Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 82.9%

Time: 30.8s

Alternatives: 25

Speedup: 0.5×

• 57.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in b around 0 37.1%

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

   3. Taylor expanded in c around 0 43.8%

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

   5. Simplified 52.3%

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

4. Final simplification 83.2%

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

Alternative 2: 56.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -3.7e-7)
     t_3
     (if (<= b -9.5e-152)
       t_2
       (if (<= b 2.7e-216)
         t_1
         (if (<= b 3.6e-157) t_2 (if (<= b 1.55e+144) 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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.7e-7) {
		tmp = t_3;
	} else if (b <= -9.5e-152) {
		tmp = t_2;
	} else if (b <= 2.7e-216) {
		tmp = t_1;
	} else if (b <= 3.6e-157) {
		tmp = t_2;
	} else if (b <= 1.55e+144) {
		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 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-3.7d-7)) then
        tmp = t_3
    else if (b <= (-9.5d-152)) then
        tmp = t_2
    else if (b <= 2.7d-216) then
        tmp = t_1
    else if (b <= 3.6d-157) then
        tmp = t_2
    else if (b <= 1.55d+144) 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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.7e-7) {
		tmp = t_3;
	} else if (b <= -9.5e-152) {
		tmp = t_2;
	} else if (b <= 2.7e-216) {
		tmp = t_1;
	} else if (b <= 3.6e-157) {
		tmp = t_2;
	} else if (b <= 1.55e+144) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.7e-7:
		tmp = t_3
	elif b <= -9.5e-152:
		tmp = t_2
	elif b <= 2.7e-216:
		tmp = t_1
	elif b <= 3.6e-157:
		tmp = t_2
	elif b <= 1.55e+144:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.7e-7)
		tmp = t_3;
	elseif (b <= -9.5e-152)
		tmp = t_2;
	elseif (b <= 2.7e-216)
		tmp = t_1;
	elseif (b <= 3.6e-157)
		tmp = t_2;
	elseif (b <= 1.55e+144)
		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 = (j * ((t * c) - (y * i))) + (x * (y * z));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.7e-7)
		tmp = t_3;
	elseif (b <= -9.5e-152)
		tmp = t_2;
	elseif (b <= 2.7e-216)
		tmp = t_1;
	elseif (b <= 3.6e-157)
		tmp = t_2;
	elseif (b <= 1.55e+144)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e-7], t$95$3, If[LessEqual[b, -9.5e-152], t$95$2, If[LessEqual[b, 2.7e-216], t$95$1, If[LessEqual[b, 3.6e-157], t$95$2, If[LessEqual[b, 1.55e+144], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.70000000000000004e-7 or 1.5500000000000001e144 < b

   1. Initial program 78.0%

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

   2. Taylor expanded in b around inf 72.6%

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

   if -3.70000000000000004e-7 < b < -9.49999999999999925e-152 or 2.6999999999999999e-216 < b < 3.6e-157

   1. Initial program 65.9%

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

   2. Taylor expanded in t around -inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. *-commutative 71.9%

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

      3. distribute-rgt-neg-in 71.9%

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

      4. +-commutative 71.9%

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

      5. mul-1-neg 71.9%

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

      6. unsub-neg 71.9%

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

   4. Simplified 71.9%

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

   if -9.49999999999999925e-152 < b < 2.6999999999999999e-216 or 3.6e-157 < b < 1.5500000000000001e144

   1. Initial program 72.9%

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

   2. Taylor expanded in b around 0 77.2%

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

   3. Taylor expanded in a around 0 67.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 3: 58.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;t_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (+ t_1 (* a (* b i)))))
   (if (<= a -2.5e+48)
     t_2
     (if (<= a 1e-172)
       (+ (* j (- (* t c) (* y i))) (* x (* y z)))
       (if (<= a 1.15e-72)
         t_2
         (if (<= a 1.1e-68)
           (* i (- (* a b) (* y j)))
           (if (<= a 1.05e+68)
             (- t_1 (* z (* b c)))
             (* a (- (* b i) (* x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (a * (b * i));
	double tmp;
	if (a <= -2.5e+48) {
		tmp = t_2;
	} else if (a <= 1e-172) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (a <= 1.15e-72) {
		tmp = t_2;
	} else if (a <= 1.1e-68) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.05e+68) {
		tmp = t_1 - (z * (b * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (a * (b * i))
    if (a <= (-2.5d+48)) then
        tmp = t_2
    else if (a <= 1d-172) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (a <= 1.15d-72) then
        tmp = t_2
    else if (a <= 1.1d-68) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 1.05d+68) then
        tmp = t_1 - (z * (b * c))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (a * (b * i));
	double tmp;
	if (a <= -2.5e+48) {
		tmp = t_2;
	} else if (a <= 1e-172) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (a <= 1.15e-72) {
		tmp = t_2;
	} else if (a <= 1.1e-68) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.05e+68) {
		tmp = t_1 - (z * (b * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (a * (b * i))
	tmp = 0
	if a <= -2.5e+48:
		tmp = t_2
	elif a <= 1e-172:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif a <= 1.15e-72:
		tmp = t_2
	elif a <= 1.1e-68:
		tmp = i * ((a * b) - (y * j))
	elif a <= 1.05e+68:
		tmp = t_1 - (z * (b * c))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(a * Float64(b * i)))
	tmp = 0.0
	if (a <= -2.5e+48)
		tmp = t_2;
	elseif (a <= 1e-172)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (a <= 1.15e-72)
		tmp = t_2;
	elseif (a <= 1.1e-68)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 1.05e+68)
		tmp = Float64(t_1 - Float64(z * Float64(b * c)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (a * (b * i));
	tmp = 0.0;
	if (a <= -2.5e+48)
		tmp = t_2;
	elseif (a <= 1e-172)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (a <= 1.15e-72)
		tmp = t_2;
	elseif (a <= 1.1e-68)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 1.05e+68)
		tmp = t_1 - (z * (b * c));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+48], t$95$2, If[LessEqual[a, 1e-172], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-72], t$95$2, If[LessEqual[a, 1.1e-68], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+68], N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.49999999999999987e48 or 1e-172 < a < 1.14999999999999997e-72

   1. Initial program 67.1%

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

   2. Taylor expanded in j around 0 70.2%

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

      1. *-commutative 70.2%

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

   4. Simplified 70.2%

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

   5. Taylor expanded in c around 0 64.5%

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

      1. associate-*r* 64.5%

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

      2. neg-mul-1 64.5%

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

   7. Simplified 64.5%

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

   if -2.49999999999999987e48 < a < 1e-172

   1. Initial program 81.0%

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

   2. Taylor expanded in b around 0 75.4%

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

   3. Taylor expanded in a around 0 71.7%

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

   if 1.14999999999999997e-72 < a < 1.10000000000000001e-68

   1. Initial program 70.0%

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

   2. Taylor expanded in i around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in i around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate-+l- 100.0%

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

      7. neg-sub0 100.0%

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

      8. +-commutative 100.0%

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

      9. fma-udef 100.0%

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

      10. fma-neg 100.0%

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

      11. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 1.10000000000000001e-68 < a < 1.05e68

   1. Initial program 76.2%

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

   2. Taylor expanded in j around 0 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in c around inf 65.5%

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

      1. associate-*r* 68.7%

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

      2. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if 1.05e68 < a

   1. Initial program 67.6%

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

   2. Taylor expanded in a around inf 77.0%

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

      1. distribute-lft-out-- 77.0%

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

      2. *-commutative 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in a around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. *-commutative 77.0%

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

      3. *-commutative 77.0%

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

      4. distribute-rgt-neg-out 77.0%

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

      5. neg-mul-1 77.0%

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

      6. distribute-lft-out-- 77.0%

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

      7. neg-mul-1 77.0%

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

      8. neg-sub0 77.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 77.0%

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

      10. distribute-rgt-neg-in 77.0%

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

      11. *-commutative 77.0%

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

      12. associate--r+ 77.0%

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

      13. +-commutative 77.0%

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

      14. associate--r+ 77.0%

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

      15. neg-sub0 77.0%

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

      16. *-commutative 77.0%

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

      17. distribute-rgt-neg-in 77.0%

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

      18. remove-double-neg 77.0%

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

      19. *-commutative 77.0%

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

      20. *-commutative 77.0%

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

   7. Simplified 77.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 10^{-172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 4: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-7} \lor \neg \left(b \leq 1.55 \cdot 10^{+146}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.7e-7) (not (<= b 1.55e+146)))
   (* b (- (* a i) (* z c)))
   (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.7e-7) || !(b <= 1.55e+146)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.7d-7)) .or. (.not. (b <= 1.55d+146))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.7e-7) || !(b <= 1.55e+146)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.7e-7) or not (b <= 1.55e+146):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.7e-7) || !(b <= 1.55e+146))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.7e-7) || ~((b <= 1.55e+146)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.7e-7], N[Not[LessEqual[b, 1.55e+146]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.70000000000000004e-7 or 1.5500000000000001e146 < b

   1. Initial program 78.0%

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

   2. Taylor expanded in b around inf 72.6%

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

   if -3.70000000000000004e-7 < b < 1.5500000000000001e146

   1. Initial program 71.1%

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

   2. Taylor expanded in b around 0 74.3%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-7} \lor \neg \left(b \leq 1.55 \cdot 10^{+146}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 5: 67.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+32} \lor \neg \left(b \leq 1.15 \cdot 10^{+141}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -5.5e+32) (not (<= b 1.15e+141)))
   (* b (- (* a i) (* z c)))
   (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.5e+32) || !(b <= 1.15e+141)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-5.5d+32)) .or. (.not. (b <= 1.15d+141))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.5e+32) || !(b <= 1.15e+141)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -5.5e+32) or not (b <= 1.15e+141):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -5.5e+32) || !(b <= 1.15e+141))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -5.5e+32) || ~((b <= 1.15e+141)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -5.5e+32], N[Not[LessEqual[b, 1.15e+141]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.49999999999999984e32 or 1.1500000000000001e141 < b

   1. Initial program 79.1%

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

   2. Taylor expanded in b around inf 74.3%

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

   if -5.49999999999999984e32 < b < 1.1500000000000001e141

   1. Initial program 70.9%

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

   2. Taylor expanded in b around 0 72.2%

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

   3. Taylor expanded in c around 0 70.2%

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

   5. Simplified 74.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+32} \lor \neg \left(b \leq 1.15 \cdot 10^{+141}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 6: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+31} \lor \neg \left(b \leq 2.3 \cdot 10^{+140}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -6.5e+31) (not (<= b 2.3e+140)))
   (+ (* b (- (* a i) (* z c))) (* x (- (* y z) (* t a))))
   (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -6.5e+31) || !(b <= 2.3e+140)) {
		tmp = (b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-6.5d+31)) .or. (.not. (b <= 2.3d+140))) then
        tmp = (b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))
    else
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -6.5e+31) || !(b <= 2.3e+140)) {
		tmp = (b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -6.5e+31) or not (b <= 2.3e+140):
		tmp = (b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -6.5e+31) || !(b <= 2.3e+140))
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -6.5e+31) || ~((b <= 2.3e+140)))
		tmp = (b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)));
	else
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -6.5e+31], N[Not[LessEqual[b, 2.3e+140]], $MachinePrecision]], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5000000000000004e31 or 2.2999999999999999e140 < b

   1. Initial program 79.1%

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

   2. Taylor expanded in j around 0 82.6%

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

      1. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   if -6.5000000000000004e31 < b < 2.2999999999999999e140

   1. Initial program 70.9%

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

   2. Taylor expanded in b around 0 72.2%

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

   3. Taylor expanded in c around 0 70.2%

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

   5. Simplified 74.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+31} \lor \neg \left(b \leq 2.3 \cdot 10^{+140}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 7: 47.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-167} \lor \neg \left(a \leq 4.5 \cdot 10^{-72}\right) \land a \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -1.3e+49)
     t_1
     (if (<= a -5.6e-56)
       (* j (* t c))
       (if (<= a -1.6e-126)
         (* y (* x z))
         (if (or (<= a 1.6e-167) (and (not (<= a 4.5e-72)) (<= a 5.2e+41)))
           (* c (- (* t j) (* z b)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.3e+49) {
		tmp = t_1;
	} else if (a <= -5.6e-56) {
		tmp = j * (t * c);
	} else if (a <= -1.6e-126) {
		tmp = y * (x * z);
	} else if ((a <= 1.6e-167) || (!(a <= 4.5e-72) && (a <= 5.2e+41))) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-1.3d+49)) then
        tmp = t_1
    else if (a <= (-5.6d-56)) then
        tmp = j * (t * c)
    else if (a <= (-1.6d-126)) then
        tmp = y * (x * z)
    else if ((a <= 1.6d-167) .or. (.not. (a <= 4.5d-72)) .and. (a <= 5.2d+41)) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.3e+49) {
		tmp = t_1;
	} else if (a <= -5.6e-56) {
		tmp = j * (t * c);
	} else if (a <= -1.6e-126) {
		tmp = y * (x * z);
	} else if ((a <= 1.6e-167) || (!(a <= 4.5e-72) && (a <= 5.2e+41))) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.3e+49:
		tmp = t_1
	elif a <= -5.6e-56:
		tmp = j * (t * c)
	elif a <= -1.6e-126:
		tmp = y * (x * z)
	elif (a <= 1.6e-167) or (not (a <= 4.5e-72) and (a <= 5.2e+41)):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.3e+49)
		tmp = t_1;
	elseif (a <= -5.6e-56)
		tmp = Float64(j * Float64(t * c));
	elseif (a <= -1.6e-126)
		tmp = Float64(y * Float64(x * z));
	elseif ((a <= 1.6e-167) || (!(a <= 4.5e-72) && (a <= 5.2e+41)))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.3e+49)
		tmp = t_1;
	elseif (a <= -5.6e-56)
		tmp = j * (t * c);
	elseif (a <= -1.6e-126)
		tmp = y * (x * z);
	elseif ((a <= 1.6e-167) || (~((a <= 4.5e-72)) && (a <= 5.2e+41)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+49], t$95$1, If[LessEqual[a, -5.6e-56], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-126], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.6e-167], And[N[Not[LessEqual[a, 4.5e-72]], $MachinePrecision], LessEqual[a, 5.2e+41]]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.29999999999999994e49 or 1.6000000000000001e-167 < a < 4.5e-72 or 5.2000000000000001e41 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in a around inf 62.4%

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

      1. distribute-lft-out-- 62.4%

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

      2. *-commutative 62.4%

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

   4. Simplified 62.4%

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

   5. Taylor expanded in a around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. *-commutative 62.4%

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

      3. *-commutative 62.4%

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

      4. distribute-rgt-neg-out 62.4%

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

      5. neg-mul-1 62.4%

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

      6. distribute-lft-out-- 62.4%

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

      7. neg-mul-1 62.4%

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

      8. neg-sub0 62.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 62.4%

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

      10. distribute-rgt-neg-in 62.4%

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

      11. *-commutative 62.4%

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

      12. associate--r+ 62.4%

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

      13. +-commutative 62.4%

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

      14. associate--r+ 62.4%

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

      15. neg-sub0 62.4%

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

      16. *-commutative 62.4%

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

      17. distribute-rgt-neg-in 62.4%

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

      18. remove-double-neg 62.4%

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

      19. *-commutative 62.4%

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

      20. *-commutative 62.4%

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

   7. Simplified 62.4%

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

   if -1.29999999999999994e49 < a < -5.59999999999999986e-56

   1. Initial program 75.0%

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

   2. Taylor expanded in c around inf 66.6%

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

      1. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in t around inf 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-*l* 69.2%

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

   7. Simplified 69.2%

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

   if -5.59999999999999986e-56 < a < -1.6e-126

   1. Initial program 85.0%

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

   2. Taylor expanded in y around inf 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around inf 47.8%

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

   if -1.6e-126 < a < 1.6000000000000001e-167 or 4.5e-72 < a < 5.2000000000000001e41

   1. Initial program 80.9%

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

   2. Taylor expanded in c around inf 51.5%

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

      1. *-commutative 51.5%

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

   4. Simplified 51.5%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-167} \lor \neg \left(a \leq 4.5 \cdot 10^{-72}\right) \land a \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 8: 42.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 160000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -9e+47)
     t_1
     (if (<= a -1.2e-60)
       (* j (* t c))
       (if (<= a -1e-165)
         (* x (* y z))
         (if (<= a -9e-295)
           (* t (* c j))
           (if (<= a 2.7e-139)
             (* y (* x z))
             (if (<= a 160000000.0) (* b (- (* a i) (* z c))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -9e+47) {
		tmp = t_1;
	} else if (a <= -1.2e-60) {
		tmp = j * (t * c);
	} else if (a <= -1e-165) {
		tmp = x * (y * z);
	} else if (a <= -9e-295) {
		tmp = t * (c * j);
	} else if (a <= 2.7e-139) {
		tmp = y * (x * z);
	} else if (a <= 160000000.0) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-9d+47)) then
        tmp = t_1
    else if (a <= (-1.2d-60)) then
        tmp = j * (t * c)
    else if (a <= (-1d-165)) then
        tmp = x * (y * z)
    else if (a <= (-9d-295)) then
        tmp = t * (c * j)
    else if (a <= 2.7d-139) then
        tmp = y * (x * z)
    else if (a <= 160000000.0d0) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -9e+47) {
		tmp = t_1;
	} else if (a <= -1.2e-60) {
		tmp = j * (t * c);
	} else if (a <= -1e-165) {
		tmp = x * (y * z);
	} else if (a <= -9e-295) {
		tmp = t * (c * j);
	} else if (a <= 2.7e-139) {
		tmp = y * (x * z);
	} else if (a <= 160000000.0) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -9e+47:
		tmp = t_1
	elif a <= -1.2e-60:
		tmp = j * (t * c)
	elif a <= -1e-165:
		tmp = x * (y * z)
	elif a <= -9e-295:
		tmp = t * (c * j)
	elif a <= 2.7e-139:
		tmp = y * (x * z)
	elif a <= 160000000.0:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9e+47)
		tmp = t_1;
	elseif (a <= -1.2e-60)
		tmp = Float64(j * Float64(t * c));
	elseif (a <= -1e-165)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -9e-295)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 2.7e-139)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 160000000.0)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -9e+47)
		tmp = t_1;
	elseif (a <= -1.2e-60)
		tmp = j * (t * c);
	elseif (a <= -1e-165)
		tmp = x * (y * z);
	elseif (a <= -9e-295)
		tmp = t * (c * j);
	elseif (a <= 2.7e-139)
		tmp = y * (x * z);
	elseif (a <= 160000000.0)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+47], t$95$1, If[LessEqual[a, -1.2e-60], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-165], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9e-295], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-139], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 160000000.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.99999999999999958e47 or 1.6e8 < a

   1. Initial program 64.9%

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

   2. Taylor expanded in a around inf 64.6%

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

      1. distribute-lft-out-- 64.6%

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

      2. *-commutative 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in a around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. *-commutative 64.6%

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

      4. distribute-rgt-neg-out 64.6%

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

      5. neg-mul-1 64.6%

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

      6. distribute-lft-out-- 64.6%

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

      7. neg-mul-1 64.6%

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

      8. neg-sub0 64.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 64.6%

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

      10. distribute-rgt-neg-in 64.6%

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

      11. *-commutative 64.6%

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

      12. associate--r+ 64.6%

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

      13. +-commutative 64.6%

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

      14. associate--r+ 64.6%

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

      15. neg-sub0 64.6%

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

      16. *-commutative 64.6%

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

      17. distribute-rgt-neg-in 64.6%

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

      18. remove-double-neg 64.6%

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

      19. *-commutative 64.6%

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

      20. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   if -8.99999999999999958e47 < a < -1.20000000000000005e-60

   1. Initial program 75.0%

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

   2. Taylor expanded in c around inf 66.6%

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

      1. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in t around inf 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-*l* 69.2%

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

   7. Simplified 69.2%

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

   if -1.20000000000000005e-60 < a < -1e-165

   1. Initial program 82.0%

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

   2. Taylor expanded in b around 0 78.0%

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

   3. Taylor expanded in z around inf 42.8%

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

   if -1e-165 < a < -9.0000000000000003e-295

   1. Initial program 81.2%

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

   2. Taylor expanded in b around 0 75.3%

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

   3. Taylor expanded in c around inf 38.3%

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

      1. *-commutative 38.3%

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

      2. *-commutative 38.3%

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

      3. associate-*r* 41.2%

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

   5. Simplified 41.2%

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

   if -9.0000000000000003e-295 < a < 2.6999999999999998e-139

   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 y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in z around inf 37.2%

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

   if 2.6999999999999998e-139 < a < 1.6e8

   1. Initial program 80.6%

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

   2. Taylor expanded in b around inf 47.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 160000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 9: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -7.5e+63)
     t_3
     (if (<= a -2.3e-34)
       t_2
       (if (<= a -4.6e-128)
         t_1
         (if (<= a 5e-165)
           t_2
           (if (<= a 5.2e-70) t_1 (if (<= a 2.65e+39) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e+63) {
		tmp = t_3;
	} else if (a <= -2.3e-34) {
		tmp = t_2;
	} else if (a <= -4.6e-128) {
		tmp = t_1;
	} else if (a <= 5e-165) {
		tmp = t_2;
	} else if (a <= 5.2e-70) {
		tmp = t_1;
	} else if (a <= 2.65e+39) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-7.5d+63)) then
        tmp = t_3
    else if (a <= (-2.3d-34)) then
        tmp = t_2
    else if (a <= (-4.6d-128)) then
        tmp = t_1
    else if (a <= 5d-165) then
        tmp = t_2
    else if (a <= 5.2d-70) then
        tmp = t_1
    else if (a <= 2.65d+39) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e+63) {
		tmp = t_3;
	} else if (a <= -2.3e-34) {
		tmp = t_2;
	} else if (a <= -4.6e-128) {
		tmp = t_1;
	} else if (a <= 5e-165) {
		tmp = t_2;
	} else if (a <= 5.2e-70) {
		tmp = t_1;
	} else if (a <= 2.65e+39) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7.5e+63:
		tmp = t_3
	elif a <= -2.3e-34:
		tmp = t_2
	elif a <= -4.6e-128:
		tmp = t_1
	elif a <= 5e-165:
		tmp = t_2
	elif a <= 5.2e-70:
		tmp = t_1
	elif a <= 2.65e+39:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.5e+63)
		tmp = t_3;
	elseif (a <= -2.3e-34)
		tmp = t_2;
	elseif (a <= -4.6e-128)
		tmp = t_1;
	elseif (a <= 5e-165)
		tmp = t_2;
	elseif (a <= 5.2e-70)
		tmp = t_1;
	elseif (a <= 2.65e+39)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7.5e+63)
		tmp = t_3;
	elseif (a <= -2.3e-34)
		tmp = t_2;
	elseif (a <= -4.6e-128)
		tmp = t_1;
	elseif (a <= 5e-165)
		tmp = t_2;
	elseif (a <= 5.2e-70)
		tmp = t_1;
	elseif (a <= 2.65e+39)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+63], t$95$3, If[LessEqual[a, -2.3e-34], t$95$2, If[LessEqual[a, -4.6e-128], t$95$1, If[LessEqual[a, 5e-165], t$95$2, If[LessEqual[a, 5.2e-70], t$95$1, If[LessEqual[a, 2.65e+39], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5000000000000005e63 or 2.64999999999999989e39 < a

   1. Initial program 62.8%

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

   2. Taylor expanded in a around inf 67.0%

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

      1. distribute-lft-out-- 67.0%

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

      2. *-commutative 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in a around 0 67.0%

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

      1. mul-1-neg 67.0%

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

      2. *-commutative 67.0%

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

      3. *-commutative 67.0%

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

      4. distribute-rgt-neg-out 67.0%

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

      5. neg-mul-1 67.0%

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

      6. distribute-lft-out-- 67.0%

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

      7. neg-mul-1 67.0%

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

      8. neg-sub0 67.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 67.0%

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

      10. distribute-rgt-neg-in 67.0%

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

      11. *-commutative 67.0%

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

      12. associate--r+ 67.0%

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

      13. +-commutative 67.0%

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

      14. associate--r+ 67.0%

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

      15. neg-sub0 67.0%

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

      16. *-commutative 67.0%

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

      17. distribute-rgt-neg-in 67.0%

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

      18. remove-double-neg 67.0%

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

      19. *-commutative 67.0%

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

      20. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -7.5000000000000005e63 < a < -2.30000000000000011e-34 or -4.6000000000000002e-128 < a < 4.99999999999999981e-165 or 5.20000000000000004e-70 < a < 2.64999999999999989e39

   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 c around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

   if -2.30000000000000011e-34 < a < -4.6000000000000002e-128 or 4.99999999999999981e-165 < a < 5.20000000000000004e-70

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf 60.5%

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

      1. distribute-lft-out-- 60.5%

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

      2. *-commutative 60.5%

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

      3. *-commutative 60.5%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in i around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. *-commutative 60.5%

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

      3. *-commutative 60.5%

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

      4. distribute-rgt-neg-in 60.5%

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

      5. neg-sub0 60.5%

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

      6. associate-+l- 60.5%

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

      7. neg-sub0 60.5%

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

      8. +-commutative 60.5%

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

      9. fma-udef 60.5%

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

      10. fma-neg 60.5%

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

      11. *-commutative 60.5%

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

   7. Simplified 60.5%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 10: 51.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -4.8e+48)
     t_3
     (if (<= a -4e-134)
       t_2
       (if (<= a -2.4e-220)
         t_1
         (if (<= a 3.3e-173)
           t_2
           (if (<= a 2.05e-69)
             (* i (- (* a b) (* y j)))
             (if (<= a 5e+38) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.8e+48) {
		tmp = t_3;
	} else if (a <= -4e-134) {
		tmp = t_2;
	} else if (a <= -2.4e-220) {
		tmp = t_1;
	} else if (a <= 3.3e-173) {
		tmp = t_2;
	} else if (a <= 2.05e-69) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 5e+38) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = j * ((t * c) - (y * i))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-4.8d+48)) then
        tmp = t_3
    else if (a <= (-4d-134)) then
        tmp = t_2
    else if (a <= (-2.4d-220)) then
        tmp = t_1
    else if (a <= 3.3d-173) then
        tmp = t_2
    else if (a <= 2.05d-69) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 5d+38) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.8e+48) {
		tmp = t_3;
	} else if (a <= -4e-134) {
		tmp = t_2;
	} else if (a <= -2.4e-220) {
		tmp = t_1;
	} else if (a <= 3.3e-173) {
		tmp = t_2;
	} else if (a <= 2.05e-69) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 5e+38) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = j * ((t * c) - (y * i))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.8e+48:
		tmp = t_3
	elif a <= -4e-134:
		tmp = t_2
	elif a <= -2.4e-220:
		tmp = t_1
	elif a <= 3.3e-173:
		tmp = t_2
	elif a <= 2.05e-69:
		tmp = i * ((a * b) - (y * j))
	elif a <= 5e+38:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.8e+48)
		tmp = t_3;
	elseif (a <= -4e-134)
		tmp = t_2;
	elseif (a <= -2.4e-220)
		tmp = t_1;
	elseif (a <= 3.3e-173)
		tmp = t_2;
	elseif (a <= 2.05e-69)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 5e+38)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = j * ((t * c) - (y * i));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.8e+48)
		tmp = t_3;
	elseif (a <= -4e-134)
		tmp = t_2;
	elseif (a <= -2.4e-220)
		tmp = t_1;
	elseif (a <= 3.3e-173)
		tmp = t_2;
	elseif (a <= 2.05e-69)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 5e+38)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+48], t$95$3, If[LessEqual[a, -4e-134], t$95$2, If[LessEqual[a, -2.4e-220], t$95$1, If[LessEqual[a, 3.3e-173], t$95$2, If[LessEqual[a, 2.05e-69], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+38], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.8000000000000002e48 or 4.9999999999999997e38 < a

   1. Initial program 62.9%

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

   2. Taylor expanded in a around inf 66.1%

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

      1. distribute-lft-out-- 66.1%

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

      2. *-commutative 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in a around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. *-commutative 66.1%

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

      3. *-commutative 66.1%

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

      4. distribute-rgt-neg-out 66.1%

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

      5. neg-mul-1 66.1%

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

      6. distribute-lft-out-- 66.1%

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

      7. neg-mul-1 66.1%

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

      8. neg-sub0 66.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 66.1%

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

      10. distribute-rgt-neg-in 66.1%

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

      11. *-commutative 66.1%

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

      12. associate--r+ 66.1%

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

      13. +-commutative 66.1%

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

      14. associate--r+ 66.1%

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

      15. neg-sub0 66.1%

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

      16. *-commutative 66.1%

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

      17. distribute-rgt-neg-in 66.1%

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

      18. remove-double-neg 66.1%

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

      19. *-commutative 66.1%

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

      20. *-commutative 66.1%

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

   7. Simplified 66.1%

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

   if -4.8000000000000002e48 < a < -4.00000000000000016e-134 or -2.4000000000000001e-220 < a < 3.3000000000000003e-173

   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 j around inf 54.9%

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

   if -4.00000000000000016e-134 < a < -2.4000000000000001e-220 or 2.04999999999999995e-69 < a < 4.9999999999999997e38

   1. Initial program 78.0%

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

   2. Taylor expanded in c around inf 58.8%

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

      1. *-commutative 58.8%

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

   4. Simplified 58.8%

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

   if 3.3000000000000003e-173 < a < 2.04999999999999995e-69

   1. Initial program 87.7%

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

   2. Taylor expanded in i around inf 55.1%

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

      1. distribute-lft-out-- 55.1%

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

      2. *-commutative 55.1%

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

      3. *-commutative 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in i around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. *-commutative 55.1%

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

      3. *-commutative 55.1%

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

      4. distribute-rgt-neg-in 55.1%

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

      5. neg-sub0 55.1%

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

      6. associate-+l- 55.1%

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

      7. neg-sub0 55.1%

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

      8. +-commutative 55.1%

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

      9. fma-udef 55.1%

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

      10. fma-neg 55.1%

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

      11. *-commutative 55.1%

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

   7. Simplified 55.1%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-134}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 11: 51.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -4.8e+83)
     t_2
     (if (<= x -1.1e+61)
       (* j (- (* t c) (* y i)))
       (if (<= x -7.8e-13)
         t_2
         (if (<= x -1.9e-300)
           t_1
           (if (<= x 7.5e+25)
             (* c (- (* t j) (* z b)))
             (if (<= x 1.95e+118) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.8e+83) {
		tmp = t_2;
	} else if (x <= -1.1e+61) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= -7.8e-13) {
		tmp = t_2;
	} else if (x <= -1.9e-300) {
		tmp = t_1;
	} else if (x <= 7.5e+25) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.95e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-4.8d+83)) then
        tmp = t_2
    else if (x <= (-1.1d+61)) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= (-7.8d-13)) then
        tmp = t_2
    else if (x <= (-1.9d-300)) then
        tmp = t_1
    else if (x <= 7.5d+25) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.95d+118) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.8e+83) {
		tmp = t_2;
	} else if (x <= -1.1e+61) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= -7.8e-13) {
		tmp = t_2;
	} else if (x <= -1.9e-300) {
		tmp = t_1;
	} else if (x <= 7.5e+25) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.95e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.8e+83:
		tmp = t_2
	elif x <= -1.1e+61:
		tmp = j * ((t * c) - (y * i))
	elif x <= -7.8e-13:
		tmp = t_2
	elif x <= -1.9e-300:
		tmp = t_1
	elif x <= 7.5e+25:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.95e+118:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.8e+83)
		tmp = t_2;
	elseif (x <= -1.1e+61)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= -7.8e-13)
		tmp = t_2;
	elseif (x <= -1.9e-300)
		tmp = t_1;
	elseif (x <= 7.5e+25)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.95e+118)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.8e+83)
		tmp = t_2;
	elseif (x <= -1.1e+61)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= -7.8e-13)
		tmp = t_2;
	elseif (x <= -1.9e-300)
		tmp = t_1;
	elseif (x <= 7.5e+25)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.95e+118)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+83], t$95$2, If[LessEqual[x, -1.1e+61], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e-13], t$95$2, If[LessEqual[x, -1.9e-300], t$95$1, If[LessEqual[x, 7.5e+25], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+118], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.79999999999999982e83 or -1.1e61 < x < -7.80000000000000009e-13 or 1.95e118 < x

   1. Initial program 76.9%

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

   2. Taylor expanded in b around 0 74.5%

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

   3. Taylor expanded in j around 0 73.7%

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

   if -4.79999999999999982e83 < x < -1.1e61

   1. Initial program 62.5%

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

   2. Taylor expanded in j around inf 74.0%

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

   if -7.80000000000000009e-13 < x < -1.90000000000000006e-300 or 7.49999999999999993e25 < x < 1.95e118

   1. Initial program 71.0%

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

   2. Taylor expanded in i around inf 60.0%

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

      1. distribute-lft-out-- 60.0%

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

      2. *-commutative 60.0%

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

      3. *-commutative 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in i around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. *-commutative 60.0%

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

      3. *-commutative 60.0%

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

      4. distribute-rgt-neg-in 60.0%

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

      5. neg-sub0 60.0%

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

      6. associate-+l- 60.0%

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

      7. neg-sub0 60.0%

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

      8. +-commutative 60.0%

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

      9. fma-udef 60.0%

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

      10. fma-neg 60.0%

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

      11. *-commutative 60.0%

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

   7. Simplified 60.0%

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

   if -1.90000000000000006e-300 < x < 7.49999999999999993e25

   1. Initial program 73.1%

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

   2. Taylor expanded in c around inf 60.9%

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

      1. *-commutative 60.9%

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

   4. Simplified 60.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 12: 51.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.96 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -4e+86)
     t_1
     (if (<= x -4.1e+56)
       (* j (- (* t c) (* y i)))
       (if (<= x -1.35e-13)
         t_1
         (if (<= x -8e-298)
           (* i (- (* a b) (* y j)))
           (if (<= x 6.1e+29)
             (* c (- (* t j) (* z b)))
             (if (<= x 1.96e+118) (* y (- (* x z) (* i j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4e+86) {
		tmp = t_1;
	} else if (x <= -4.1e+56) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= -1.35e-13) {
		tmp = t_1;
	} else if (x <= -8e-298) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 6.1e+29) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.96e+118) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-4d+86)) then
        tmp = t_1
    else if (x <= (-4.1d+56)) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= (-1.35d-13)) then
        tmp = t_1
    else if (x <= (-8d-298)) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 6.1d+29) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.96d+118) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4e+86) {
		tmp = t_1;
	} else if (x <= -4.1e+56) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= -1.35e-13) {
		tmp = t_1;
	} else if (x <= -8e-298) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 6.1e+29) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.96e+118) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4e+86:
		tmp = t_1
	elif x <= -4.1e+56:
		tmp = j * ((t * c) - (y * i))
	elif x <= -1.35e-13:
		tmp = t_1
	elif x <= -8e-298:
		tmp = i * ((a * b) - (y * j))
	elif x <= 6.1e+29:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.96e+118:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4e+86)
		tmp = t_1;
	elseif (x <= -4.1e+56)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= -1.35e-13)
		tmp = t_1;
	elseif (x <= -8e-298)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 6.1e+29)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.96e+118)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4e+86)
		tmp = t_1;
	elseif (x <= -4.1e+56)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= -1.35e-13)
		tmp = t_1;
	elseif (x <= -8e-298)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 6.1e+29)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.96e+118)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+86], t$95$1, If[LessEqual[x, -4.1e+56], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-13], t$95$1, If[LessEqual[x, -8e-298], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.1e+29], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.96e+118], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.0000000000000001e86 or -4.1000000000000004e56 < x < -1.35000000000000005e-13 or 1.96e118 < x

   1. Initial program 76.9%

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

   2. Taylor expanded in b around 0 74.5%

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

   3. Taylor expanded in j around 0 73.7%

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

   if -4.0000000000000001e86 < x < -4.1000000000000004e56

   1. Initial program 62.5%

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

   2. Taylor expanded in j around inf 74.0%

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

   if -1.35000000000000005e-13 < x < -7.9999999999999993e-298

   1. Initial program 70.5%

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

   2. Taylor expanded in i around inf 59.2%

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

      1. distribute-lft-out-- 59.2%

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

      2. *-commutative 59.2%

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

      3. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in i around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. *-commutative 59.2%

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

      3. *-commutative 59.2%

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

      4. distribute-rgt-neg-in 59.2%

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

      5. neg-sub0 59.2%

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

      6. associate-+l- 59.2%

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

      7. neg-sub0 59.2%

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

      8. +-commutative 59.2%

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

      9. fma-udef 59.2%

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

      10. fma-neg 59.2%

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

      11. *-commutative 59.2%

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

   7. Simplified 59.2%

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

   if -7.9999999999999993e-298 < x < 6.0999999999999998e29

   1. Initial program 72.0%

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

   2. Taylor expanded in c around inf 61.5%

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

      1. *-commutative 61.5%

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

   4. Simplified 61.5%

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

   if 6.0999999999999998e29 < x < 1.96e118

   1. Initial program 76.9%

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

   2. Taylor expanded in y around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   4. Simplified 60.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.96 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 13: 58.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -1.15e+147)
     t_1
     (if (<= a 1.6e-125)
       (+ (* j (- (* t c) (* y i))) (* x (* y z)))
       (if (<= a 5.2e+67) (- (* x (- (* y z) (* t a))) (* z (* b c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.15e+147) {
		tmp = t_1;
	} else if (a <= 1.6e-125) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (a <= 5.2e+67) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-1.15d+147)) then
        tmp = t_1
    else if (a <= 1.6d-125) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (a <= 5.2d+67) then
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.15e+147) {
		tmp = t_1;
	} else if (a <= 1.6e-125) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (a <= 5.2e+67) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.15e+147:
		tmp = t_1
	elif a <= 1.6e-125:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif a <= 5.2e+67:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.15e+147)
		tmp = t_1;
	elseif (a <= 1.6e-125)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (a <= 5.2e+67)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.15e+147)
		tmp = t_1;
	elseif (a <= 1.6e-125)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (a <= 5.2e+67)
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+147], t$95$1, If[LessEqual[a, 1.6e-125], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+67], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e147 or 5.2000000000000001e67 < a

   1. Initial program 61.8%

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

   2. Taylor expanded in a around inf 74.1%

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

      1. distribute-lft-out-- 74.1%

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

      2. *-commutative 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in a around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. *-commutative 74.1%

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

      3. *-commutative 74.1%

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

      4. distribute-rgt-neg-out 74.1%

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

      5. neg-mul-1 74.1%

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

      6. distribute-lft-out-- 74.1%

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

      7. neg-mul-1 74.1%

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

      8. neg-sub0 74.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 74.1%

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

      10. distribute-rgt-neg-in 74.1%

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

      11. *-commutative 74.1%

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

      12. associate--r+ 74.1%

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

      13. +-commutative 74.1%

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

      14. associate--r+ 74.1%

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

      15. neg-sub0 74.1%

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

      16. *-commutative 74.1%

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

      17. distribute-rgt-neg-in 74.1%

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

      18. remove-double-neg 74.1%

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

      19. *-commutative 74.1%

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

      20. *-commutative 74.1%

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

   7. Simplified 74.1%

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

   if -1.15e147 < a < 1.5999999999999999e-125

   1. Initial program 78.0%

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

   2. Taylor expanded in b around 0 72.5%

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

   3. Taylor expanded in a around 0 66.9%

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

   if 1.5999999999999999e-125 < a < 5.2000000000000001e67

   1. Initial program 80.9%

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

   2. Taylor expanded in j around 0 74.5%

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

      1. *-commutative 74.5%

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

   4. Simplified 74.5%

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

   5. Taylor expanded in c around inf 62.5%

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

      1. associate-*r* 60.9%

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

      2. *-commutative 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+147}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 14: 28.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(-y \cdot j\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7500000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* y j)))) (t_2 (* a (* t (- x)))))
   (if (<= x -1.55e+168)
     t_2
     (if (<= x -1.05e-151)
       (* t (* c j))
       (if (<= x -5.4e-290)
         (* i (* a b))
         (if (<= x 2.1e-277)
           (* b (* z (- c)))
           (if (<= x 2.3e-230)
             t_1
             (if (<= x 7500000000000.0)
               (* c (* z (- b)))
               (if (<= x 5e+120) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * -(y * j);
	double t_2 = a * (t * -x);
	double tmp;
	if (x <= -1.55e+168) {
		tmp = t_2;
	} else if (x <= -1.05e-151) {
		tmp = t * (c * j);
	} else if (x <= -5.4e-290) {
		tmp = i * (a * b);
	} else if (x <= 2.1e-277) {
		tmp = b * (z * -c);
	} else if (x <= 2.3e-230) {
		tmp = t_1;
	} else if (x <= 7500000000000.0) {
		tmp = c * (z * -b);
	} else if (x <= 5e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * -(y * j)
    t_2 = a * (t * -x)
    if (x <= (-1.55d+168)) then
        tmp = t_2
    else if (x <= (-1.05d-151)) then
        tmp = t * (c * j)
    else if (x <= (-5.4d-290)) then
        tmp = i * (a * b)
    else if (x <= 2.1d-277) then
        tmp = b * (z * -c)
    else if (x <= 2.3d-230) then
        tmp = t_1
    else if (x <= 7500000000000.0d0) then
        tmp = c * (z * -b)
    else if (x <= 5d+120) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * -(y * j);
	double t_2 = a * (t * -x);
	double tmp;
	if (x <= -1.55e+168) {
		tmp = t_2;
	} else if (x <= -1.05e-151) {
		tmp = t * (c * j);
	} else if (x <= -5.4e-290) {
		tmp = i * (a * b);
	} else if (x <= 2.1e-277) {
		tmp = b * (z * -c);
	} else if (x <= 2.3e-230) {
		tmp = t_1;
	} else if (x <= 7500000000000.0) {
		tmp = c * (z * -b);
	} else if (x <= 5e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * -(y * j)
	t_2 = a * (t * -x)
	tmp = 0
	if x <= -1.55e+168:
		tmp = t_2
	elif x <= -1.05e-151:
		tmp = t * (c * j)
	elif x <= -5.4e-290:
		tmp = i * (a * b)
	elif x <= 2.1e-277:
		tmp = b * (z * -c)
	elif x <= 2.3e-230:
		tmp = t_1
	elif x <= 7500000000000.0:
		tmp = c * (z * -b)
	elif x <= 5e+120:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(-Float64(y * j)))
	t_2 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (x <= -1.55e+168)
		tmp = t_2;
	elseif (x <= -1.05e-151)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= -5.4e-290)
		tmp = Float64(i * Float64(a * b));
	elseif (x <= 2.1e-277)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 2.3e-230)
		tmp = t_1;
	elseif (x <= 7500000000000.0)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (x <= 5e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * -(y * j);
	t_2 = a * (t * -x);
	tmp = 0.0;
	if (x <= -1.55e+168)
		tmp = t_2;
	elseif (x <= -1.05e-151)
		tmp = t * (c * j);
	elseif (x <= -5.4e-290)
		tmp = i * (a * b);
	elseif (x <= 2.1e-277)
		tmp = b * (z * -c);
	elseif (x <= 2.3e-230)
		tmp = t_1;
	elseif (x <= 7500000000000.0)
		tmp = c * (z * -b);
	elseif (x <= 5e+120)
		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[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+168], t$95$2, If[LessEqual[x, -1.05e-151], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.4e-290], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-277], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-230], t$95$1, If[LessEqual[x, 7500000000000.0], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+120], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.54999999999999998e168 or 5.00000000000000019e120 < x

   1. Initial program 77.1%

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

   2. Taylor expanded in b around 0 76.1%

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

   3. Taylor expanded in a around inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. distribute-rgt-neg-in 46.7%

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

      3. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   if -1.54999999999999998e168 < x < -1.04999999999999995e-151

   1. Initial program 72.9%

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

   2. Taylor expanded in b around 0 60.4%

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

   3. Taylor expanded in c around inf 29.7%

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

      1. *-commutative 29.7%

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

      2. *-commutative 29.7%

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

      3. associate-*r* 34.1%

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

   5. Simplified 34.1%

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

   if -1.04999999999999995e-151 < x < -5.39999999999999997e-290

   1. Initial program 67.0%

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

   2. Taylor expanded in i around inf 79.6%

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

      1. distribute-lft-out-- 79.6%

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

      2. *-commutative 79.6%

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

      3. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in y around 0 47.1%

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

      1. *-commutative 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-*l* 47.2%

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

   7. Simplified 47.2%

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

   if -5.39999999999999997e-290 < x < 2.09999999999999995e-277

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 72.5%

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

   3. Taylor expanded in a around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-lft-neg-out 61.4%

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

      3. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if 2.09999999999999995e-277 < x < 2.2999999999999998e-230 or 7.5e12 < x < 5.00000000000000019e120

   1. Initial program 64.6%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

      4. *-commutative 51.8%

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

   4. Simplified 51.8%

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

   5. Taylor expanded in z around 0 51.6%

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

      1. associate-*r* 51.6%

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

      2. neg-mul-1 51.6%

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

      3. *-commutative 51.6%

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

   7. Simplified 51.6%

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

   if 2.2999999999999998e-230 < x < 7.5e12

   1. Initial program 73.8%

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

   2. Taylor expanded in c around inf 57.8%

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

      1. *-commutative 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 41.0%

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

      1. associate-*r* 41.0%

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

      2. neg-mul-1 41.0%

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

   7. Simplified 41.0%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+168}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 7500000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 15: 28.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-149}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= x -1.4e+168)
     t_1
     (if (<= x -5e-149)
       (* t (* c j))
       (if (<= x -1.6e-290)
         (* i (* a b))
         (if (<= x 2.2e-277)
           (* b (* z (- c)))
           (if (<= x 4.5e-230)
             (* y (- (* i j)))
             (if (<= x 1.4e+14)
               (* c (* z (- b)))
               (if (<= x 3.7e+118) (* i (- (* y j))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (x <= -1.4e+168) {
		tmp = t_1;
	} else if (x <= -5e-149) {
		tmp = t * (c * j);
	} else if (x <= -1.6e-290) {
		tmp = i * (a * b);
	} else if (x <= 2.2e-277) {
		tmp = b * (z * -c);
	} else if (x <= 4.5e-230) {
		tmp = y * -(i * j);
	} else if (x <= 1.4e+14) {
		tmp = c * (z * -b);
	} else if (x <= 3.7e+118) {
		tmp = i * -(y * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * -x)
    if (x <= (-1.4d+168)) then
        tmp = t_1
    else if (x <= (-5d-149)) then
        tmp = t * (c * j)
    else if (x <= (-1.6d-290)) then
        tmp = i * (a * b)
    else if (x <= 2.2d-277) then
        tmp = b * (z * -c)
    else if (x <= 4.5d-230) then
        tmp = y * -(i * j)
    else if (x <= 1.4d+14) then
        tmp = c * (z * -b)
    else if (x <= 3.7d+118) then
        tmp = i * -(y * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (x <= -1.4e+168) {
		tmp = t_1;
	} else if (x <= -5e-149) {
		tmp = t * (c * j);
	} else if (x <= -1.6e-290) {
		tmp = i * (a * b);
	} else if (x <= 2.2e-277) {
		tmp = b * (z * -c);
	} else if (x <= 4.5e-230) {
		tmp = y * -(i * j);
	} else if (x <= 1.4e+14) {
		tmp = c * (z * -b);
	} else if (x <= 3.7e+118) {
		tmp = i * -(y * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if x <= -1.4e+168:
		tmp = t_1
	elif x <= -5e-149:
		tmp = t * (c * j)
	elif x <= -1.6e-290:
		tmp = i * (a * b)
	elif x <= 2.2e-277:
		tmp = b * (z * -c)
	elif x <= 4.5e-230:
		tmp = y * -(i * j)
	elif x <= 1.4e+14:
		tmp = c * (z * -b)
	elif x <= 3.7e+118:
		tmp = i * -(y * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (x <= -1.4e+168)
		tmp = t_1;
	elseif (x <= -5e-149)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= -1.6e-290)
		tmp = Float64(i * Float64(a * b));
	elseif (x <= 2.2e-277)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 4.5e-230)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (x <= 1.4e+14)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (x <= 3.7e+118)
		tmp = Float64(i * Float64(-Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	tmp = 0.0;
	if (x <= -1.4e+168)
		tmp = t_1;
	elseif (x <= -5e-149)
		tmp = t * (c * j);
	elseif (x <= -1.6e-290)
		tmp = i * (a * b);
	elseif (x <= 2.2e-277)
		tmp = b * (z * -c);
	elseif (x <= 4.5e-230)
		tmp = y * -(i * j);
	elseif (x <= 1.4e+14)
		tmp = c * (z * -b);
	elseif (x <= 3.7e+118)
		tmp = i * -(y * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+168], t$95$1, If[LessEqual[x, -5e-149], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e-290], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-277], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e-230], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.4e+14], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+118], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.39999999999999995e168 or 3.69999999999999987e118 < x

   1. Initial program 77.1%

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

   2. Taylor expanded in b around 0 76.1%

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

   3. Taylor expanded in a around inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. distribute-rgt-neg-in 46.7%

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

      3. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   if -1.39999999999999995e168 < x < -4.99999999999999968e-149

   1. Initial program 72.9%

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

   2. Taylor expanded in b around 0 60.4%

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

   3. Taylor expanded in c around inf 29.7%

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

      1. *-commutative 29.7%

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

      2. *-commutative 29.7%

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

      3. associate-*r* 34.1%

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

   5. Simplified 34.1%

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

   if -4.99999999999999968e-149 < x < -1.59999999999999994e-290

   1. Initial program 67.0%

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

   2. Taylor expanded in i around inf 79.6%

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

      1. distribute-lft-out-- 79.6%

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

      2. *-commutative 79.6%

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

      3. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in y around 0 47.1%

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

      1. *-commutative 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-*l* 47.2%

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

   7. Simplified 47.2%

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

   if -1.59999999999999994e-290 < x < 2.19999999999999996e-277

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 72.5%

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

   3. Taylor expanded in a around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-lft-neg-out 61.4%

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

      3. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if 2.19999999999999996e-277 < x < 4.50000000000000004e-230

   1. Initial program 50.4%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in z around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-*r* 52.2%

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

      3. distribute-rgt-neg-in 52.2%

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

      4. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if 4.50000000000000004e-230 < x < 1.4e14

   1. Initial program 73.8%

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

   2. Taylor expanded in c around inf 57.8%

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

      1. *-commutative 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 41.0%

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

      1. associate-*r* 41.0%

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

      2. neg-mul-1 41.0%

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

   7. Simplified 41.0%

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

   if 1.4e14 < x < 3.69999999999999987e118

   1. Initial program 70.3%

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

   2. Taylor expanded in y around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around 0 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

      3. *-commutative 51.4%

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

   7. Simplified 51.4%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+168}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-149}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 16: 29.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -6500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* t (* c j))))
   (if (<= j -6500000.0)
     t_2
     (if (<= j -4.8e-180)
       (* b (* a i))
       (if (<= j 2.5e-197)
         t_1
         (if (<= j 8e-160)
           (* i (* a b))
           (if (<= j 6.3e-27)
             t_1
             (if (<= j 1.8e+47)
               (* a (* b i))
               (if (<= j 3.6e+113) (* x (* y z)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = t * (c * j);
	double tmp;
	if (j <= -6500000.0) {
		tmp = t_2;
	} else if (j <= -4.8e-180) {
		tmp = b * (a * i);
	} else if (j <= 2.5e-197) {
		tmp = t_1;
	} else if (j <= 8e-160) {
		tmp = i * (a * b);
	} else if (j <= 6.3e-27) {
		tmp = t_1;
	} else if (j <= 1.8e+47) {
		tmp = a * (b * i);
	} else if (j <= 3.6e+113) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = t * (c * j)
    if (j <= (-6500000.0d0)) then
        tmp = t_2
    else if (j <= (-4.8d-180)) then
        tmp = b * (a * i)
    else if (j <= 2.5d-197) then
        tmp = t_1
    else if (j <= 8d-160) then
        tmp = i * (a * b)
    else if (j <= 6.3d-27) then
        tmp = t_1
    else if (j <= 1.8d+47) then
        tmp = a * (b * i)
    else if (j <= 3.6d+113) then
        tmp = x * (y * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = t * (c * j);
	double tmp;
	if (j <= -6500000.0) {
		tmp = t_2;
	} else if (j <= -4.8e-180) {
		tmp = b * (a * i);
	} else if (j <= 2.5e-197) {
		tmp = t_1;
	} else if (j <= 8e-160) {
		tmp = i * (a * b);
	} else if (j <= 6.3e-27) {
		tmp = t_1;
	} else if (j <= 1.8e+47) {
		tmp = a * (b * i);
	} else if (j <= 3.6e+113) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = t * (c * j)
	tmp = 0
	if j <= -6500000.0:
		tmp = t_2
	elif j <= -4.8e-180:
		tmp = b * (a * i)
	elif j <= 2.5e-197:
		tmp = t_1
	elif j <= 8e-160:
		tmp = i * (a * b)
	elif j <= 6.3e-27:
		tmp = t_1
	elif j <= 1.8e+47:
		tmp = a * (b * i)
	elif j <= 3.6e+113:
		tmp = x * (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (j <= -6500000.0)
		tmp = t_2;
	elseif (j <= -4.8e-180)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= 2.5e-197)
		tmp = t_1;
	elseif (j <= 8e-160)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 6.3e-27)
		tmp = t_1;
	elseif (j <= 1.8e+47)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 3.6e+113)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = t * (c * j);
	tmp = 0.0;
	if (j <= -6500000.0)
		tmp = t_2;
	elseif (j <= -4.8e-180)
		tmp = b * (a * i);
	elseif (j <= 2.5e-197)
		tmp = t_1;
	elseif (j <= 8e-160)
		tmp = i * (a * b);
	elseif (j <= 6.3e-27)
		tmp = t_1;
	elseif (j <= 1.8e+47)
		tmp = a * (b * i);
	elseif (j <= 3.6e+113)
		tmp = x * (y * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6500000.0], t$95$2, If[LessEqual[j, -4.8e-180], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-197], t$95$1, If[LessEqual[j, 8e-160], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.3e-27], t$95$1, If[LessEqual[j, 1.8e+47], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+113], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -6.5e6 or 3.59999999999999992e113 < j

   1. Initial program 73.4%

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

   2. Taylor expanded in b around 0 67.5%

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

   3. Taylor expanded in c around inf 44.9%

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

      1. *-commutative 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*r* 48.1%

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

   5. Simplified 48.1%

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

   if -6.5e6 < j < -4.79999999999999959e-180

   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 48.8%

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

   3. Taylor expanded in a around inf 38.8%

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

   if -4.79999999999999959e-180 < j < 2.5000000000000001e-197 or 7.9999999999999999e-160 < j < 6.3000000000000001e-27

   1. Initial program 75.5%

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

   2. Taylor expanded in y around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

      4. *-commutative 46.1%

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

   4. Simplified 46.1%

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

   5. Taylor expanded in z around inf 40.0%

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

   if 2.5000000000000001e-197 < j < 7.9999999999999999e-160

   1. Initial program 70.8%

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

   2. Taylor expanded in i around inf 71.3%

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

      1. distribute-lft-out-- 71.3%

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

      2. *-commutative 71.3%

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

      3. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in y around 0 51.9%

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

      1. *-commutative 51.9%

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

      2. *-commutative 51.9%

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

      3. associate-*l* 61.4%

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

   7. Simplified 61.4%

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

   if 6.3000000000000001e-27 < j < 1.80000000000000004e47

   1. Initial program 65.3%

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

   2. Taylor expanded in b around inf 31.8%

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

   3. Taylor expanded in a around inf 41.6%

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

   if 1.80000000000000004e47 < j < 3.59999999999999992e113

   1. Initial program 70.3%

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

   2. Taylor expanded in b around 0 66.7%

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

   3. Taylor expanded in z around inf 47.7%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6500000:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 17: 29.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-289}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 1220000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))))
   (if (<= x -1.4e+79)
     t_1
     (if (<= x -9e-153)
       (* t (* c j))
       (if (<= x -1.8e-289)
         (* i (* a b))
         (if (<= x 2.5e-277)
           (* b (* z (- c)))
           (if (<= x 3.8e-230)
             (* y (- (* i j)))
             (if (<= x 1220000000000.0) (* c (* z (- b))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (x <= -1.4e+79) {
		tmp = t_1;
	} else if (x <= -9e-153) {
		tmp = t * (c * j);
	} else if (x <= -1.8e-289) {
		tmp = i * (a * b);
	} else if (x <= 2.5e-277) {
		tmp = b * (z * -c);
	} else if (x <= 3.8e-230) {
		tmp = y * -(i * j);
	} else if (x <= 1220000000000.0) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x * -a)
    if (x <= (-1.4d+79)) then
        tmp = t_1
    else if (x <= (-9d-153)) then
        tmp = t * (c * j)
    else if (x <= (-1.8d-289)) then
        tmp = i * (a * b)
    else if (x <= 2.5d-277) then
        tmp = b * (z * -c)
    else if (x <= 3.8d-230) then
        tmp = y * -(i * j)
    else if (x <= 1220000000000.0d0) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (x <= -1.4e+79) {
		tmp = t_1;
	} else if (x <= -9e-153) {
		tmp = t * (c * j);
	} else if (x <= -1.8e-289) {
		tmp = i * (a * b);
	} else if (x <= 2.5e-277) {
		tmp = b * (z * -c);
	} else if (x <= 3.8e-230) {
		tmp = y * -(i * j);
	} else if (x <= 1220000000000.0) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	tmp = 0
	if x <= -1.4e+79:
		tmp = t_1
	elif x <= -9e-153:
		tmp = t * (c * j)
	elif x <= -1.8e-289:
		tmp = i * (a * b)
	elif x <= 2.5e-277:
		tmp = b * (z * -c)
	elif x <= 3.8e-230:
		tmp = y * -(i * j)
	elif x <= 1220000000000.0:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (x <= -1.4e+79)
		tmp = t_1;
	elseif (x <= -9e-153)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= -1.8e-289)
		tmp = Float64(i * Float64(a * b));
	elseif (x <= 2.5e-277)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 3.8e-230)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (x <= 1220000000000.0)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * -a);
	tmp = 0.0;
	if (x <= -1.4e+79)
		tmp = t_1;
	elseif (x <= -9e-153)
		tmp = t * (c * j);
	elseif (x <= -1.8e-289)
		tmp = i * (a * b);
	elseif (x <= 2.5e-277)
		tmp = b * (z * -c);
	elseif (x <= 3.8e-230)
		tmp = y * -(i * j);
	elseif (x <= 1220000000000.0)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+79], t$95$1, If[LessEqual[x, -9e-153], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.8e-289], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-277], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-230], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1220000000000.0], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.4000000000000001e79 or 1.22e12 < x

   1. Initial program 74.4%

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

   2. Taylor expanded in t around -inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. *-commutative 55.4%

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

      3. distribute-rgt-neg-in 55.4%

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

      4. +-commutative 55.4%

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

      5. mul-1-neg 55.4%

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

      6. unsub-neg 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in a around inf 46.5%

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

      1. *-commutative 46.5%

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

   7. Simplified 46.5%

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

   if -1.4000000000000001e79 < x < -9e-153

   1. Initial program 75.2%

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

   2. Taylor expanded in b around 0 59.2%

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

   3. Taylor expanded in c around inf 29.5%

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

      1. *-commutative 29.5%

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

      2. *-commutative 29.5%

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

      3. associate-*r* 35.0%

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

   5. Simplified 35.0%

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

   if -9e-153 < x < -1.8e-289

   1. Initial program 65.6%

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

   2. Taylor expanded in i around inf 78.7%

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

      1. distribute-lft-out-- 78.7%

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

      2. *-commutative 78.7%

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

      3. *-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around 0 49.1%

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

      1. *-commutative 49.1%

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

      2. *-commutative 49.1%

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

      3. associate-*l* 49.2%

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

   7. Simplified 49.2%

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

   if -1.8e-289 < x < 2.5e-277

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 65.3%

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

   3. Taylor expanded in a around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-lft-neg-out 55.4%

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

      3. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if 2.5e-277 < x < 3.7999999999999998e-230

   1. Initial program 50.4%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in z around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-*r* 52.2%

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

      3. distribute-rgt-neg-in 52.2%

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

      4. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if 3.7999999999999998e-230 < x < 1.22e12

   1. Initial program 73.3%

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

   2. Taylor expanded in c around inf 57.1%

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

      1. *-commutative 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in t around 0 39.9%

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

      1. associate-*r* 39.9%

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

      2. neg-mul-1 39.9%

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

   7. Simplified 39.9%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-289}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;x \leq 1220000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 18: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -3500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-173}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* t (* c j))))
   (if (<= j -3500000.0)
     t_2
     (if (<= j -2.45e-173)
       (* b (* a i))
       (if (<= j -1.8e-289)
         t_1
         (if (<= j 5.8e-144) (* i (* a b)) (if (<= j 3.6e+113) 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 = t * (c * j);
	double tmp;
	if (j <= -3500000.0) {
		tmp = t_2;
	} else if (j <= -2.45e-173) {
		tmp = b * (a * i);
	} else if (j <= -1.8e-289) {
		tmp = t_1;
	} else if (j <= 5.8e-144) {
		tmp = i * (a * b);
	} else if (j <= 3.6e+113) {
		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 = t * (c * j)
    if (j <= (-3500000.0d0)) then
        tmp = t_2
    else if (j <= (-2.45d-173)) then
        tmp = b * (a * i)
    else if (j <= (-1.8d-289)) then
        tmp = t_1
    else if (j <= 5.8d-144) then
        tmp = i * (a * b)
    else if (j <= 3.6d+113) 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 = t * (c * j);
	double tmp;
	if (j <= -3500000.0) {
		tmp = t_2;
	} else if (j <= -2.45e-173) {
		tmp = b * (a * i);
	} else if (j <= -1.8e-289) {
		tmp = t_1;
	} else if (j <= 5.8e-144) {
		tmp = i * (a * b);
	} else if (j <= 3.6e+113) {
		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 = t * (c * j)
	tmp = 0
	if j <= -3500000.0:
		tmp = t_2
	elif j <= -2.45e-173:
		tmp = b * (a * i)
	elif j <= -1.8e-289:
		tmp = t_1
	elif j <= 5.8e-144:
		tmp = i * (a * b)
	elif j <= 3.6e+113:
		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(t * Float64(c * j))
	tmp = 0.0
	if (j <= -3500000.0)
		tmp = t_2;
	elseif (j <= -2.45e-173)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= -1.8e-289)
		tmp = t_1;
	elseif (j <= 5.8e-144)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 3.6e+113)
		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 = t * (c * j);
	tmp = 0.0;
	if (j <= -3500000.0)
		tmp = t_2;
	elseif (j <= -2.45e-173)
		tmp = b * (a * i);
	elseif (j <= -1.8e-289)
		tmp = t_1;
	elseif (j <= 5.8e-144)
		tmp = i * (a * b);
	elseif (j <= 3.6e+113)
		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[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3500000.0], t$95$2, If[LessEqual[j, -2.45e-173], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e-289], t$95$1, If[LessEqual[j, 5.8e-144], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+113], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.5e6 or 3.59999999999999992e113 < j

   1. Initial program 73.4%

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

   2. Taylor expanded in b around 0 67.5%

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

   3. Taylor expanded in c around inf 44.9%

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

      1. *-commutative 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*r* 48.1%

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

   5. Simplified 48.1%

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

   if -3.5e6 < j < -2.44999999999999996e-173

   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 48.8%

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

   3. Taylor expanded in a around inf 38.8%

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

   if -2.44999999999999996e-173 < j < -1.8e-289 or 5.8000000000000004e-144 < j < 3.59999999999999992e113

   1. Initial program 73.4%

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

   2. Taylor expanded in b around 0 66.4%

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

   3. Taylor expanded in z around inf 39.9%

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

   if -1.8e-289 < j < 5.8000000000000004e-144

   1. Initial program 71.3%

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

   2. Taylor expanded in i around inf 39.4%

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

      1. distribute-lft-out-- 39.4%

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

      2. *-commutative 39.4%

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

      3. *-commutative 39.4%

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

   4. Simplified 39.4%

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

   5. Taylor expanded in y around 0 34.3%

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

      1. *-commutative 34.3%

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

      2. *-commutative 34.3%

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

      3. associate-*l* 36.9%

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

   7. Simplified 36.9%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3500000:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-173}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 19: 41.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.25e+86)
   (* y (* x z))
   (if (<= z -9.5e+31)
     (* i (- (* y j)))
     (if (<= z 3e+54) (* a (- (* b i) (* x t))) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.25e+86) {
		tmp = y * (x * z);
	} else if (z <= -9.5e+31) {
		tmp = i * -(y * j);
	} else if (z <= 3e+54) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.25d+86)) then
        tmp = y * (x * z)
    else if (z <= (-9.5d+31)) then
        tmp = i * -(y * j)
    else if (z <= 3d+54) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.25e+86) {
		tmp = y * (x * z);
	} else if (z <= -9.5e+31) {
		tmp = i * -(y * j);
	} else if (z <= 3e+54) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.25e+86:
		tmp = y * (x * z)
	elif z <= -9.5e+31:
		tmp = i * -(y * j)
	elif z <= 3e+54:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.25e+86)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -9.5e+31)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (z <= 3e+54)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.25e+86)
		tmp = y * (x * z);
	elseif (z <= -9.5e+31)
		tmp = i * -(y * j);
	elseif (z <= 3e+54)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.25e+86], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e+31], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3e+54], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.24999999999999996e86

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. *-commutative 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in z around inf 51.5%

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

   if -2.24999999999999996e86 < z < -9.5000000000000008e31

   1. Initial program 65.3%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in z around 0 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -9.5000000000000008e31 < z < 2.9999999999999999e54

   1. Initial program 82.7%

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

   2. Taylor expanded in a around inf 52.1%

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

      1. distribute-lft-out-- 52.1%

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

      2. *-commutative 52.1%

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

   4. Simplified 52.1%

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

   5. Taylor expanded in a around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. *-commutative 52.1%

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

      3. *-commutative 52.1%

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

      4. distribute-rgt-neg-out 52.1%

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

      5. neg-mul-1 52.1%

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

      6. distribute-lft-out-- 52.1%

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

      7. neg-mul-1 52.1%

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

      8. neg-sub0 52.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(i \cdot b\right)\right) \]

      9. neg-mul-1 52.1%

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

      10. distribute-rgt-neg-in 52.1%

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

      11. *-commutative 52.1%

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

      12. associate--r+ 52.1%

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

      13. +-commutative 52.1%

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

      14. associate--r+ 52.1%

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

      15. neg-sub0 52.1%

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

      16. *-commutative 52.1%

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

      17. distribute-rgt-neg-in 52.1%

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

      18. remove-double-neg 52.1%

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

      19. *-commutative 52.1%

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

      20. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if 2.9999999999999999e54 < z

   1. Initial program 68.0%

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

   2. Taylor expanded in b around 0 58.0%

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

   3. Taylor expanded in z around inf 41.0%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 20: 28.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1100000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))))
   (if (<= x -7.6e+169)
     t_1
     (if (<= x -1.9e-153)
       (* t (* c j))
       (if (<= x -4.2e-298)
         (* i (* a b))
         (if (<= x 1100000000000.0) (* c (* z (- b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (x <= -7.6e+169) {
		tmp = t_1;
	} else if (x <= -1.9e-153) {
		tmp = t * (c * j);
	} else if (x <= -4.2e-298) {
		tmp = i * (a * b);
	} else if (x <= 1100000000000.0) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * -x)
    if (x <= (-7.6d+169)) then
        tmp = t_1
    else if (x <= (-1.9d-153)) then
        tmp = t * (c * j)
    else if (x <= (-4.2d-298)) then
        tmp = i * (a * b)
    else if (x <= 1100000000000.0d0) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double tmp;
	if (x <= -7.6e+169) {
		tmp = t_1;
	} else if (x <= -1.9e-153) {
		tmp = t * (c * j);
	} else if (x <= -4.2e-298) {
		tmp = i * (a * b);
	} else if (x <= 1100000000000.0) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	tmp = 0
	if x <= -7.6e+169:
		tmp = t_1
	elif x <= -1.9e-153:
		tmp = t * (c * j)
	elif x <= -4.2e-298:
		tmp = i * (a * b)
	elif x <= 1100000000000.0:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (x <= -7.6e+169)
		tmp = t_1;
	elseif (x <= -1.9e-153)
		tmp = Float64(t * Float64(c * j));
	elseif (x <= -4.2e-298)
		tmp = Float64(i * Float64(a * b));
	elseif (x <= 1100000000000.0)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	tmp = 0.0;
	if (x <= -7.6e+169)
		tmp = t_1;
	elseif (x <= -1.9e-153)
		tmp = t * (c * j);
	elseif (x <= -4.2e-298)
		tmp = i * (a * b);
	elseif (x <= 1100000000000.0)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.6e+169], t$95$1, If[LessEqual[x, -1.9e-153], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-298], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1100000000000.0], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.59999999999999983e169 or 1.1e12 < x

   1. Initial program 76.0%

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

   2. Taylor expanded in b around 0 75.2%

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

   3. Taylor expanded in a around inf 43.0%

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

      1. mul-1-neg 43.0%

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

      2. distribute-rgt-neg-in 43.0%

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

      3. *-commutative 43.0%

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

   5. Simplified 43.0%

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

   if -7.59999999999999983e169 < x < -1.90000000000000011e-153

   1. Initial program 72.9%

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

   2. Taylor expanded in b around 0 60.4%

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

   3. Taylor expanded in c around inf 29.7%

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

      1. *-commutative 29.7%

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

      2. *-commutative 29.7%

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

      3. associate-*r* 34.1%

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

   5. Simplified 34.1%

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

   if -1.90000000000000011e-153 < x < -4.2000000000000001e-298

   1. Initial program 69.6%

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

   2. Taylor expanded in i around inf 77.4%

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

      1. distribute-lft-out-- 77.4%

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

      2. *-commutative 77.4%

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

      3. *-commutative 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in y around 0 47.4%

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

      1. *-commutative 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-*l* 47.5%

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

   7. Simplified 47.5%

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

   if -4.2000000000000001e-298 < x < 1.1e12

   1. Initial program 73.3%

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

   2. Taylor expanded in c around inf 59.2%

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

      1. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in t around 0 38.0%

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

      1. associate-*r* 38.0%

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

      2. neg-mul-1 38.0%

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

   7. Simplified 38.0%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1100000000000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 21: 29.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3850000 \lor \neg \left(j \leq 2.5 \cdot 10^{+45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3850000.0) (not (<= j 2.5e+45))) (* 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 ((j <= -3850000.0) || !(j <= 2.5e+45)) {
		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 ((j <= (-3850000.0d0)) .or. (.not. (j <= 2.5d+45))) 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 ((j <= -3850000.0) || !(j <= 2.5e+45)) {
		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 (j <= -3850000.0) or not (j <= 2.5e+45):
		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 ((j <= -3850000.0) || !(j <= 2.5e+45))
		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 ((j <= -3850000.0) || ~((j <= 2.5e+45)))
		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[j, -3850000.0], N[Not[LessEqual[j, 2.5e+45]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.85e6 or 2.5e45 < j

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 53.4%

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

      1. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in t around inf 40.2%

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

   if -3.85e6 < j < 2.5e45

   1. Initial program 74.1%

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

   2. Taylor expanded in b around inf 39.8%

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

   3. Taylor expanded in a around inf 28.3%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3850000 \lor \neg \left(j \leq 2.5 \cdot 10^{+45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 22: 29.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+47} \lor \neg \left(c \leq 3.2 \cdot 10^{-128}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.55e+47) (not (<= c 3.2e-128))) (* j (* t c)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.55e+47) || !(c <= 3.2e-128)) {
		tmp = j * (t * c);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.55d+47)) .or. (.not. (c <= 3.2d-128))) then
        tmp = j * (t * c)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.55e+47) || !(c <= 3.2e-128)) {
		tmp = j * (t * c);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.55e+47) or not (c <= 3.2e-128):
		tmp = j * (t * c)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.55e+47) || !(c <= 3.2e-128))
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.55e+47) || ~((c <= 3.2e-128)))
		tmp = j * (t * c);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.55e+47], N[Not[LessEqual[c, 3.2e-128]], $MachinePrecision]], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.55e47 or 3.1999999999999998e-128 < c

   1. Initial program 72.2%

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

   2. Taylor expanded in c around inf 55.1%

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

      1. *-commutative 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in t around inf 33.5%

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

      1. *-commutative 33.5%

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

      2. associate-*l* 35.7%

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

   7. Simplified 35.7%

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

   if -1.55e47 < c < 3.1999999999999998e-128

   1. Initial program 76.1%

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

   2. Taylor expanded in i around inf 52.8%

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

      1. distribute-lft-out-- 52.8%

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

      2. *-commutative 52.8%

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

      3. *-commutative 52.8%

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

   4. Simplified 52.8%

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

   5. Taylor expanded in y around 0 31.6%

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

      1. *-commutative 31.6%

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

      2. *-commutative 31.6%

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

      3. associate-*l* 32.6%

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

   7. Simplified 32.6%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+47} \lor \neg \left(c \leq 3.2 \cdot 10^{-128}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 23: 29.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.45e+64)
   (* i (* a b))
   (if (<= a 9.2e+91) (* 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 (a <= -2.45e+64) {
		tmp = i * (a * b);
	} else if (a <= 9.2e+91) {
		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 (a <= (-2.45d+64)) then
        tmp = i * (a * b)
    else if (a <= 9.2d+91) 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 (a <= -2.45e+64) {
		tmp = i * (a * b);
	} else if (a <= 9.2e+91) {
		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 a <= -2.45e+64:
		tmp = i * (a * b)
	elif a <= 9.2e+91:
		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 (a <= -2.45e+64)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= 9.2e+91)
		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 (a <= -2.45e+64)
		tmp = i * (a * b);
	elseif (a <= 9.2e+91)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.45e+64], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+91], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4500000000000001e64

   1. Initial program 55.5%

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

   2. Taylor expanded in i around inf 53.4%

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

      1. distribute-lft-out-- 53.4%

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

      2. *-commutative 53.4%

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

      3. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in y around 0 32.5%

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

      1. *-commutative 32.5%

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

      2. *-commutative 32.5%

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

      3. associate-*l* 36.7%

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

   7. Simplified 36.7%

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

   if -2.4500000000000001e64 < a < 9.19999999999999965e91

   1. Initial program 79.4%

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

   2. Taylor expanded in c around inf 45.3%

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

      1. *-commutative 45.3%

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

   4. Simplified 45.3%

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

   5. Taylor expanded in t around inf 27.3%

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

   if 9.19999999999999965e91 < a

   1. Initial program 71.0%

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

   2. Taylor expanded in b around inf 54.8%

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

   3. Taylor expanded in a around inf 52.1%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 24: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -13500:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+46}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -13500.0)
   (* t (* c j))
   (if (<= j 2.65e+46) (* i (* a b)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -13500.0) {
		tmp = t * (c * j);
	} else if (j <= 2.65e+46) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-13500.0d0)) then
        tmp = t * (c * j)
    else if (j <= 2.65d+46) then
        tmp = i * (a * b)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -13500.0) {
		tmp = t * (c * j);
	} else if (j <= 2.65e+46) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -13500.0:
		tmp = t * (c * j)
	elif j <= 2.65e+46:
		tmp = i * (a * b)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -13500.0)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 2.65e+46)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -13500.0)
		tmp = t * (c * j);
	elseif (j <= 2.65e+46)
		tmp = i * (a * b);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -13500.0], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.65e+46], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -13500

   1. Initial program 82.1%

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

   2. Taylor expanded in b around 0 70.1%

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

   3. Taylor expanded in c around inf 35.8%

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

      1. *-commutative 35.8%

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

      2. *-commutative 35.8%

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

      3. associate-*r* 40.9%

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

   5. Simplified 40.9%

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

   if -13500 < j < 2.64999999999999989e46

   1. Initial program 74.1%

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

   2. Taylor expanded in i around inf 38.9%

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

      1. distribute-lft-out-- 38.9%

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

      2. *-commutative 38.9%

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

      3. *-commutative 38.9%

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

   4. Simplified 38.9%

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

   5. Taylor expanded in y around 0 28.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 28.3%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 28.3%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*l* 28.9%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   7. Simplified 28.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   if 2.64999999999999989e46 < j

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 51.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.9%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

   4. Simplified 51.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   5. Taylor expanded in t around inf 44.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -13500:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+46}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 25: 22.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in b around inf 36.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

3. Taylor expanded in a around inf 23.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

4. Final simplification 23.2%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.5% 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 2023318 
(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)))))