= 9e-189)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= 3.1e-9)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 7.8e+83)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3.4e+34)
		tmp = -a * (x * t);
	elseif (x <= -4.5e-243)
		tmp = (b * c) * -z;
	elseif (x <= 9e-189)
		tmp = t * (c * j);
	elseif (x <= 3.1e-9)
		tmp = b * (a * i);
	elseif (x <= 7.8e+83)
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.4e+34], N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-243], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[x, 9e-189], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-9], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+83], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.3999999999999999e34

   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 a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in t around inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. mul-1-neg 44.4%

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

   7. Simplified 44.4%

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

   if -3.3999999999999999e34 < x < -4.50000000000000017e-243

   1. Initial program 83.4%

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

   2. Taylor expanded in t around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. cancel-sign-sub-inv 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*r* 70.3%

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

      5. associate-*r* 70.4%

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

      6. associate-*r* 70.4%

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

      7. distribute-rgt-in 70.4%

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

      8. +-commutative 70.4%

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

      9. mul-1-neg 70.4%

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

      10. unsub-neg 70.4%

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

      11. *-commutative 70.4%

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

      12. distribute-lft-neg-in 70.4%

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

      13. distribute-rgt-neg-in 70.4%

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

      14. neg-sub0 70.4%

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

      15. *-commutative 70.4%

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

      16. associate--r- 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in z around inf 57.1%

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

   6. Taylor expanded in c around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-*r* 42.6%

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

      3. *-commutative 42.6%

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

      4. distribute-rgt-neg-in 42.6%

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

      5. *-commutative 42.6%

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

      6. distribute-rgt-neg-in 42.6%

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

   8. Simplified 42.6%

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

   if -4.50000000000000017e-243 < x < 8.9999999999999992e-189

   1. Initial program 77.3%

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

   2. Taylor expanded in j around inf 52.7%

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

   3. Taylor expanded in c around inf 37.0%

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

      1. associate-*r* 43.4%

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

   5. Simplified 43.4%

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

   if 8.9999999999999992e-189 < x < 3.10000000000000005e-9

   1. Initial program 77.8%

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

   2. Taylor expanded in b around inf 52.9%

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

   3. Taylor expanded in a around inf 37.5%

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

   if 3.10000000000000005e-9 < x < 7.8000000000000003e83

   1. Initial program 81.6%

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

   2. Taylor expanded in j around inf 39.6%

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

   3. Taylor expanded in c around inf 38.8%

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

   if 7.8000000000000003e83 < x

   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 t around 0 57.2%

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

      1. *-commutative 57.2%

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

      2. cancel-sign-sub-inv 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-*r* 57.2%

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

      5. associate-*r* 60.1%

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

      6. associate-*r* 60.1%

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

      7. distribute-rgt-in 62.8%

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

      8. +-commutative 62.8%

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

      9. mul-1-neg 62.8%

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

      10. unsub-neg 62.8%

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

      11. *-commutative 62.8%

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

      12. distribute-lft-neg-in 62.8%

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

      13. distribute-rgt-neg-in 62.8%

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

      14. neg-sub0 62.8%

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

      15. *-commutative 62.8%

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

      16. associate--r- 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-243}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -6.5e+33)
   (* (- a) (* x t))
   (if (<= x -8.2e-247)
     (* c (- (* z b)))
     (if (<= x 6.1e-189)
       (* t (* c j))
       (if (<= x 2.1e-10)
         (* b (* a i))
         (if (<= x 6.8e+80) (* c (* t j)) (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -6.5e+33) {
		tmp = -a * (x * t);
	} else if (x <= -8.2e-247) {
		tmp = c * -(z * b);
	} else if (x <= 6.1e-189) {
		tmp = t * (c * j);
	} else if (x <= 2.1e-10) {
		tmp = b * (a * i);
	} else if (x <= 6.8e+80) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-6.5d+33)) then
        tmp = -a * (x * t)
    else if (x <= (-8.2d-247)) then
        tmp = c * -(z * b)
    else if (x <= 6.1d-189) then
        tmp = t * (c * j)
    else if (x <= 2.1d-10) then
        tmp = b * (a * i)
    else if (x <= 6.8d+80) then
        tmp = c * (t * j)
    else
        tmp = z * (x * y)
    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 (x <= -6.5e+33) {
		tmp = -a * (x * t);
	} else if (x <= -8.2e-247) {
		tmp = c * -(z * b);
	} else if (x <= 6.1e-189) {
		tmp = t * (c * j);
	} else if (x <= 2.1e-10) {
		tmp = b * (a * i);
	} else if (x <= 6.8e+80) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -6.5e+33:
		tmp = -a * (x * t)
	elif x <= -8.2e-247:
		tmp = c * -(z * b)
	elif x <= 6.1e-189:
		tmp = t * (c * j)
	elif x <= 2.1e-10:
		tmp = b * (a * i)
	elif x <= 6.8e+80:
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -6.5e+33)
		tmp = Float64(Float64(-a) * Float64(x * t));
	elseif (x <= -8.2e-247)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (x <= 6.1e-189)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= 2.1e-10)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 6.8e+80)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -6.5e+33)
		tmp = -a * (x * t);
	elseif (x <= -8.2e-247)
		tmp = c * -(z * b);
	elseif (x <= 6.1e-189)
		tmp = t * (c * j);
	elseif (x <= 2.1e-10)
		tmp = b * (a * i);
	elseif (x <= 6.8e+80)
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -6.5e+33], N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.2e-247], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 6.1e-189], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-10], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+80], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.49999999999999993e33

   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 a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in t around inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. mul-1-neg 44.4%

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

   7. Simplified 44.4%

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

   if -6.49999999999999993e33 < x < -8.1999999999999997e-247

   1. Initial program 83.4%

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

   2. Taylor expanded in t around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. cancel-sign-sub-inv 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*r* 70.3%

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

      5. associate-*r* 70.4%

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

      6. associate-*r* 70.4%

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

      7. distribute-rgt-in 70.4%

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

      8. +-commutative 70.4%

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

      9. mul-1-neg 70.4%

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

      10. unsub-neg 70.4%

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

      11. *-commutative 70.4%

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

      12. distribute-lft-neg-in 70.4%

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

      13. distribute-rgt-neg-in 70.4%

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

      14. neg-sub0 70.4%

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

      15. *-commutative 70.4%

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

      16. associate--r- 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in c around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. *-commutative 44.0%

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

      3. associate-*r* 42.7%

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

      4. distribute-lft-neg-in 42.7%

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

      5. *-commutative 42.7%

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

   7. Simplified 42.7%

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

   if -8.1999999999999997e-247 < x < 6.1e-189

   1. Initial program 77.3%

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

   2. Taylor expanded in j around inf 52.7%

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

   3. Taylor expanded in c around inf 37.0%

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

      1. associate-*r* 43.4%

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

   5. Simplified 43.4%

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

   if 6.1e-189 < x < 2.1e-10

   1. Initial program 77.8%

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

   2. Taylor expanded in b around inf 52.9%

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

   3. Taylor expanded in a around inf 37.5%

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

   if 2.1e-10 < x < 6.79999999999999984e80

   1. Initial program 81.6%

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

   2. Taylor expanded in j around inf 39.6%

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

   3. Taylor expanded in c around inf 38.8%

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

   if 6.79999999999999984e80 < x

   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 t around 0 57.2%

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

      1. *-commutative 57.2%

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

      2. cancel-sign-sub-inv 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-*r* 57.2%

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

      5. associate-*r* 60.1%

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

      6. associate-*r* 60.1%

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

      7. distribute-rgt-in 62.8%

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

      8. +-commutative 62.8%

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

      9. mul-1-neg 62.8%

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

      10. unsub-neg 62.8%

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

      11. *-commutative 62.8%

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

      12. distribute-lft-neg-in 62.8%

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

      13. distribute-rgt-neg-in 62.8%

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

      14. neg-sub0 62.8%

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

      15. *-commutative 62.8%

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

      16. associate--r- 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.4e+35)
   (* (- a) (* x t))
   (if (<= x -1.6e-241)
     (* b (* z (- c)))
     (if (<= x 5.3e-189)
       (* t (* c j))
       (if (<= x 7.5e-11)
         (* b (* a i))
         (if (<= x 2.1e+84) (* c (* t j)) (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.4e+35) {
		tmp = -a * (x * t);
	} else if (x <= -1.6e-241) {
		tmp = b * (z * -c);
	} else if (x <= 5.3e-189) {
		tmp = t * (c * j);
	} else if (x <= 7.5e-11) {
		tmp = b * (a * i);
	} else if (x <= 2.1e+84) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-1.4d+35)) then
        tmp = -a * (x * t)
    else if (x <= (-1.6d-241)) then
        tmp = b * (z * -c)
    else if (x <= 5.3d-189) then
        tmp = t * (c * j)
    else if (x <= 7.5d-11) then
        tmp = b * (a * i)
    else if (x <= 2.1d+84) then
        tmp = c * (t * j)
    else
        tmp = z * (x * y)
    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 (x <= -1.4e+35) {
		tmp = -a * (x * t);
	} else if (x <= -1.6e-241) {
		tmp = b * (z * -c);
	} else if (x <= 5.3e-189) {
		tmp = t * (c * j);
	} else if (x <= 7.5e-11) {
		tmp = b * (a * i);
	} else if (x <= 2.1e+84) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.4e+35:
		tmp = -a * (x * t)
	elif x <= -1.6e-241:
		tmp = b * (z * -c)
	elif x <= 5.3e-189:
		tmp = t * (c * j)
	elif x <= 7.5e-11:
		tmp = b * (a * i)
	elif x <= 2.1e+84:
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.4e+35)
		tmp = Float64(Float64(-a) * Float64(x * t));
	elseif (x <= -1.6e-241)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 5.3e-189)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= 7.5e-11)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 2.1e+84)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.4e+35)
		tmp = -a * (x * t);
	elseif (x <= -1.6e-241)
		tmp = b * (z * -c);
	elseif (x <= 5.3e-189)
		tmp = t * (c * j);
	elseif (x <= 7.5e-11)
		tmp = b * (a * i);
	elseif (x <= 2.1e+84)
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.4e+35], N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e-241], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.3e-189], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-11], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+84], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.39999999999999999e35

   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 a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in t around inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. mul-1-neg 44.4%

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

   7. Simplified 44.4%

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

   if -1.39999999999999999e35 < x < -1.6e-241

   1. Initial program 83.4%

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

   2. Taylor expanded in b around inf 48.9%

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

   3. Taylor expanded in a around 0 44.0%

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

      1. mul-1-neg 44.0%

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

      2. *-commutative 44.0%

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

      3. *-commutative 44.0%

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

      4. distribute-rgt-neg-in 44.0%

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

      5. *-commutative 44.0%

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

   5. Simplified 44.0%

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

   if -1.6e-241 < x < 5.2999999999999998e-189

   1. Initial program 77.3%

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

   2. Taylor expanded in j around inf 52.7%

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

   3. Taylor expanded in c around inf 37.0%

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

      1. associate-*r* 43.4%

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

   5. Simplified 43.4%

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

   if 5.2999999999999998e-189 < x < 7.5e-11

   1. Initial program 77.8%

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

   2. Taylor expanded in b around inf 52.9%

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

   3. Taylor expanded in a around inf 37.5%

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

   if 7.5e-11 < x < 2.10000000000000019e84

   1. Initial program 81.6%

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

   2. Taylor expanded in j around inf 39.6%

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

   3. Taylor expanded in c around inf 38.8%

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

   if 2.10000000000000019e84 < x

   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 t around 0 57.2%

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

      1. *-commutative 57.2%

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

      2. cancel-sign-sub-inv 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-*r* 57.2%

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

      5. associate-*r* 60.1%

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

      6. associate-*r* 60.1%

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

      7. distribute-rgt-in 62.8%

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

      8. +-commutative 62.8%

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

      9. mul-1-neg 62.8%

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

      10. unsub-neg 62.8%

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

      11. *-commutative 62.8%

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

      12. distribute-lft-neg-in 62.8%

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

      13. distribute-rgt-neg-in 62.8%

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

      14. neg-sub0 62.8%

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

      15. *-commutative 62.8%

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

      16. associate--r- 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 15: 29.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.95 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* j (* t c))))
   (if (<= c -8.2e-22)
     t_2
     (if (<= c 3.2e-149)
       t_1
       (if (<= c 2.95e-59) (* a (* b i)) (if (<= c 1.35e+101) 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);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -8.2e-22) {
		tmp = t_2;
	} else if (c <= 3.2e-149) {
		tmp = t_1;
	} else if (c <= 2.95e-59) {
		tmp = a * (b * i);
	} else if (c <= 1.35e+101) {
		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_2 = j * (t * c)
    if (c <= (-8.2d-22)) then
        tmp = t_2
    else if (c <= 3.2d-149) then
        tmp = t_1
    else if (c <= 2.95d-59) then
        tmp = a * (b * i)
    else if (c <= 1.35d+101) 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);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -8.2e-22) {
		tmp = t_2;
	} else if (c <= 3.2e-149) {
		tmp = t_1;
	} else if (c <= 2.95e-59) {
		tmp = a * (b * i);
	} else if (c <= 1.35e+101) {
		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_2 = j * (t * c)
	tmp = 0
	if c <= -8.2e-22:
		tmp = t_2
	elif c <= 3.2e-149:
		tmp = t_1
	elif c <= 2.95e-59:
		tmp = a * (b * i)
	elif c <= 1.35e+101:
		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(y * z))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -8.2e-22)
		tmp = t_2;
	elseif (c <= 3.2e-149)
		tmp = t_1;
	elseif (c <= 2.95e-59)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 1.35e+101)
		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_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -8.2e-22)
		tmp = t_2;
	elseif (c <= 3.2e-149)
		tmp = t_1;
	elseif (c <= 2.95e-59)
		tmp = a * (b * i);
	elseif (c <= 1.35e+101)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e-22], t$95$2, If[LessEqual[c, 3.2e-149], t$95$1, If[LessEqual[c, 2.95e-59], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e+101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.1999999999999999e-22 or 1.35000000000000003e101 < c

   1. Initial program 77.3%

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

   2. Taylor expanded in j around inf 57.8%

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

   3. Taylor expanded in c around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   if -8.1999999999999999e-22 < c < 3.20000000000000002e-149 or 2.9499999999999999e-59 < c < 1.35000000000000003e101

   1. Initial program 84.4%

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

   2. Taylor expanded in t around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. cancel-sign-sub-inv 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*r* 65.3%

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

      5. associate-*r* 65.3%

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

      6. associate-*r* 65.3%

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

      7. distribute-rgt-in 66.1%

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

      8. +-commutative 66.1%

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

      9. mul-1-neg 66.1%

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

      10. unsub-neg 66.1%

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

      11. *-commutative 66.1%

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

      12. distribute-lft-neg-in 66.1%

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

      13. distribute-rgt-neg-in 66.1%

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

      14. neg-sub0 66.1%

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

      15. *-commutative 66.1%

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

      16. associate--r- 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in x around inf 32.3%

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

      1. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   if 3.20000000000000002e-149 < c < 2.9499999999999999e-59

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 71.3%

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

      1. *-commutative 71.3%

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

      2. cancel-sign-sub-inv 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-*r* 71.2%

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

      5. associate-*r* 71.2%

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

      6. associate-*r* 71.2%

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

      7. distribute-rgt-in 75.3%

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

      8. +-commutative 75.3%

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

      9. mul-1-neg 75.3%

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

      10. unsub-neg 75.3%

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

      11. *-commutative 75.3%

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

      12. distribute-lft-neg-in 75.3%

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

      13. distribute-rgt-neg-in 75.3%

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

      14. neg-sub0 75.3%

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

      15. *-commutative 75.3%

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

      16. associate--r- 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in a around inf 39.3%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.95 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 16: 41.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+217}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3e+217)
   (* (- a) (* x t))
   (if (<= x 6.5e+99) (* b (- (* a i) (* z c))) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3e+217) {
		tmp = -a * (x * t);
	} else if (x <= 6.5e+99) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-3d+217)) then
        tmp = -a * (x * t)
    else if (x <= 6.5d+99) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = z * (x * y)
    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 (x <= -3e+217) {
		tmp = -a * (x * t);
	} else if (x <= 6.5e+99) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3e+217:
		tmp = -a * (x * t)
	elif x <= 6.5e+99:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3e+217)
		tmp = Float64(Float64(-a) * Float64(x * t));
	elseif (x <= 6.5e+99)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3e+217)
		tmp = -a * (x * t);
	elseif (x <= 6.5e+99)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3e+217], N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+99], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.99999999999999976e217

   1. Initial program 84.9%

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

   2. Taylor expanded in a around inf 75.2%

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

      1. distribute-lft-out-- 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in t around inf 70.4%

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

      1. associate-*r* 70.4%

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

      2. mul-1-neg 70.4%

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

   7. Simplified 70.4%

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

   if -2.99999999999999976e217 < x < 6.5000000000000004e99

   1. Initial program 81.0%

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

   2. Taylor expanded in b around inf 47.5%

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

   if 6.5000000000000004e99 < x

   1. Initial program 83.8%

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

   2. Taylor expanded in t around 0 52.1%

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

      1. *-commutative 52.1%

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

      2. cancel-sign-sub-inv 52.1%

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

      3. *-commutative 52.1%

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

      4. associate-*r* 52.1%

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

      5. associate-*r* 55.6%

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

      6. associate-*r* 55.6%

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

      7. distribute-rgt-in 55.6%

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

      8. +-commutative 55.6%

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

      9. mul-1-neg 55.6%

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

      10. unsub-neg 55.6%

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

      11. *-commutative 55.6%

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

      12. distribute-lft-neg-in 55.6%

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

      13. distribute-rgt-neg-in 55.6%

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

      14. neg-sub0 55.6%

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

      15. *-commutative 55.6%

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

      16. associate--r- 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in x around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*r* 56.2%

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

   7. Simplified 56.2%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+217}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 28.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-49} \lor \neg \left(c \leq 2.15 \cdot 10^{+101}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.15e-49) (not (<= c 2.15e+101))) (* 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 ((c <= -1.15e-49) || !(c <= 2.15e+101)) {
		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 ((c <= (-1.15d-49)) .or. (.not. (c <= 2.15d+101))) 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 ((c <= -1.15e-49) || !(c <= 2.15e+101)) {
		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 (c <= -1.15e-49) or not (c <= 2.15e+101):
		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 ((c <= -1.15e-49) || !(c <= 2.15e+101))
		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 ((c <= -1.15e-49) || ~((c <= 2.15e+101)))
		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[Or[LessEqual[c, -1.15e-49], N[Not[LessEqual[c, 2.15e+101]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.15e-49 or 2.15e101 < c

   1. Initial program 78.1%

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

   2. Taylor expanded in j around inf 57.6%

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

   3. Taylor expanded in c around inf 50.0%

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

   if -1.15e-49 < c < 2.15e101

   1. Initial program 84.5%

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

   2. Taylor expanded in t around 0 66.0%

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

      1. *-commutative 66.0%

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

      2. cancel-sign-sub-inv 66.0%

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

      3. *-commutative 66.0%

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

      4. associate-*r* 66.0%

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

      5. associate-*r* 66.0%

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

      6. associate-*r* 66.0%

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

      7. distribute-rgt-in 67.4%

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

      8. +-commutative 67.4%

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

      9. mul-1-neg 67.4%

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

      10. unsub-neg 67.4%

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

      11. *-commutative 67.4%

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

      12. distribute-lft-neg-in 67.4%

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

      13. distribute-rgt-neg-in 67.4%

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

      14. neg-sub0 67.4%

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

      15. *-commutative 67.4%

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

      16. associate--r- 67.4%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in a around inf 24.8%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-49} \lor \neg \left(c \leq 2.15 \cdot 10^{+101}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 18: 29.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-50} \lor \neg \left(c \leq 1.05 \cdot 10^{+101}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4.8e-50) (not (<= c 1.05e+101))) (* j (* t c)) (* 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 ((c <= -4.8e-50) || !(c <= 1.05e+101)) {
		tmp = j * (t * c);
	} 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 ((c <= (-4.8d-50)) .or. (.not. (c <= 1.05d+101))) then
        tmp = j * (t * c)
    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 ((c <= -4.8e-50) || !(c <= 1.05e+101)) {
		tmp = j * (t * c);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -4.8e-50) or not (c <= 1.05e+101):
		tmp = j * (t * c)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -4.8e-50) || !(c <= 1.05e+101))
		tmp = Float64(j * Float64(t * c));
	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 ((c <= -4.8e-50) || ~((c <= 1.05e+101)))
		tmp = j * (t * c);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -4.8e-50], N[Not[LessEqual[c, 1.05e+101]], $MachinePrecision]], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.80000000000000004e-50 or 1.05e101 < c

   1. Initial program 78.1%

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

   2. Taylor expanded in j around inf 57.6%

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

   3. Taylor expanded in c around inf 51.6%

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

      1. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   if -4.80000000000000004e-50 < c < 1.05e101

   1. Initial program 84.5%

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

   2. Taylor expanded in t around 0 66.0%

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

      1. *-commutative 66.0%

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

      2. cancel-sign-sub-inv 66.0%

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

      3. *-commutative 66.0%

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

      4. associate-*r* 66.0%

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

      5. associate-*r* 66.0%

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

      6. associate-*r* 66.0%

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

      7. distribute-rgt-in 67.4%

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

      8. +-commutative 67.4%

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

      9. mul-1-neg 67.4%

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

      10. unsub-neg 67.4%

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

      11. *-commutative 67.4%

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

      12. distribute-lft-neg-in 67.4%

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

      13. distribute-rgt-neg-in 67.4%

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

      14. neg-sub0 67.4%

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

      15. *-commutative 67.4%

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

      16. associate--r- 67.4%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in a around inf 24.8%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-50} \lor \neg \left(c \leq 1.05 \cdot 10^{+101}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 19: 21.7% 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 81.6%

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

2. Taylor expanded in t around 0 62.1%

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

   1. *-commutative 62.1%

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

   2. cancel-sign-sub-inv 62.1%

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

   3. *-commutative 62.1%

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

   4. associate-*r* 62.8%

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

   5. associate-*r* 62.2%

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

   6. associate-*r* 62.2%

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

   7. distribute-rgt-in 63.3%

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

   8. +-commutative 63.3%

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

   9. mul-1-neg 63.3%

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

   10. unsub-neg 63.3%

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

   11. *-commutative 63.3%

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

   12. distribute-lft-neg-in 63.3%

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

   13. distribute-rgt-neg-in 63.3%

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

   14. neg-sub0 63.3%

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

   15. *-commutative 63.3%

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

   16. associate--r- 63.3%

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

4. Simplified 63.3%

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

5. Taylor expanded in a around inf 20.3%

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

6. Final simplification 20.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 20: 21.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.6%

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

2. Taylor expanded in b around inf 42.6%

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

3. Taylor expanded in a around inf 20.7%

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

4. Final simplification 20.7%

   \[\leadsto b \cdot \left(a \cdot i\right) \]

Developer target: 68.2% 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 2023293 
(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)))))