Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 83.0%

Time: 22.8s

Alternatives: 22

Speedup: 0.5×

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

Specification

Math

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

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: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(i * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $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 91.0%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 49.8%

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

   4. Taylor expanded in i around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. mul-1-neg 57.6%

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

      3. unsub-neg 57.6%

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

      4. associate-/l* 63.5%

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

   6. Simplified 63.5%

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

4. Final simplification 85.8%

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

Alternative 2: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ t_3 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -1.48 \cdot 10^{+149}:\\ \;\;\;\;j \cdot t\_3\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{t\_3}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* z (- (* x (- y (* a (/ t z)))) (* b c))))
        (t_3 (- (* t c) (* y i))))
   (if (<= j -1.48e+149)
     (* j t_3)
     (if (<= j -3.2e-74)
       t_2
       (if (<= j -5e-155)
         t_1
         (if (<= j 2.7e-305)
           t_2
           (if (<= j 1.9e-279)
             t_1
             (if (<= j 8e+97) t_2 (* (* z j) (/ t_3 z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = z * ((x * (y - (a * (t / z)))) - (b * c));
	double t_3 = (t * c) - (y * i);
	double tmp;
	if (j <= -1.48e+149) {
		tmp = j * t_3;
	} else if (j <= -3.2e-74) {
		tmp = t_2;
	} else if (j <= -5e-155) {
		tmp = t_1;
	} else if (j <= 2.7e-305) {
		tmp = t_2;
	} else if (j <= 1.9e-279) {
		tmp = t_1;
	} else if (j <= 8e+97) {
		tmp = t_2;
	} else {
		tmp = (z * j) * (t_3 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = z * ((x * (y - (a * (t / z)))) - (b * c))
    t_3 = (t * c) - (y * i)
    if (j <= (-1.48d+149)) then
        tmp = j * t_3
    else if (j <= (-3.2d-74)) then
        tmp = t_2
    else if (j <= (-5d-155)) then
        tmp = t_1
    else if (j <= 2.7d-305) then
        tmp = t_2
    else if (j <= 1.9d-279) then
        tmp = t_1
    else if (j <= 8d+97) then
        tmp = t_2
    else
        tmp = (z * j) * (t_3 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = z * ((x * (y - (a * (t / z)))) - (b * c));
	double t_3 = (t * c) - (y * i);
	double tmp;
	if (j <= -1.48e+149) {
		tmp = j * t_3;
	} else if (j <= -3.2e-74) {
		tmp = t_2;
	} else if (j <= -5e-155) {
		tmp = t_1;
	} else if (j <= 2.7e-305) {
		tmp = t_2;
	} else if (j <= 1.9e-279) {
		tmp = t_1;
	} else if (j <= 8e+97) {
		tmp = t_2;
	} else {
		tmp = (z * j) * (t_3 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = z * ((x * (y - (a * (t / z)))) - (b * c))
	t_3 = (t * c) - (y * i)
	tmp = 0
	if j <= -1.48e+149:
		tmp = j * t_3
	elif j <= -3.2e-74:
		tmp = t_2
	elif j <= -5e-155:
		tmp = t_1
	elif j <= 2.7e-305:
		tmp = t_2
	elif j <= 1.9e-279:
		tmp = t_1
	elif j <= 8e+97:
		tmp = t_2
	else:
		tmp = (z * j) * (t_3 / z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(z * Float64(Float64(x * Float64(y - Float64(a * Float64(t / z)))) - Float64(b * c)))
	t_3 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -1.48e+149)
		tmp = Float64(j * t_3);
	elseif (j <= -3.2e-74)
		tmp = t_2;
	elseif (j <= -5e-155)
		tmp = t_1;
	elseif (j <= 2.7e-305)
		tmp = t_2;
	elseif (j <= 1.9e-279)
		tmp = t_1;
	elseif (j <= 8e+97)
		tmp = t_2;
	else
		tmp = Float64(Float64(z * j) * Float64(t_3 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = z * ((x * (y - (a * (t / z)))) - (b * c));
	t_3 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -1.48e+149)
		tmp = j * t_3;
	elseif (j <= -3.2e-74)
		tmp = t_2;
	elseif (j <= -5e-155)
		tmp = t_1;
	elseif (j <= 2.7e-305)
		tmp = t_2;
	elseif (j <= 1.9e-279)
		tmp = t_1;
	elseif (j <= 8e+97)
		tmp = t_2;
	else
		tmp = (z * j) * (t_3 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.48e+149], N[(j * t$95$3), $MachinePrecision], If[LessEqual[j, -3.2e-74], t$95$2, If[LessEqual[j, -5e-155], t$95$1, If[LessEqual[j, 2.7e-305], t$95$2, If[LessEqual[j, 1.9e-279], t$95$1, If[LessEqual[j, 8e+97], t$95$2, N[(N[(z * j), $MachinePrecision] * N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.4800000000000001e149

   1. Initial program 67.4%

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

   3. Taylor expanded in j around inf 80.1%

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

   if -1.4800000000000001e149 < j < -3.1999999999999999e-74 or -4.9999999999999999e-155 < j < 2.6999999999999999e-305 or 1.90000000000000016e-279 < j < 8.0000000000000006e97

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf 64.7%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

      3. associate-/l* 63.2%

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

   8. Simplified 63.2%

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

   if -3.1999999999999999e-74 < j < -4.9999999999999999e-155 or 2.6999999999999999e-305 < j < 1.90000000000000016e-279

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 68.7%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in a around -inf 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

   8. Simplified 83.6%

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

   if 8.0000000000000006e97 < j

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf 62.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in j around inf 76.2%

      \[\leadsto \color{blue}{j \cdot \left(z \cdot \left(\frac{c \cdot t}{z} - \frac{i \cdot y}{z}\right)\right)} \]
   7. Step-by-step derivation

      1. div-sub 78.2%

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

      2. associate-*r* 79.9%

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

      3. *-commutative 79.9%

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

   8. Simplified 79.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.48 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{t \cdot c - y \cdot i}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2600000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -7.5e+129)
     t_1
     (if (<= a -3.8e+90)
       (* y (* x z))
       (if (<= a -2600000000000.0)
         t_1
         (if (<= a -3.2e-216)
           (* c (* t j))
           (if (<= a -2.35e-303)
             (* i (- (* y j)))
             (if (<= a 1.35e-213)
               (* b (- (* a i) (* z c)))
               (if (<= a 7.4e-122) (* x (* y z)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e+129) {
		tmp = t_1;
	} else if (a <= -3.8e+90) {
		tmp = y * (x * z);
	} else if (a <= -2600000000000.0) {
		tmp = t_1;
	} else if (a <= -3.2e-216) {
		tmp = c * (t * j);
	} else if (a <= -2.35e-303) {
		tmp = i * -(y * j);
	} else if (a <= 1.35e-213) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 7.4e-122) {
		tmp = x * (y * z);
	} 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 <= (-7.5d+129)) then
        tmp = t_1
    else if (a <= (-3.8d+90)) then
        tmp = y * (x * z)
    else if (a <= (-2600000000000.0d0)) then
        tmp = t_1
    else if (a <= (-3.2d-216)) then
        tmp = c * (t * j)
    else if (a <= (-2.35d-303)) then
        tmp = i * -(y * j)
    else if (a <= 1.35d-213) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 7.4d-122) then
        tmp = x * (y * z)
    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 <= -7.5e+129) {
		tmp = t_1;
	} else if (a <= -3.8e+90) {
		tmp = y * (x * z);
	} else if (a <= -2600000000000.0) {
		tmp = t_1;
	} else if (a <= -3.2e-216) {
		tmp = c * (t * j);
	} else if (a <= -2.35e-303) {
		tmp = i * -(y * j);
	} else if (a <= 1.35e-213) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 7.4e-122) {
		tmp = x * (y * z);
	} 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 <= -7.5e+129:
		tmp = t_1
	elif a <= -3.8e+90:
		tmp = y * (x * z)
	elif a <= -2600000000000.0:
		tmp = t_1
	elif a <= -3.2e-216:
		tmp = c * (t * j)
	elif a <= -2.35e-303:
		tmp = i * -(y * j)
	elif a <= 1.35e-213:
		tmp = b * ((a * i) - (z * c))
	elif a <= 7.4e-122:
		tmp = x * (y * z)
	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 <= -7.5e+129)
		tmp = t_1;
	elseif (a <= -3.8e+90)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -2600000000000.0)
		tmp = t_1;
	elseif (a <= -3.2e-216)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= -2.35e-303)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (a <= 1.35e-213)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 7.4e-122)
		tmp = Float64(x * Float64(y * z));
	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 <= -7.5e+129)
		tmp = t_1;
	elseif (a <= -3.8e+90)
		tmp = y * (x * z);
	elseif (a <= -2600000000000.0)
		tmp = t_1;
	elseif (a <= -3.2e-216)
		tmp = c * (t * j);
	elseif (a <= -2.35e-303)
		tmp = i * -(y * j);
	elseif (a <= 1.35e-213)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 7.4e-122)
		tmp = x * (y * z);
	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, -7.5e+129], t$95$1, If[LessEqual[a, -3.8e+90], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2600000000000.0], t$95$1, If[LessEqual[a, -3.2e-216], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.35e-303], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 1.35e-213], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e-122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.4999999999999998e129 or -3.8000000000000001e90 < a < -2.6e12 or 7.3999999999999995e-122 < a

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf 61.7%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in a around -inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

   8. Simplified 56.7%

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

   if -7.4999999999999998e129 < a < -3.8000000000000001e90

   1. Initial program 63.4%

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

   3. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 76.2%

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

   8. Simplified 76.2%

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

   if -2.6e12 < a < -3.20000000000000026e-216

   1. Initial program 84.4%

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

   3. Taylor expanded in z around inf 66.9%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 45.6%

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

      1. associate-*r* 39.7%

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

      2. +-commutative 39.7%

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

      3. mul-1-neg 39.7%

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

      4. unsub-neg 39.7%

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

      5. div-sub 42.3%

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

      6. *-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in j around inf 43.7%

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

   if -3.20000000000000026e-216 < a < -2.3499999999999999e-303

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 66.5%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-rgt-neg-in 55.2%

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

      3. *-commutative 55.2%

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

      4. distribute-rgt-neg-in 55.2%

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

   6. Simplified 55.2%

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

   if -2.3499999999999999e-303 < a < 1.35e-213

   1. Initial program 68.7%

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

   3. Taylor expanded in b around inf 47.0%

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

      1. *-commutative 47.0%

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

   5. Simplified 47.0%

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

   if 1.35e-213 < a < 7.3999999999999995e-122

   1. Initial program 75.1%

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

   3. Taylor expanded in x around inf 50.8%

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

      1. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf 50.9%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2600000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -520000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-216}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -7.5e+129)
     t_1
     (if (<= a -3.8e+90)
       (* y (* x z))
       (if (<= a -520000000000.0)
         t_1
         (if (<= a -4.9e-216)
           (* c (* t j))
           (if (<= a -5e-302)
             (* i (- (* y j)))
             (if (<= a 6.8e-216)
               (* (* b c) (- z))
               (if (<= a 2.5e-123) (* x (* y z)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e+129) {
		tmp = t_1;
	} else if (a <= -3.8e+90) {
		tmp = y * (x * z);
	} else if (a <= -520000000000.0) {
		tmp = t_1;
	} else if (a <= -4.9e-216) {
		tmp = c * (t * j);
	} else if (a <= -5e-302) {
		tmp = i * -(y * j);
	} else if (a <= 6.8e-216) {
		tmp = (b * c) * -z;
	} else if (a <= 2.5e-123) {
		tmp = x * (y * z);
	} 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 <= (-7.5d+129)) then
        tmp = t_1
    else if (a <= (-3.8d+90)) then
        tmp = y * (x * z)
    else if (a <= (-520000000000.0d0)) then
        tmp = t_1
    else if (a <= (-4.9d-216)) then
        tmp = c * (t * j)
    else if (a <= (-5d-302)) then
        tmp = i * -(y * j)
    else if (a <= 6.8d-216) then
        tmp = (b * c) * -z
    else if (a <= 2.5d-123) then
        tmp = x * (y * z)
    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 <= -7.5e+129) {
		tmp = t_1;
	} else if (a <= -3.8e+90) {
		tmp = y * (x * z);
	} else if (a <= -520000000000.0) {
		tmp = t_1;
	} else if (a <= -4.9e-216) {
		tmp = c * (t * j);
	} else if (a <= -5e-302) {
		tmp = i * -(y * j);
	} else if (a <= 6.8e-216) {
		tmp = (b * c) * -z;
	} else if (a <= 2.5e-123) {
		tmp = x * (y * z);
	} 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 <= -7.5e+129:
		tmp = t_1
	elif a <= -3.8e+90:
		tmp = y * (x * z)
	elif a <= -520000000000.0:
		tmp = t_1
	elif a <= -4.9e-216:
		tmp = c * (t * j)
	elif a <= -5e-302:
		tmp = i * -(y * j)
	elif a <= 6.8e-216:
		tmp = (b * c) * -z
	elif a <= 2.5e-123:
		tmp = x * (y * z)
	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 <= -7.5e+129)
		tmp = t_1;
	elseif (a <= -3.8e+90)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -520000000000.0)
		tmp = t_1;
	elseif (a <= -4.9e-216)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= -5e-302)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (a <= 6.8e-216)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (a <= 2.5e-123)
		tmp = Float64(x * Float64(y * z));
	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 <= -7.5e+129)
		tmp = t_1;
	elseif (a <= -3.8e+90)
		tmp = y * (x * z);
	elseif (a <= -520000000000.0)
		tmp = t_1;
	elseif (a <= -4.9e-216)
		tmp = c * (t * j);
	elseif (a <= -5e-302)
		tmp = i * -(y * j);
	elseif (a <= 6.8e-216)
		tmp = (b * c) * -z;
	elseif (a <= 2.5e-123)
		tmp = x * (y * z);
	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, -7.5e+129], t$95$1, If[LessEqual[a, -3.8e+90], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -520000000000.0], t$95$1, If[LessEqual[a, -4.9e-216], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-302], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 6.8e-216], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[a, 2.5e-123], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.4999999999999998e129 or -3.8000000000000001e90 < a < -5.2e11 or 2.50000000000000015e-123 < a

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf 61.7%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in a around -inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

   8. Simplified 56.7%

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

   if -7.4999999999999998e129 < a < -3.8000000000000001e90

   1. Initial program 63.4%

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

   3. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 76.2%

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

   8. Simplified 76.2%

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

   if -5.2e11 < a < -4.9000000000000001e-216

   1. Initial program 84.4%

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

   3. Taylor expanded in z around inf 66.9%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 45.6%

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

      1. associate-*r* 39.7%

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

      2. +-commutative 39.7%

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

      3. mul-1-neg 39.7%

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

      4. unsub-neg 39.7%

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

      5. div-sub 42.3%

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

      6. *-commutative 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in j around inf 43.7%

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

   if -4.9000000000000001e-216 < a < -5.00000000000000033e-302

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 66.5%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-rgt-neg-in 55.2%

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

      3. *-commutative 55.2%

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

      4. distribute-rgt-neg-in 55.2%

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

   6. Simplified 55.2%

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

   if -5.00000000000000033e-302 < a < 6.7999999999999995e-216

   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. Add Preprocessing

   3. Taylor expanded in b around inf 44.4%

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

      1. *-commutative 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in c around inf 44.5%

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

   7. Taylor expanded in c around inf 35.5%

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

      1. mul-1-neg 35.5%

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

      2. associate-*r* 43.0%

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

   9. Simplified 43.0%

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

   if 6.7999999999999995e-216 < a < 2.50000000000000015e-123

   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. Add Preprocessing

   3. Taylor expanded in x around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around inf 49.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -520000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-216}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+89}:\\ \;\;\;\;\left(y - a \cdot \frac{t}{z}\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -48000000000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+33}:\\ \;\;\;\;\left(c \cdot j\right) \cdot \left(t - b \cdot \frac{z}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -1.8e+196)
     t_1
     (if (<= a -5.8e+89)
       (* (- y (* a (/ t z))) (* x z))
       (if (<= a -48000000000000.0)
         (* i (- (* a b) (* y j)))
         (if (<= a 5e-232)
           (* j (- (* t c) (* y i)))
           (if (<= a 6.8e-88)
             (* z (- (* x y) (* b c)))
             (if (<= a 4.3e+33) (* (* c j) (- t (* b (/ z 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 * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.8e+196) {
		tmp = t_1;
	} else if (a <= -5.8e+89) {
		tmp = (y - (a * (t / z))) * (x * z);
	} else if (a <= -48000000000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 5e-232) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 6.8e-88) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 4.3e+33) {
		tmp = (c * j) * (t - (b * (z / 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 * ((b * i) - (x * t))
    if (a <= (-1.8d+196)) then
        tmp = t_1
    else if (a <= (-5.8d+89)) then
        tmp = (y - (a * (t / z))) * (x * z)
    else if (a <= (-48000000000000.0d0)) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 5d-232) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 6.8d-88) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 4.3d+33) then
        tmp = (c * j) * (t - (b * (z / 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 * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.8e+196) {
		tmp = t_1;
	} else if (a <= -5.8e+89) {
		tmp = (y - (a * (t / z))) * (x * z);
	} else if (a <= -48000000000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 5e-232) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 6.8e-88) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 4.3e+33) {
		tmp = (c * j) * (t - (b * (z / j)));
	} 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 <= -1.8e+196:
		tmp = t_1
	elif a <= -5.8e+89:
		tmp = (y - (a * (t / z))) * (x * z)
	elif a <= -48000000000000.0:
		tmp = i * ((a * b) - (y * j))
	elif a <= 5e-232:
		tmp = j * ((t * c) - (y * i))
	elif a <= 6.8e-88:
		tmp = z * ((x * y) - (b * c))
	elif a <= 4.3e+33:
		tmp = (c * j) * (t - (b * (z / j)))
	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 <= -1.8e+196)
		tmp = t_1;
	elseif (a <= -5.8e+89)
		tmp = Float64(Float64(y - Float64(a * Float64(t / z))) * Float64(x * z));
	elseif (a <= -48000000000000.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 5e-232)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 6.8e-88)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 4.3e+33)
		tmp = Float64(Float64(c * j) * Float64(t - Float64(b * Float64(z / 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 * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.8e+196)
		tmp = t_1;
	elseif (a <= -5.8e+89)
		tmp = (y - (a * (t / z))) * (x * z);
	elseif (a <= -48000000000000.0)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 5e-232)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 6.8e-88)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 4.3e+33)
		tmp = (c * j) * (t - (b * (z / 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[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+196], t$95$1, If[LessEqual[a, -5.8e+89], N[(N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -48000000000000.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-232], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-88], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e+33], N[(N[(c * j), $MachinePrecision] * N[(t - N[(b * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.80000000000000004e196 or 4.30000000000000028e33 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 58.6%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in a around -inf 70.9%

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

      1. +-commutative 70.9%

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

      2. mul-1-neg 70.9%

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

      3. unsub-neg 70.9%

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

   8. Simplified 70.9%

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

   if -1.80000000000000004e196 < a < -5.80000000000000051e89

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 54.2%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in x around inf 66.7%

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

      1. associate-*r* 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

      4. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   if -5.80000000000000051e89 < a < -4.8e13

   1. Initial program 60.0%

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

   3. Taylor expanded in i around inf 60.9%

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

      1. distribute-lft-out-- 60.9%

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

      2. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -4.8e13 < a < 4.9999999999999999e-232

   1. Initial program 79.5%

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

   3. Taylor expanded in j around inf 59.9%

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

   if 4.9999999999999999e-232 < a < 6.79999999999999949e-88

   1. Initial program 79.2%

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

   3. Taylor expanded in z around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if 6.79999999999999949e-88 < a < 4.30000000000000028e33

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 67.1%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in j around -inf 67.3%

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

   8. Simplified 64.1%

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

   9. Taylor expanded in c around inf 54.8%

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

       1. associate-*r* 54.8%

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

       2. *-commutative 54.8%

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

       3. mul-1-neg 54.8%

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

       4. unsub-neg 54.8%

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

       5. associate-/l* 61.1%

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

   11. Simplified 61.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+89}:\\ \;\;\;\;\left(y - a \cdot \frac{t}{z}\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -48000000000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+33}:\\ \;\;\;\;\left(c \cdot j\right) \cdot \left(t - b \cdot \frac{z}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+14}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;\left(c \cdot j\right) \cdot \left(t - b \cdot \frac{z}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -8.8e+165)
     t_2
     (if (<= a -2.15e+89)
       t_1
       (if (<= a -1.65e+14)
         (* i (- (* a b) (* y j)))
         (if (<= a 7e-233)
           (* j (- (* t c) (* y i)))
           (if (<= a 1.85e-88)
             t_1
             (if (<= a 3.7e+30) (* (* c j) (- t (* b (/ z j)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.8e+165) {
		tmp = t_2;
	} else if (a <= -2.15e+89) {
		tmp = t_1;
	} else if (a <= -1.65e+14) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 7e-233) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 1.85e-88) {
		tmp = t_1;
	} else if (a <= 3.7e+30) {
		tmp = (c * j) * (t - (b * (z / j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-8.8d+165)) then
        tmp = t_2
    else if (a <= (-2.15d+89)) then
        tmp = t_1
    else if (a <= (-1.65d+14)) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 7d-233) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 1.85d-88) then
        tmp = t_1
    else if (a <= 3.7d+30) then
        tmp = (c * j) * (t - (b * (z / j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.8e+165) {
		tmp = t_2;
	} else if (a <= -2.15e+89) {
		tmp = t_1;
	} else if (a <= -1.65e+14) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 7e-233) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 1.85e-88) {
		tmp = t_1;
	} else if (a <= 3.7e+30) {
		tmp = (c * j) * (t - (b * (z / j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -8.8e+165:
		tmp = t_2
	elif a <= -2.15e+89:
		tmp = t_1
	elif a <= -1.65e+14:
		tmp = i * ((a * b) - (y * j))
	elif a <= 7e-233:
		tmp = j * ((t * c) - (y * i))
	elif a <= 1.85e-88:
		tmp = t_1
	elif a <= 3.7e+30:
		tmp = (c * j) * (t - (b * (z / j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.8e+165)
		tmp = t_2;
	elseif (a <= -2.15e+89)
		tmp = t_1;
	elseif (a <= -1.65e+14)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 7e-233)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 1.85e-88)
		tmp = t_1;
	elseif (a <= 3.7e+30)
		tmp = Float64(Float64(c * j) * Float64(t - Float64(b * Float64(z / j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -8.8e+165)
		tmp = t_2;
	elseif (a <= -2.15e+89)
		tmp = t_1;
	elseif (a <= -1.65e+14)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 7e-233)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 1.85e-88)
		tmp = t_1;
	elseif (a <= 3.7e+30)
		tmp = (c * j) * (t - (b * (z / j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+165], t$95$2, If[LessEqual[a, -2.15e+89], t$95$1, If[LessEqual[a, -1.65e+14], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-233], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-88], t$95$1, If[LessEqual[a, 3.7e+30], N[(N[(c * j), $MachinePrecision] * N[(t - N[(b * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.7999999999999996e165 or 3.70000000000000016e30 < a

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 60.2%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around -inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   8. Simplified 70.2%

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

   if -8.7999999999999996e165 < a < -2.1500000000000001e89 or 6.99999999999999982e-233 < a < 1.8499999999999999e-88

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -2.1500000000000001e89 < a < -1.65e14

   1. Initial program 60.0%

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

   3. Taylor expanded in i around inf 60.9%

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

      1. distribute-lft-out-- 60.9%

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

      2. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -1.65e14 < a < 6.99999999999999982e-233

   1. Initial program 79.5%

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

   3. Taylor expanded in j around inf 59.9%

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

   if 1.8499999999999999e-88 < a < 3.70000000000000016e30

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 67.1%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in j around -inf 67.3%

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

   8. Simplified 64.1%

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

   9. Taylor expanded in c around inf 54.8%

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

       1. associate-*r* 54.8%

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

       2. *-commutative 54.8%

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

       3. mul-1-neg 54.8%

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

       4. unsub-neg 54.8%

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

       5. associate-/l* 61.1%

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

   11. Simplified 61.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+14}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;\left(c \cdot j\right) \cdot \left(t - b \cdot \frac{z}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.75 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))))
   (if (<= i -2.6e+145)
     t_2
     (if (<= i -1.75e+41)
       (* y (* i (- j)))
       (if (<= i -2.1e-43)
         t_1
         (if (<= i -2.9e-118)
           (* (* b c) (- z))
           (if (<= i -2.85e-273)
             (* a (* t (- x)))
             (if (<= i 3.1e-274)
               (* y (* x z))
               (if (<= i 2.8e+22) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -2.6e+145) {
		tmp = t_2;
	} else if (i <= -1.75e+41) {
		tmp = y * (i * -j);
	} else if (i <= -2.1e-43) {
		tmp = t_1;
	} else if (i <= -2.9e-118) {
		tmp = (b * c) * -z;
	} else if (i <= -2.85e-273) {
		tmp = a * (t * -x);
	} else if (i <= 3.1e-274) {
		tmp = y * (x * z);
	} else if (i <= 2.8e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = a * (b * i)
    if (i <= (-2.6d+145)) then
        tmp = t_2
    else if (i <= (-1.75d+41)) then
        tmp = y * (i * -j)
    else if (i <= (-2.1d-43)) then
        tmp = t_1
    else if (i <= (-2.9d-118)) then
        tmp = (b * c) * -z
    else if (i <= (-2.85d-273)) then
        tmp = a * (t * -x)
    else if (i <= 3.1d-274) then
        tmp = y * (x * z)
    else if (i <= 2.8d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -2.6e+145) {
		tmp = t_2;
	} else if (i <= -1.75e+41) {
		tmp = y * (i * -j);
	} else if (i <= -2.1e-43) {
		tmp = t_1;
	} else if (i <= -2.9e-118) {
		tmp = (b * c) * -z;
	} else if (i <= -2.85e-273) {
		tmp = a * (t * -x);
	} else if (i <= 3.1e-274) {
		tmp = y * (x * z);
	} else if (i <= 2.8e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -2.6e+145:
		tmp = t_2
	elif i <= -1.75e+41:
		tmp = y * (i * -j)
	elif i <= -2.1e-43:
		tmp = t_1
	elif i <= -2.9e-118:
		tmp = (b * c) * -z
	elif i <= -2.85e-273:
		tmp = a * (t * -x)
	elif i <= 3.1e-274:
		tmp = y * (x * z)
	elif i <= 2.8e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -2.6e+145)
		tmp = t_2;
	elseif (i <= -1.75e+41)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -2.1e-43)
		tmp = t_1;
	elseif (i <= -2.9e-118)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (i <= -2.85e-273)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 3.1e-274)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 2.8e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -2.6e+145)
		tmp = t_2;
	elseif (i <= -1.75e+41)
		tmp = y * (i * -j);
	elseif (i <= -2.1e-43)
		tmp = t_1;
	elseif (i <= -2.9e-118)
		tmp = (b * c) * -z;
	elseif (i <= -2.85e-273)
		tmp = a * (t * -x);
	elseif (i <= 3.1e-274)
		tmp = y * (x * z);
	elseif (i <= 2.8e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+145], t$95$2, If[LessEqual[i, -1.75e+41], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.1e-43], t$95$1, If[LessEqual[i, -2.9e-118], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[i, -2.85e-273], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e-274], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e+22], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.60000000000000003e145 or 2.8e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -2.60000000000000003e145 < i < -1.75e41

   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. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

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

   4. Taylor expanded in i around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. associate-*r* 54.3%

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

      3. *-commutative 54.3%

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

      4. distribute-lft-neg-out 54.3%

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

      5. *-commutative 54.3%

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

      6. distribute-lft-neg-in 54.3%

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

   6. Simplified 54.3%

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

   if -1.75e41 < i < -2.1000000000000001e-43 or 3.09999999999999978e-274 < i < 2.8e22

   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. Add Preprocessing

   3. Taylor expanded in z around inf 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in t around inf 43.9%

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

      1. associate-*r* 40.3%

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

      2. +-commutative 40.3%

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

      3. mul-1-neg 40.3%

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

      4. unsub-neg 40.3%

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

      5. div-sub 41.6%

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

      6. *-commutative 41.6%

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

   8. Simplified 41.6%

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

   9. Taylor expanded in j around inf 37.2%

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

   if -2.1000000000000001e-43 < i < -2.8999999999999998e-118

   1. Initial program 61.0%

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

   3. Taylor expanded in b around inf 35.3%

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

      1. *-commutative 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in c around inf 35.1%

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

   7. Taylor expanded in c around inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. associate-*r* 54.2%

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

   9. Simplified 54.2%

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

   if -2.8999999999999998e-118 < i < -2.84999999999999986e-273

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-rgt-neg-in 49.6%

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

      3. distribute-rgt-neg-in 49.6%

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

   8. Simplified 49.6%

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

   if -2.84999999999999986e-273 < i < 3.09999999999999978e-274

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-*r* 53.7%

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

   8. Simplified 53.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.75 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))))
   (if (<= i -3e+146)
     t_2
     (if (<= i -4.4e+45)
       (* i (- (* y j)))
       (if (<= i -1.1e-42)
         t_1
         (if (<= i -2.4e-118)
           (* (* b c) (- z))
           (if (<= i -2.8e-272)
             (* a (* t (- x)))
             (if (<= i 8.2e-274)
               (* y (* x z))
               (if (<= i 2.5e+22) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -3e+146) {
		tmp = t_2;
	} else if (i <= -4.4e+45) {
		tmp = i * -(y * j);
	} else if (i <= -1.1e-42) {
		tmp = t_1;
	} else if (i <= -2.4e-118) {
		tmp = (b * c) * -z;
	} else if (i <= -2.8e-272) {
		tmp = a * (t * -x);
	} else if (i <= 8.2e-274) {
		tmp = y * (x * z);
	} else if (i <= 2.5e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = a * (b * i)
    if (i <= (-3d+146)) then
        tmp = t_2
    else if (i <= (-4.4d+45)) then
        tmp = i * -(y * j)
    else if (i <= (-1.1d-42)) then
        tmp = t_1
    else if (i <= (-2.4d-118)) then
        tmp = (b * c) * -z
    else if (i <= (-2.8d-272)) then
        tmp = a * (t * -x)
    else if (i <= 8.2d-274) then
        tmp = y * (x * z)
    else if (i <= 2.5d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -3e+146) {
		tmp = t_2;
	} else if (i <= -4.4e+45) {
		tmp = i * -(y * j);
	} else if (i <= -1.1e-42) {
		tmp = t_1;
	} else if (i <= -2.4e-118) {
		tmp = (b * c) * -z;
	} else if (i <= -2.8e-272) {
		tmp = a * (t * -x);
	} else if (i <= 8.2e-274) {
		tmp = y * (x * z);
	} else if (i <= 2.5e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -3e+146:
		tmp = t_2
	elif i <= -4.4e+45:
		tmp = i * -(y * j)
	elif i <= -1.1e-42:
		tmp = t_1
	elif i <= -2.4e-118:
		tmp = (b * c) * -z
	elif i <= -2.8e-272:
		tmp = a * (t * -x)
	elif i <= 8.2e-274:
		tmp = y * (x * z)
	elif i <= 2.5e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -3e+146)
		tmp = t_2;
	elseif (i <= -4.4e+45)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (i <= -1.1e-42)
		tmp = t_1;
	elseif (i <= -2.4e-118)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (i <= -2.8e-272)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 8.2e-274)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 2.5e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -3e+146)
		tmp = t_2;
	elseif (i <= -4.4e+45)
		tmp = i * -(y * j);
	elseif (i <= -1.1e-42)
		tmp = t_1;
	elseif (i <= -2.4e-118)
		tmp = (b * c) * -z;
	elseif (i <= -2.8e-272)
		tmp = a * (t * -x);
	elseif (i <= 8.2e-274)
		tmp = y * (x * z);
	elseif (i <= 2.5e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3e+146], t$95$2, If[LessEqual[i, -4.4e+45], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, -1.1e-42], t$95$1, If[LessEqual[i, -2.4e-118], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[i, -2.8e-272], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e-274], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+22], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.00000000000000002e146 or 2.4999999999999998e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -3.00000000000000002e146 < i < -4.4000000000000001e45

   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. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

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

   4. Taylor expanded in i around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

      3. *-commutative 54.3%

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

      4. distribute-rgt-neg-in 54.3%

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

   6. Simplified 54.3%

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

   if -4.4000000000000001e45 < i < -1.10000000000000003e-42 or 8.19999999999999975e-274 < i < 2.4999999999999998e22

   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. Add Preprocessing

   3. Taylor expanded in z around inf 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in t around inf 43.9%

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

      1. associate-*r* 40.3%

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

      2. +-commutative 40.3%

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

      3. mul-1-neg 40.3%

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

      4. unsub-neg 40.3%

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

      5. div-sub 41.6%

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

      6. *-commutative 41.6%

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

   8. Simplified 41.6%

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

   9. Taylor expanded in j around inf 37.2%

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

   if -1.10000000000000003e-42 < i < -2.4000000000000001e-118

   1. Initial program 61.0%

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

   3. Taylor expanded in b around inf 35.3%

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

      1. *-commutative 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in c around inf 35.1%

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

   7. Taylor expanded in c around inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. associate-*r* 54.2%

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

   9. Simplified 54.2%

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

   if -2.4000000000000001e-118 < i < -2.79999999999999994e-272

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-rgt-neg-in 49.6%

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

      3. distribute-rgt-neg-in 49.6%

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

   8. Simplified 49.6%

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

   if -2.79999999999999994e-272 < i < 8.19999999999999975e-274

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-*r* 53.7%

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

   8. Simplified 53.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -92000000000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -8.8e+165)
     t_2
     (if (<= a -2.1e+88)
       t_1
       (if (<= a -92000000000000.0)
         (* i (- (* a b) (* y j)))
         (if (<= a 2e-232)
           (* j (- (* t c) (* y i)))
           (if (<= a 5.9e-89)
             t_1
             (if (<= a 3.7e+27) (* c (- (* t j) (* z b))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.8e+165) {
		tmp = t_2;
	} else if (a <= -2.1e+88) {
		tmp = t_1;
	} else if (a <= -92000000000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 2e-232) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5.9e-89) {
		tmp = t_1;
	} else if (a <= 3.7e+27) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-8.8d+165)) then
        tmp = t_2
    else if (a <= (-2.1d+88)) then
        tmp = t_1
    else if (a <= (-92000000000000.0d0)) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 2d-232) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 5.9d-89) then
        tmp = t_1
    else if (a <= 3.7d+27) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.8e+165) {
		tmp = t_2;
	} else if (a <= -2.1e+88) {
		tmp = t_1;
	} else if (a <= -92000000000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 2e-232) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5.9e-89) {
		tmp = t_1;
	} else if (a <= 3.7e+27) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -8.8e+165:
		tmp = t_2
	elif a <= -2.1e+88:
		tmp = t_1
	elif a <= -92000000000000.0:
		tmp = i * ((a * b) - (y * j))
	elif a <= 2e-232:
		tmp = j * ((t * c) - (y * i))
	elif a <= 5.9e-89:
		tmp = t_1
	elif a <= 3.7e+27:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.8e+165)
		tmp = t_2;
	elseif (a <= -2.1e+88)
		tmp = t_1;
	elseif (a <= -92000000000000.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 2e-232)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 5.9e-89)
		tmp = t_1;
	elseif (a <= 3.7e+27)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -8.8e+165)
		tmp = t_2;
	elseif (a <= -2.1e+88)
		tmp = t_1;
	elseif (a <= -92000000000000.0)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 2e-232)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 5.9e-89)
		tmp = t_1;
	elseif (a <= 3.7e+27)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+165], t$95$2, If[LessEqual[a, -2.1e+88], t$95$1, If[LessEqual[a, -92000000000000.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-232], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.9e-89], t$95$1, If[LessEqual[a, 3.7e+27], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.7999999999999996e165 or 3.70000000000000002e27 < a

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 60.2%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around -inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   8. Simplified 70.2%

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

   if -8.7999999999999996e165 < a < -2.1e88 or 2.00000000000000005e-232 < a < 5.90000000000000021e-89

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -2.1e88 < a < -9.2e13

   1. Initial program 60.0%

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

   3. Taylor expanded in i around inf 60.9%

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

      1. distribute-lft-out-- 60.9%

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

      2. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -9.2e13 < a < 2.00000000000000005e-232

   1. Initial program 79.5%

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

   3. Taylor expanded in j around inf 59.9%

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

   if 5.90000000000000021e-89 < a < 3.70000000000000002e27

   1. Initial program 73.5%

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

   3. Taylor expanded in c around inf 57.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -92000000000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1950000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -4.6e+166)
     t_2
     (if (<= a -1.3e+89)
       t_1
       (if (<= a -1950000000000.0)
         t_2
         (if (<= a 2.6e-232)
           (* j (- (* t c) (* y i)))
           (if (<= a 5e-88)
             t_1
             (if (<= a 2.8e+32) (* c (- (* t j) (* z b))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.6e+166) {
		tmp = t_2;
	} else if (a <= -1.3e+89) {
		tmp = t_1;
	} else if (a <= -1950000000000.0) {
		tmp = t_2;
	} else if (a <= 2.6e-232) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5e-88) {
		tmp = t_1;
	} else if (a <= 2.8e+32) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-4.6d+166)) then
        tmp = t_2
    else if (a <= (-1.3d+89)) then
        tmp = t_1
    else if (a <= (-1950000000000.0d0)) then
        tmp = t_2
    else if (a <= 2.6d-232) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 5d-88) then
        tmp = t_1
    else if (a <= 2.8d+32) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.6e+166) {
		tmp = t_2;
	} else if (a <= -1.3e+89) {
		tmp = t_1;
	} else if (a <= -1950000000000.0) {
		tmp = t_2;
	} else if (a <= 2.6e-232) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5e-88) {
		tmp = t_1;
	} else if (a <= 2.8e+32) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.6e+166:
		tmp = t_2
	elif a <= -1.3e+89:
		tmp = t_1
	elif a <= -1950000000000.0:
		tmp = t_2
	elif a <= 2.6e-232:
		tmp = j * ((t * c) - (y * i))
	elif a <= 5e-88:
		tmp = t_1
	elif a <= 2.8e+32:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.6e+166)
		tmp = t_2;
	elseif (a <= -1.3e+89)
		tmp = t_1;
	elseif (a <= -1950000000000.0)
		tmp = t_2;
	elseif (a <= 2.6e-232)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 5e-88)
		tmp = t_1;
	elseif (a <= 2.8e+32)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.6e+166)
		tmp = t_2;
	elseif (a <= -1.3e+89)
		tmp = t_1;
	elseif (a <= -1950000000000.0)
		tmp = t_2;
	elseif (a <= 2.6e-232)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 5e-88)
		tmp = t_1;
	elseif (a <= 2.8e+32)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+166], t$95$2, If[LessEqual[a, -1.3e+89], t$95$1, If[LessEqual[a, -1950000000000.0], t$95$2, If[LessEqual[a, 2.6e-232], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-88], t$95$1, If[LessEqual[a, 2.8e+32], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.60000000000000015e166 or -1.3e89 < a < -1.95e12 or 2.8e32 < a

   1. Initial program 67.5%

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

   3. Taylor expanded in z around inf 60.1%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in a around -inf 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

   8. Simplified 67.5%

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

   if -4.60000000000000015e166 < a < -1.3e89 or 2.59999999999999996e-232 < a < 5.00000000000000009e-88

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -1.95e12 < a < 2.59999999999999996e-232

   1. Initial program 79.5%

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

   3. Taylor expanded in j around inf 59.9%

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

   if 5.00000000000000009e-88 < a < 2.8e32

   1. Initial program 73.5%

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

   3. Taylor expanded in c around inf 57.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1950000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -8.3 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{elif}\;j \leq -1.56 \cdot 10^{+50}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t - b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;t\_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= j -8.3e+148)
     t_1
     (if (<= j -2.8e+64)
       (* z (- (* x (- y (* a (/ t z)))) (* b c)))
       (if (<= j -1.56e+50)
         (- t_1 (* a (- (* x t) (* b i))))
         (if (<= j 1.52e-33)
           (+ t_2 (* b (- (* a i) (* z c))))
           (+ t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -8.3e+148) {
		tmp = t_1;
	} else if (j <= -2.8e+64) {
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c));
	} else if (j <= -1.56e+50) {
		tmp = t_1 - (a * ((x * t) - (b * i)));
	} else if (j <= 1.52e-33) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (j <= (-8.3d+148)) then
        tmp = t_1
    else if (j <= (-2.8d+64)) then
        tmp = z * ((x * (y - (a * (t / z)))) - (b * c))
    else if (j <= (-1.56d+50)) then
        tmp = t_1 - (a * ((x * t) - (b * i)))
    else if (j <= 1.52d-33) then
        tmp = t_2 + (b * ((a * i) - (z * c)))
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -8.3e+148) {
		tmp = t_1;
	} else if (j <= -2.8e+64) {
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c));
	} else if (j <= -1.56e+50) {
		tmp = t_1 - (a * ((x * t) - (b * i)));
	} else if (j <= 1.52e-33) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -8.3e+148:
		tmp = t_1
	elif j <= -2.8e+64:
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c))
	elif j <= -1.56e+50:
		tmp = t_1 - (a * ((x * t) - (b * i)))
	elif j <= 1.52e-33:
		tmp = t_2 + (b * ((a * i) - (z * c)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -8.3e+148)
		tmp = t_1;
	elseif (j <= -2.8e+64)
		tmp = Float64(z * Float64(Float64(x * Float64(y - Float64(a * Float64(t / z)))) - Float64(b * c)));
	elseif (j <= -1.56e+50)
		tmp = Float64(t_1 - Float64(a * Float64(Float64(x * t) - Float64(b * i))));
	elseif (j <= 1.52e-33)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -8.3e+148)
		tmp = t_1;
	elseif (j <= -2.8e+64)
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c));
	elseif (j <= -1.56e+50)
		tmp = t_1 - (a * ((x * t) - (b * i)));
	elseif (j <= 1.52e-33)
		tmp = t_2 + (b * ((a * i) - (z * c)));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.3e+148], t$95$1, If[LessEqual[j, -2.8e+64], N[(z * N[(N[(x * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.56e+50], N[(t$95$1 - N[(a * N[(N[(x * t), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.52e-33], N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.3000000000000003e148

   1. Initial program 67.4%

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

   3. Taylor expanded in j around inf 80.1%

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

   if -8.3000000000000003e148 < j < -2.80000000000000024e64

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 47.1%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

      3. associate-/l* 71.0%

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

   8. Simplified 71.0%

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

   if -2.80000000000000024e64 < j < -1.56e50

   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. Add Preprocessing

   3. Taylor expanded in z around inf 34.6%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in z around 0 99.5%

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

   if -1.56e50 < j < 1.52e-33

   1. Initial program 78.4%

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

   3. Taylor expanded in j around 0 77.6%

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

      1. *-commutative 77.6%

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

      2. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   if 1.52e-33 < j

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 79.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.3 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{elif}\;j \leq -1.56 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.52 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))))
   (if (<= i -3e+144)
     t_2
     (if (<= i -2.3e-43)
       t_1
       (if (<= i -2.3e-118)
         (* (* b c) (- z))
         (if (<= i -2.85e-273)
           (* a (* t (- x)))
           (if (<= i 2.15e-272) (* y (* x z)) (if (<= i 3e+22) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -3e+144) {
		tmp = t_2;
	} else if (i <= -2.3e-43) {
		tmp = t_1;
	} else if (i <= -2.3e-118) {
		tmp = (b * c) * -z;
	} else if (i <= -2.85e-273) {
		tmp = a * (t * -x);
	} else if (i <= 2.15e-272) {
		tmp = y * (x * z);
	} else if (i <= 3e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = a * (b * i)
    if (i <= (-3d+144)) then
        tmp = t_2
    else if (i <= (-2.3d-43)) then
        tmp = t_1
    else if (i <= (-2.3d-118)) then
        tmp = (b * c) * -z
    else if (i <= (-2.85d-273)) then
        tmp = a * (t * -x)
    else if (i <= 2.15d-272) then
        tmp = y * (x * z)
    else if (i <= 3d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -3e+144) {
		tmp = t_2;
	} else if (i <= -2.3e-43) {
		tmp = t_1;
	} else if (i <= -2.3e-118) {
		tmp = (b * c) * -z;
	} else if (i <= -2.85e-273) {
		tmp = a * (t * -x);
	} else if (i <= 2.15e-272) {
		tmp = y * (x * z);
	} else if (i <= 3e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -3e+144:
		tmp = t_2
	elif i <= -2.3e-43:
		tmp = t_1
	elif i <= -2.3e-118:
		tmp = (b * c) * -z
	elif i <= -2.85e-273:
		tmp = a * (t * -x)
	elif i <= 2.15e-272:
		tmp = y * (x * z)
	elif i <= 3e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -3e+144)
		tmp = t_2;
	elseif (i <= -2.3e-43)
		tmp = t_1;
	elseif (i <= -2.3e-118)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (i <= -2.85e-273)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 2.15e-272)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 3e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -3e+144)
		tmp = t_2;
	elseif (i <= -2.3e-43)
		tmp = t_1;
	elseif (i <= -2.3e-118)
		tmp = (b * c) * -z;
	elseif (i <= -2.85e-273)
		tmp = a * (t * -x);
	elseif (i <= 2.15e-272)
		tmp = y * (x * z);
	elseif (i <= 3e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3e+144], t$95$2, If[LessEqual[i, -2.3e-43], t$95$1, If[LessEqual[i, -2.3e-118], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[i, -2.85e-273], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e-272], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e+22], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.9999999999999999e144 or 3e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -2.9999999999999999e144 < i < -2.2999999999999999e-43 or 2.1499999999999999e-272 < i < 3e22

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf 65.0%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around inf 43.4%

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

      1. associate-*r* 40.4%

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

      2. +-commutative 40.4%

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

      3. mul-1-neg 40.4%

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

      4. unsub-neg 40.4%

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

      5. div-sub 41.5%

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

      6. *-commutative 41.5%

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

   8. Simplified 41.5%

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

   9. Taylor expanded in j around inf 34.6%

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

   if -2.2999999999999999e-43 < i < -2.30000000000000021e-118

   1. Initial program 61.0%

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

   3. Taylor expanded in b around inf 35.3%

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

      1. *-commutative 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in c around inf 35.1%

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

   7. Taylor expanded in c around inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. associate-*r* 54.2%

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

   9. Simplified 54.2%

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

   if -2.30000000000000021e-118 < i < -2.84999999999999986e-273

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-rgt-neg-in 49.6%

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

      3. distribute-rgt-neg-in 49.6%

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

   8. Simplified 49.6%

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

   if -2.84999999999999986e-273 < i < 2.1499999999999999e-272

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-*r* 53.7%

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

   8. Simplified 53.7%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+144}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.6 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-124}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))))
   (if (<= i -1.6e+145)
     t_2
     (if (<= i -5.6e-43)
       t_1
       (if (<= i -7.6e-124)
         (* (* b c) (- z))
         (if (<= i -1.1e-237)
           t_1
           (if (<= i 1.95e-272)
             (* y (* x z))
             (if (<= i 1.85e+22) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -1.6e+145) {
		tmp = t_2;
	} else if (i <= -5.6e-43) {
		tmp = t_1;
	} else if (i <= -7.6e-124) {
		tmp = (b * c) * -z;
	} else if (i <= -1.1e-237) {
		tmp = t_1;
	} else if (i <= 1.95e-272) {
		tmp = y * (x * z);
	} else if (i <= 1.85e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = a * (b * i)
    if (i <= (-1.6d+145)) then
        tmp = t_2
    else if (i <= (-5.6d-43)) then
        tmp = t_1
    else if (i <= (-7.6d-124)) then
        tmp = (b * c) * -z
    else if (i <= (-1.1d-237)) then
        tmp = t_1
    else if (i <= 1.95d-272) then
        tmp = y * (x * z)
    else if (i <= 1.85d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -1.6e+145) {
		tmp = t_2;
	} else if (i <= -5.6e-43) {
		tmp = t_1;
	} else if (i <= -7.6e-124) {
		tmp = (b * c) * -z;
	} else if (i <= -1.1e-237) {
		tmp = t_1;
	} else if (i <= 1.95e-272) {
		tmp = y * (x * z);
	} else if (i <= 1.85e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -1.6e+145:
		tmp = t_2
	elif i <= -5.6e-43:
		tmp = t_1
	elif i <= -7.6e-124:
		tmp = (b * c) * -z
	elif i <= -1.1e-237:
		tmp = t_1
	elif i <= 1.95e-272:
		tmp = y * (x * z)
	elif i <= 1.85e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -1.6e+145)
		tmp = t_2;
	elseif (i <= -5.6e-43)
		tmp = t_1;
	elseif (i <= -7.6e-124)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (i <= -1.1e-237)
		tmp = t_1;
	elseif (i <= 1.95e-272)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.85e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -1.6e+145)
		tmp = t_2;
	elseif (i <= -5.6e-43)
		tmp = t_1;
	elseif (i <= -7.6e-124)
		tmp = (b * c) * -z;
	elseif (i <= -1.1e-237)
		tmp = t_1;
	elseif (i <= 1.95e-272)
		tmp = y * (x * z);
	elseif (i <= 1.85e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.6e+145], t$95$2, If[LessEqual[i, -5.6e-43], t$95$1, If[LessEqual[i, -7.6e-124], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[i, -1.1e-237], t$95$1, If[LessEqual[i, 1.95e-272], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.85e+22], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.60000000000000004e145 or 1.8499999999999999e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -1.60000000000000004e145 < i < -5.5999999999999996e-43 or -7.60000000000000025e-124 < i < -1.09999999999999999e-237 or 1.9499999999999999e-272 < i < 1.8499999999999999e22

   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. Add Preprocessing

   3. Taylor expanded in z around inf 68.6%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around inf 50.9%

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

      1. associate-*r* 48.6%

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

      2. +-commutative 48.6%

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

      3. mul-1-neg 48.6%

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

      4. unsub-neg 48.6%

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

      5. div-sub 50.3%

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

      6. *-commutative 50.3%

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

   8. Simplified 50.3%

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

   9. Taylor expanded in j around inf 38.3%

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

   if -5.5999999999999996e-43 < i < -7.60000000000000025e-124

   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. Add Preprocessing

   3. Taylor expanded in b around inf 37.1%

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

      1. *-commutative 37.1%

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

   5. Simplified 37.1%

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

   6. Taylor expanded in c around inf 37.0%

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

   7. Taylor expanded in c around inf 37.0%

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

      1. mul-1-neg 37.0%

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

      2. associate-*r* 53.9%

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

   9. Simplified 53.9%

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

   if -1.09999999999999999e-237 < i < 1.9499999999999999e-272

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

      2. associate-*r* 47.5%

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

   8. Simplified 47.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.6 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-124}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-237}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -5 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))))
   (if (<= i -5e+145)
     t_2
     (if (<= i -1e-70)
       t_1
       (if (<= i -3.1e-124)
         (* x (* y z))
         (if (<= i -8.8e-240)
           t_1
           (if (<= i 1.3e-274) (* y (* x z)) (if (<= i 2.3e+22) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -5e+145) {
		tmp = t_2;
	} else if (i <= -1e-70) {
		tmp = t_1;
	} else if (i <= -3.1e-124) {
		tmp = x * (y * z);
	} else if (i <= -8.8e-240) {
		tmp = t_1;
	} else if (i <= 1.3e-274) {
		tmp = y * (x * z);
	} else if (i <= 2.3e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = a * (b * i)
    if (i <= (-5d+145)) then
        tmp = t_2
    else if (i <= (-1d-70)) then
        tmp = t_1
    else if (i <= (-3.1d-124)) then
        tmp = x * (y * z)
    else if (i <= (-8.8d-240)) then
        tmp = t_1
    else if (i <= 1.3d-274) then
        tmp = y * (x * z)
    else if (i <= 2.3d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -5e+145) {
		tmp = t_2;
	} else if (i <= -1e-70) {
		tmp = t_1;
	} else if (i <= -3.1e-124) {
		tmp = x * (y * z);
	} else if (i <= -8.8e-240) {
		tmp = t_1;
	} else if (i <= 1.3e-274) {
		tmp = y * (x * z);
	} else if (i <= 2.3e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -5e+145:
		tmp = t_2
	elif i <= -1e-70:
		tmp = t_1
	elif i <= -3.1e-124:
		tmp = x * (y * z)
	elif i <= -8.8e-240:
		tmp = t_1
	elif i <= 1.3e-274:
		tmp = y * (x * z)
	elif i <= 2.3e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -5e+145)
		tmp = t_2;
	elseif (i <= -1e-70)
		tmp = t_1;
	elseif (i <= -3.1e-124)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= -8.8e-240)
		tmp = t_1;
	elseif (i <= 1.3e-274)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 2.3e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -5e+145)
		tmp = t_2;
	elseif (i <= -1e-70)
		tmp = t_1;
	elseif (i <= -3.1e-124)
		tmp = x * (y * z);
	elseif (i <= -8.8e-240)
		tmp = t_1;
	elseif (i <= 1.3e-274)
		tmp = y * (x * z);
	elseif (i <= 2.3e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5e+145], t$95$2, If[LessEqual[i, -1e-70], t$95$1, If[LessEqual[i, -3.1e-124], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.8e-240], t$95$1, If[LessEqual[i, 1.3e-274], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e+22], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.99999999999999967e145 or 2.3000000000000002e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -4.99999999999999967e145 < i < -9.99999999999999996e-71 or -3.0999999999999998e-124 < i < -8.7999999999999997e-240 or 1.3e-274 < i < 2.3000000000000002e22

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf 69.0%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in t around inf 49.9%

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

      1. associate-*r* 47.7%

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

      2. +-commutative 47.7%

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

      3. mul-1-neg 47.7%

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

      4. unsub-neg 47.7%

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

      5. div-sub 49.3%

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

      6. *-commutative 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in j around inf 38.4%

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

   if -9.99999999999999996e-71 < i < -3.0999999999999998e-124

   1. Initial program 67.9%

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

   3. Taylor expanded in x around inf 51.5%

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

      1. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around inf 39.2%

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

   if -8.7999999999999997e-240 < i < 1.3e-274

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

      2. associate-*r* 47.5%

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

   8. Simplified 47.5%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -3 \cdot 10^{+144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* x (* y z))) (t_3 (* a (* b i))))
   (if (<= i -3e+144)
     t_3
     (if (<= i -1.5e-68)
       t_1
       (if (<= i -1e-124)
         t_2
         (if (<= i -2.8e-239)
           t_1
           (if (<= i 1.3e-274) t_2 (if (<= i 3e+22) 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);
	double t_2 = x * (y * z);
	double t_3 = a * (b * i);
	double tmp;
	if (i <= -3e+144) {
		tmp = t_3;
	} else if (i <= -1.5e-68) {
		tmp = t_1;
	} else if (i <= -1e-124) {
		tmp = t_2;
	} else if (i <= -2.8e-239) {
		tmp = t_1;
	} else if (i <= 1.3e-274) {
		tmp = t_2;
	} else if (i <= 3e+22) {
		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)
    t_2 = x * (y * z)
    t_3 = a * (b * i)
    if (i <= (-3d+144)) then
        tmp = t_3
    else if (i <= (-1.5d-68)) then
        tmp = t_1
    else if (i <= (-1d-124)) then
        tmp = t_2
    else if (i <= (-2.8d-239)) then
        tmp = t_1
    else if (i <= 1.3d-274) then
        tmp = t_2
    else if (i <= 3d+22) 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);
	double t_2 = x * (y * z);
	double t_3 = a * (b * i);
	double tmp;
	if (i <= -3e+144) {
		tmp = t_3;
	} else if (i <= -1.5e-68) {
		tmp = t_1;
	} else if (i <= -1e-124) {
		tmp = t_2;
	} else if (i <= -2.8e-239) {
		tmp = t_1;
	} else if (i <= 1.3e-274) {
		tmp = t_2;
	} else if (i <= 3e+22) {
		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)
	t_2 = x * (y * z)
	t_3 = a * (b * i)
	tmp = 0
	if i <= -3e+144:
		tmp = t_3
	elif i <= -1.5e-68:
		tmp = t_1
	elif i <= -1e-124:
		tmp = t_2
	elif i <= -2.8e-239:
		tmp = t_1
	elif i <= 1.3e-274:
		tmp = t_2
	elif i <= 3e+22:
		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(t * j))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -3e+144)
		tmp = t_3;
	elseif (i <= -1.5e-68)
		tmp = t_1;
	elseif (i <= -1e-124)
		tmp = t_2;
	elseif (i <= -2.8e-239)
		tmp = t_1;
	elseif (i <= 1.3e-274)
		tmp = t_2;
	elseif (i <= 3e+22)
		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);
	t_2 = x * (y * z);
	t_3 = a * (b * i);
	tmp = 0.0;
	if (i <= -3e+144)
		tmp = t_3;
	elseif (i <= -1.5e-68)
		tmp = t_1;
	elseif (i <= -1e-124)
		tmp = t_2;
	elseif (i <= -2.8e-239)
		tmp = t_1;
	elseif (i <= 1.3e-274)
		tmp = t_2;
	elseif (i <= 3e+22)
		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[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3e+144], t$95$3, If[LessEqual[i, -1.5e-68], t$95$1, If[LessEqual[i, -1e-124], t$95$2, If[LessEqual[i, -2.8e-239], t$95$1, If[LessEqual[i, 1.3e-274], t$95$2, If[LessEqual[i, 3e+22], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.9999999999999999e144 or 3e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -2.9999999999999999e144 < i < -1.5e-68 or -9.99999999999999933e-125 < i < -2.80000000000000013e-239 or 1.3e-274 < i < 3e22

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf 69.0%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in t around inf 49.9%

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

      1. associate-*r* 47.7%

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

      2. +-commutative 47.7%

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

      3. mul-1-neg 47.7%

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

      4. unsub-neg 47.7%

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

      5. div-sub 49.3%

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

      6. *-commutative 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in j around inf 38.4%

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

   if -1.5e-68 < i < -9.99999999999999933e-125 or -2.80000000000000013e-239 < i < 1.3e-274

   1. Initial program 77.9%

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

   3. Taylor expanded in x around inf 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in y around inf 42.7%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+144}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-68}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+22}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -1.75e+196)
     t_1
     (if (<= a -1.5e+90)
       (* x (- (* y z) (* t a)))
       (if (<= a -1.1e+14)
         t_1
         (if (<= a 8.6e-79)
           (* j (- (* t c) (* y i)))
           (if (<= a 5.8e+30) (* 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 <= -1.75e+196) {
		tmp = t_1;
	} else if (a <= -1.5e+90) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1.1e+14) {
		tmp = t_1;
	} else if (a <= 8.6e-79) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5.8e+30) {
		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 <= (-1.75d+196)) then
        tmp = t_1
    else if (a <= (-1.5d+90)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-1.1d+14)) then
        tmp = t_1
    else if (a <= 8.6d-79) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 5.8d+30) 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 <= -1.75e+196) {
		tmp = t_1;
	} else if (a <= -1.5e+90) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1.1e+14) {
		tmp = t_1;
	} else if (a <= 8.6e-79) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5.8e+30) {
		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 <= -1.75e+196:
		tmp = t_1
	elif a <= -1.5e+90:
		tmp = x * ((y * z) - (t * a))
	elif a <= -1.1e+14:
		tmp = t_1
	elif a <= 8.6e-79:
		tmp = j * ((t * c) - (y * i))
	elif a <= 5.8e+30:
		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 <= -1.75e+196)
		tmp = t_1;
	elseif (a <= -1.5e+90)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -1.1e+14)
		tmp = t_1;
	elseif (a <= 8.6e-79)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 5.8e+30)
		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 <= -1.75e+196)
		tmp = t_1;
	elseif (a <= -1.5e+90)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -1.1e+14)
		tmp = t_1;
	elseif (a <= 8.6e-79)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 5.8e+30)
		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, -1.75e+196], t$95$1, If[LessEqual[a, -1.5e+90], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e+14], t$95$1, If[LessEqual[a, 8.6e-79], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+30], 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 < -1.7499999999999999e196 or -1.49999999999999989e90 < a < -1.1e14 or 5.7999999999999996e30 < a

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 58.9%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in a around -inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   8. Simplified 67.8%

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

   if -1.7499999999999999e196 < a < -1.49999999999999989e90

   1. Initial program 75.1%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -1.1e14 < a < 8.59999999999999963e-79

   1. Initial program 78.9%

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

   3. Taylor expanded in j around inf 54.5%

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

   if 8.59999999999999963e-79 < a < 5.7999999999999996e30

   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. Add Preprocessing

   3. Taylor expanded in c around inf 62.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -7.5e+129)
     t_1
     (if (<= a -3.8e+90)
       (* y (* x z))
       (if (<= a -1.75e+14)
         t_1
         (if (<= a 1.35e-83)
           (* j (- (* t c) (* y i)))
           (if (<= a 1.25e+28) (* 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 <= -7.5e+129) {
		tmp = t_1;
	} else if (a <= -3.8e+90) {
		tmp = y * (x * z);
	} else if (a <= -1.75e+14) {
		tmp = t_1;
	} else if (a <= 1.35e-83) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 1.25e+28) {
		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 <= (-7.5d+129)) then
        tmp = t_1
    else if (a <= (-3.8d+90)) then
        tmp = y * (x * z)
    else if (a <= (-1.75d+14)) then
        tmp = t_1
    else if (a <= 1.35d-83) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 1.25d+28) 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 <= -7.5e+129) {
		tmp = t_1;
	} else if (a <= -3.8e+90) {
		tmp = y * (x * z);
	} else if (a <= -1.75e+14) {
		tmp = t_1;
	} else if (a <= 1.35e-83) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 1.25e+28) {
		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 <= -7.5e+129:
		tmp = t_1
	elif a <= -3.8e+90:
		tmp = y * (x * z)
	elif a <= -1.75e+14:
		tmp = t_1
	elif a <= 1.35e-83:
		tmp = j * ((t * c) - (y * i))
	elif a <= 1.25e+28:
		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 <= -7.5e+129)
		tmp = t_1;
	elseif (a <= -3.8e+90)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -1.75e+14)
		tmp = t_1;
	elseif (a <= 1.35e-83)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 1.25e+28)
		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 <= -7.5e+129)
		tmp = t_1;
	elseif (a <= -3.8e+90)
		tmp = y * (x * z);
	elseif (a <= -1.75e+14)
		tmp = t_1;
	elseif (a <= 1.35e-83)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 1.25e+28)
		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, -7.5e+129], t$95$1, If[LessEqual[a, -3.8e+90], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.75e+14], t$95$1, If[LessEqual[a, 1.35e-83], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+28], 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 < -7.4999999999999998e129 or -3.8000000000000001e90 < a < -1.75e14 or 1.24999999999999989e28 < a

   1. Initial program 68.9%

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

   3. Taylor expanded in z around inf 59.4%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in a around -inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

   8. Simplified 66.0%

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

   if -7.4999999999999998e129 < a < -3.8000000000000001e90

   1. Initial program 63.4%

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

   3. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 76.2%

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

   8. Simplified 76.2%

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

   if -1.75e14 < a < 1.34999999999999996e-83

   1. Initial program 78.9%

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

   3. Taylor expanded in j around inf 54.5%

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

   if 1.34999999999999996e-83 < a < 1.24999999999999989e28

   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. Add Preprocessing

   3. Taylor expanded in c around inf 62.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.46 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -4.5e-45)
     t_2
     (if (<= c -1.46e-301)
       t_1
       (if (<= c 4.2e-295) (* x (* y z)) (if (<= c 3e-23) 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.5e-45) {
		tmp = t_2;
	} else if (c <= -1.46e-301) {
		tmp = t_1;
	} else if (c <= 4.2e-295) {
		tmp = x * (y * z);
	} else if (c <= 3e-23) {
		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 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-4.5d-45)) then
        tmp = t_2
    else if (c <= (-1.46d-301)) then
        tmp = t_1
    else if (c <= 4.2d-295) then
        tmp = x * (y * z)
    else if (c <= 3d-23) 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.5e-45) {
		tmp = t_2;
	} else if (c <= -1.46e-301) {
		tmp = t_1;
	} else if (c <= 4.2e-295) {
		tmp = x * (y * z);
	} else if (c <= 3e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.5e-45:
		tmp = t_2
	elif c <= -1.46e-301:
		tmp = t_1
	elif c <= 4.2e-295:
		tmp = x * (y * z)
	elif c <= 3e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.5e-45)
		tmp = t_2;
	elseif (c <= -1.46e-301)
		tmp = t_1;
	elseif (c <= 4.2e-295)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 3e-23)
		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 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.5e-45)
		tmp = t_2;
	elseif (c <= -1.46e-301)
		tmp = t_1;
	elseif (c <= 4.2e-295)
		tmp = x * (y * z);
	elseif (c <= 3e-23)
		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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e-45], t$95$2, If[LessEqual[c, -1.46e-301], t$95$1, If[LessEqual[c, 4.2e-295], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e-23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.4999999999999999e-45 or 3.00000000000000003e-23 < c

   1. Initial program 62.4%

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

   3. Taylor expanded in c around inf 61.4%

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

   if -4.4999999999999999e-45 < c < -1.46000000000000002e-301 or 4.19999999999999986e-295 < c < 3.00000000000000003e-23

   1. Initial program 85.1%

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

   3. Taylor expanded in z around inf 69.3%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in a around -inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

   8. Simplified 54.1%

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

   if -1.46000000000000002e-301 < c < 4.19999999999999986e-295

   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. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 78.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.46 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+102} \lor \neg \left(z \leq 2.75 \cdot 10^{+63}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -9.5e+102) (not (<= z 2.75e+63)))
   (* z (- (* x (- y (* a (/ t z)))) (* b c)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y 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 ((z <= -9.5e+102) || !(z <= 2.75e+63)) {
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 ((z <= (-9.5d+102)) .or. (.not. (z <= 2.75d+63))) then
        tmp = z * ((x * (y - (a * (t / z)))) - (b * c))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 ((z <= -9.5e+102) || !(z <= 2.75e+63)) {
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -9.5e+102) or not (z <= 2.75e+63):
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -9.5e+102) || !(z <= 2.75e+63))
		tmp = Float64(z * Float64(Float64(x * Float64(y - Float64(a * Float64(t / z)))) - Float64(b * c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -9.5e+102) || ~((z <= 2.75e+63)))
		tmp = z * ((x * (y - (a * (t / z)))) - (b * c));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -9.5e+102], N[Not[LessEqual[z, 2.75e+63]], $MachinePrecision]], N[(z * N[(N[(x * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999992e102 or 2.75000000000000002e63 < z

   1. Initial program 59.0%

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

   3. Taylor expanded in z around inf 68.4%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

      3. associate-/l* 68.9%

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

   8. Simplified 68.9%

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

   if -9.4999999999999992e102 < z < 2.75000000000000002e63

   1. Initial program 83.2%

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

   3. Taylor expanded in b around 0 72.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+102} \lor \neg \left(z \leq 2.75 \cdot 10^{+63}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y - a \cdot \frac{t}{z}\right) - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-33}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -1.7e+149)
     t_2
     (if (<= j 2.25e-33) (+ t_1 (* b (- (* a i) (* z c)))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+149) {
		tmp = t_2;
	} else if (j <= 2.25e-33) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-1.7d+149)) then
        tmp = t_2
    else if (j <= 2.25d-33) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+149) {
		tmp = t_2;
	} else if (j <= 2.25e-33) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.7e+149:
		tmp = t_2
	elif j <= 2.25e-33:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.7e+149)
		tmp = t_2;
	elseif (j <= 2.25e-33)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e+149)
		tmp = t_2;
	elseif (j <= 2.25e-33)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+149], t$95$2, If[LessEqual[j, 2.25e-33], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.6999999999999999e149

   1. Initial program 67.4%

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

   3. Taylor expanded in j around inf 80.1%

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

   if -1.6999999999999999e149 < j < 2.24999999999999995e-33

   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. Add Preprocessing

   3. Taylor expanded in j around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if 2.24999999999999995e-33 < j

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 79.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+145} \lor \neg \left(i \leq 2.8 \cdot 10^{+22}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -4e+145) (not (<= i 2.8e+22))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4e+145) || !(i <= 2.8e+22)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-4d+145)) .or. (.not. (i <= 2.8d+22))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4e+145) || !(i <= 2.8e+22)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -4e+145) or not (i <= 2.8e+22):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -4e+145) || !(i <= 2.8e+22))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -4e+145) || ~((i <= 2.8e+22)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -4e+145], N[Not[LessEqual[i, 2.8e+22]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4e145 or 2.8e22 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in i around inf 42.9%

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

   7. Taylor expanded in b around 0 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if -4e145 < i < 2.8e22

   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. Add Preprocessing

   3. Taylor expanded in z around inf 68.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around inf 44.2%

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

      1. associate-*r* 43.1%

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

      2. +-commutative 43.1%

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

      3. mul-1-neg 43.1%

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

      4. unsub-neg 43.1%

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

      5. div-sub 45.0%

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

      6. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   9. Taylor expanded in j around inf 31.2%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+145} \lor \neg \left(i \leq 2.8 \cdot 10^{+22}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.9% 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 73.6%

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

3. Taylor expanded in b around inf 33.1%

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

   1. *-commutative 33.1%

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

5. Simplified 33.1%

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

6. Taylor expanded in i around inf 21.1%

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

7. Taylor expanded in b around 0 22.4%

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

   1. *-commutative 22.4%

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

9. Simplified 22.4%

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

10. Final simplification 22.4%

    \[\leadsto a \cdot \left(b \cdot i\right) \]
11. Add Preprocessing

Developer target: 68.7% 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 2024086 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))