Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.0% → 80.9%

Time: 19.8s

Alternatives: 26

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j + \left(\frac{y \cdot \left(x \cdot z - i \cdot j\right) + t\_1}{t} - x \cdot a\right)\right)\\ t_3 := \left(t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{+305}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2
         (* t (+ (* c j) (- (/ (+ (* y (- (* x z) (* i j))) t_1) t) (* x a)))))
        (t_3 (+ (- t_1 (* x (- (* t a) (* y z)))) (* j (- (* t c) (* y i))))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 1e+305)
       t_3
       (if (<= t_3 INFINITY) t_2 (* y (* x (- z (* i (/ j x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) + ((((y * ((x * z) - (i * j))) + t_1) / t) - (x * a)));
	double t_3 = (t_1 - (x * ((t * a) - (y * z)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= 1e+305) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) + ((((y * ((x * z) - (i * j))) + t_1) / t) - (x * a)));
	double t_3 = (t_1 - (x * ((t * a) - (y * z)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= 1e+305) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) + ((((y * ((x * z) - (i * j))) + t_1) / t) - (x * a)))
	t_3 = (t_1 - (x * ((t * a) - (y * z)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= 1e+305:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = y * (x * (z - (i * (j / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) + Float64(Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1) / t) - Float64(x * a))))
	t_3 = Float64(Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= 1e+305)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) + ((((y * ((x * z) - (i * j))) + t_1) / t) - (x * a)));
	t_3 = (t_1 - (x * ((t * a) - (y * z)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= 1e+305)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = y * (x * (z - (i * (j / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] + N[(N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / t), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, 1e+305], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 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 or 9.9999999999999994e304 < (+.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 83.5%

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

   3. Taylor expanded in t around -inf 88.6%

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

   5. Simplified 90.7%

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 9.9999999999999994e304

   1. Initial program 99.6%

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

   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 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in x around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. unsub-neg 59.6%

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

      3. associate-/l* 59.5%

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

   8. Simplified 59.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq -\infty:\\ \;\;\;\;t \cdot \left(c \cdot j + \left(\frac{y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)}{t} - x \cdot a\right)\right)\\ \mathbf{elif}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq 10^{+305}:\\ \;\;\;\;\left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;t \cdot \left(c \cdot j + \left(\frac{y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)}{t} - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.9%

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

   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 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in x around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. unsub-neg 59.6%

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

      3. associate-/l* 59.5%

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

   8. Simplified 59.5%

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

4. Final simplification 84.1%

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

Alternative 3: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(c \cdot j + \left(a \cdot \frac{b \cdot i}{t} - x \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= z -4e+178)
     (* x (- (* y z) (* t a)))
     (if (<= z -1.15e-30)
       (+ (* t (* c j)) (* b (- (* a i) (* z c))))
       (if (<= z -1.9e-115)
         t_1
         (if (<= z -1.85e-229)
           (* i (- (* a b) (* y j)))
           (if (<= z 2.8e-236)
             (* t (+ (* c j) (- (* a (/ (* b i) t)) (* x a))))
             (if (<= z 1.75e-130)
               t_1
               (if (<= z 6e+106)
                 (- (* t (- (* c j) (* x a))) (* b (* z c)))
                 (* z (- (* x y) (* b c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (z <= -4e+178) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -1.15e-30) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else if (z <= -1.9e-115) {
		tmp = t_1;
	} else if (z <= -1.85e-229) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.8e-236) {
		tmp = t * ((c * j) + ((a * ((b * i) / t)) - (x * a)));
	} else if (z <= 1.75e-130) {
		tmp = t_1;
	} else if (z <= 6e+106) {
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (z <= (-4d+178)) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= (-1.15d-30)) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else if (z <= (-1.9d-115)) then
        tmp = t_1
    else if (z <= (-1.85d-229)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 2.8d-236) then
        tmp = t * ((c * j) + ((a * ((b * i) / t)) - (x * a)))
    else if (z <= 1.75d-130) then
        tmp = t_1
    else if (z <= 6d+106) then
        tmp = (t * ((c * j) - (x * a))) - (b * (z * c))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (z <= -4e+178) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -1.15e-30) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else if (z <= -1.9e-115) {
		tmp = t_1;
	} else if (z <= -1.85e-229) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.8e-236) {
		tmp = t * ((c * j) + ((a * ((b * i) / t)) - (x * a)));
	} else if (z <= 1.75e-130) {
		tmp = t_1;
	} else if (z <= 6e+106) {
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if z <= -4e+178:
		tmp = x * ((y * z) - (t * a))
	elif z <= -1.15e-30:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	elif z <= -1.9e-115:
		tmp = t_1
	elif z <= -1.85e-229:
		tmp = i * ((a * b) - (y * j))
	elif z <= 2.8e-236:
		tmp = t * ((c * j) + ((a * ((b * i) / t)) - (x * a)))
	elif z <= 1.75e-130:
		tmp = t_1
	elif z <= 6e+106:
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c))
	else:
		tmp = z * ((x * y) - (b * c))
	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 (z <= -4e+178)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= -1.15e-30)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (z <= -1.9e-115)
		tmp = t_1;
	elseif (z <= -1.85e-229)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 2.8e-236)
		tmp = Float64(t * Float64(Float64(c * j) + Float64(Float64(a * Float64(Float64(b * i) / t)) - Float64(x * a))));
	elseif (z <= 1.75e-130)
		tmp = t_1;
	elseif (z <= 6e+106)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	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 (z <= -4e+178)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= -1.15e-30)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	elseif (z <= -1.9e-115)
		tmp = t_1;
	elseif (z <= -1.85e-229)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 2.8e-236)
		tmp = t * ((c * j) + ((a * ((b * i) / t)) - (x * a)));
	elseif (z <= 1.75e-130)
		tmp = t_1;
	elseif (z <= 6e+106)
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	else
		tmp = z * ((x * y) - (b * c));
	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[z, -4e+178], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-30], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-115], t$95$1, If[LessEqual[z, -1.85e-229], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-236], N[(t * N[(N[(c * j), $MachinePrecision] + N[(N[(a * N[(N[(b * i), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-130], t$95$1, If[LessEqual[z, 6e+106], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -4.0000000000000002e178

   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. Step-by-step derivation

      1. +-commutative 66.9%

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

      2. fma-define 66.9%

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

      3. *-commutative 66.9%

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

      4. *-commutative 66.9%

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

      5. cancel-sign-sub-inv 66.9%

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

      6. cancel-sign-sub 66.9%

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

      7. sub-neg 66.9%

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

      8. sub-neg 66.9%

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

      9. *-commutative 66.9%

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

      10. fma-neg 66.9%

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

      11. *-commutative 66.9%

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

      12. distribute-rgt-neg-out 66.9%

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

      13. remove-double-neg 66.9%

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

      14. *-commutative 66.9%

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

      15. *-commutative 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in x around inf 81.8%

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

   if -4.0000000000000002e178 < z < -1.14999999999999992e-30

   1. Initial program 71.4%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-*l* 75.7%

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

      6. mul-1-neg 75.7%

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

      7. associate-*r* 71.6%

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

      8. *-commutative 71.6%

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

      9. associate-*l* 75.8%

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

      10. distribute-rgt-neg-in 75.8%

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

      11. mul-1-neg 75.8%

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

      12. distribute-lft-in 75.8%

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

      13. mul-1-neg 75.8%

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

      14. unsub-neg 75.8%

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

      15. *-commutative 75.8%

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

      16. *-commutative 75.8%

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

      17. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in j around inf 82.1%

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

      1. associate-*r* 82.0%

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

      2. *-commutative 82.0%

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

      3. *-commutative 82.0%

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

      4. *-commutative 82.0%

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

   8. Simplified 82.0%

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

   if -1.14999999999999992e-30 < z < -1.89999999999999996e-115 or 2.79999999999999986e-236 < z < 1.75e-130

   1. Initial program 77.6%

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

   3. Taylor expanded in y around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 61.9%

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

      4. *-commutative 61.9%

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

      5. associate-*l* 61.0%

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

      6. mul-1-neg 61.0%

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

      7. associate-*r* 53.8%

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

      8. *-commutative 53.8%

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

      9. associate-*l* 53.8%

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

      10. distribute-rgt-neg-in 53.8%

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

      11. mul-1-neg 53.8%

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

      12. distribute-lft-in 56.3%

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

      13. mul-1-neg 56.3%

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

      14. unsub-neg 56.3%

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

      15. *-commutative 56.3%

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

      16. *-commutative 56.3%

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

      17. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in c around 0 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. mul-1-neg 59.8%

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

      5. distribute-rgt-neg-in 59.8%

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

      6. mul-1-neg 59.8%

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

      7. distribute-lft-in 62.3%

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

      8. +-commutative 62.3%

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

      9. mul-1-neg 62.3%

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

      10. unsub-neg 62.3%

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

   8. Simplified 62.3%

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

   if -1.89999999999999996e-115 < z < -1.8499999999999999e-229

   1. Initial program 82.3%

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

   3. Taylor expanded in i around inf 77.8%

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

      1. distribute-lft-out-- 77.8%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   if -1.8499999999999999e-229 < z < 2.79999999999999986e-236

   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 t around -inf 81.1%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in a around inf 77.9%

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

      1. associate-/l* 77.9%

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

   8. Simplified 77.9%

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

   if 1.75e-130 < z < 6.0000000000000001e106

   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 0 63.8%

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

      1. +-commutative 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

      5. associate-*l* 63.9%

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

      6. mul-1-neg 63.9%

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

      7. associate-*r* 66.0%

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

      8. *-commutative 66.0%

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

      9. associate-*l* 68.0%

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

      10. distribute-rgt-neg-in 68.0%

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

      11. mul-1-neg 68.0%

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

      12. distribute-lft-in 70.1%

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

      13. mul-1-neg 70.1%

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

      14. unsub-neg 70.1%

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

      15. *-commutative 70.1%

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

      16. *-commutative 70.1%

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

      17. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in z around inf 66.1%

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

   if 6.0000000000000001e106 < z

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(c \cdot j + \left(a \cdot \frac{b \cdot i}{t} - x \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-48}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -4.3e-48)
     t_3
     (if (<= y -1.18e-206)
       t_2
       (if (<= y -5.6e-272)
         t_1
         (if (<= y -6.5e-304)
           t_2
           (if (<= y 8.5e-279)
             t_1
             (if (<= y 3.3e-220) t_2 (if (<= y 1.6e+64) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.3e-48) {
		tmp = t_3;
	} else if (y <= -1.18e-206) {
		tmp = t_2;
	} else if (y <= -5.6e-272) {
		tmp = t_1;
	} else if (y <= -6.5e-304) {
		tmp = t_2;
	} else if (y <= 8.5e-279) {
		tmp = t_1;
	} else if (y <= 3.3e-220) {
		tmp = t_2;
	} else if (y <= 1.6e+64) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-4.3d-48)) then
        tmp = t_3
    else if (y <= (-1.18d-206)) then
        tmp = t_2
    else if (y <= (-5.6d-272)) then
        tmp = t_1
    else if (y <= (-6.5d-304)) then
        tmp = t_2
    else if (y <= 8.5d-279) then
        tmp = t_1
    else if (y <= 3.3d-220) then
        tmp = t_2
    else if (y <= 1.6d+64) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.3e-48) {
		tmp = t_3;
	} else if (y <= -1.18e-206) {
		tmp = t_2;
	} else if (y <= -5.6e-272) {
		tmp = t_1;
	} else if (y <= -6.5e-304) {
		tmp = t_2;
	} else if (y <= 8.5e-279) {
		tmp = t_1;
	} else if (y <= 3.3e-220) {
		tmp = t_2;
	} else if (y <= 1.6e+64) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.3e-48:
		tmp = t_3
	elif y <= -1.18e-206:
		tmp = t_2
	elif y <= -5.6e-272:
		tmp = t_1
	elif y <= -6.5e-304:
		tmp = t_2
	elif y <= 8.5e-279:
		tmp = t_1
	elif y <= 3.3e-220:
		tmp = t_2
	elif y <= 1.6e+64:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.3e-48)
		tmp = t_3;
	elseif (y <= -1.18e-206)
		tmp = t_2;
	elseif (y <= -5.6e-272)
		tmp = t_1;
	elseif (y <= -6.5e-304)
		tmp = t_2;
	elseif (y <= 8.5e-279)
		tmp = t_1;
	elseif (y <= 3.3e-220)
		tmp = t_2;
	elseif (y <= 1.6e+64)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.3e-48)
		tmp = t_3;
	elseif (y <= -1.18e-206)
		tmp = t_2;
	elseif (y <= -5.6e-272)
		tmp = t_1;
	elseif (y <= -6.5e-304)
		tmp = t_2;
	elseif (y <= 8.5e-279)
		tmp = t_1;
	elseif (y <= 3.3e-220)
		tmp = t_2;
	elseif (y <= 1.6e+64)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-48], t$95$3, If[LessEqual[y, -1.18e-206], t$95$2, If[LessEqual[y, -5.6e-272], t$95$1, If[LessEqual[y, -6.5e-304], t$95$2, If[LessEqual[y, 8.5e-279], t$95$1, If[LessEqual[y, 3.3e-220], t$95$2, If[LessEqual[y, 1.6e+64], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3e-48 or 1.60000000000000009e64 < y

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   5. Simplified 71.1%

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

   if -4.3e-48 < y < -1.17999999999999994e-206 or -5.59999999999999987e-272 < y < -6.50000000000000011e-304 or 8.5000000000000002e-279 < y < 3.29999999999999999e-220

   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 c around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -1.17999999999999994e-206 < y < -5.59999999999999987e-272 or -6.50000000000000011e-304 < y < 8.5000000000000002e-279 or 3.29999999999999999e-220 < y < 1.60000000000000009e64

   1. Initial program 86.7%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. *-commutative 81.3%

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

      3. associate-*r* 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-*l* 81.2%

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

      6. mul-1-neg 81.2%

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

      7. associate-*r* 76.3%

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

      8. *-commutative 76.3%

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

      9. associate-*l* 79.3%

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

      10. distribute-rgt-neg-in 79.3%

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

      11. mul-1-neg 79.3%

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

      12. distribute-lft-in 81.4%

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

      13. mul-1-neg 81.4%

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

      14. unsub-neg 81.4%

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

      15. *-commutative 81.4%

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

      16. *-commutative 81.4%

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

      17. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in c around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. neg-mul-1 59.4%

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

      3. cancel-sign-sub 59.4%

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

      4. mul-1-neg 59.4%

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

      5. distribute-rgt-neg-in 59.4%

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

      6. mul-1-neg 59.4%

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

      7. distribute-lft-in 59.4%

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

      8. +-commutative 59.4%

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

      9. mul-1-neg 59.4%

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

      10. unsub-neg 59.4%

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

   8. Simplified 59.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-206}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))))
   (if (<= b -2.6e+110)
     (+ (* t (* c j)) (* b (- (* a i) (* z c))))
     (if (<= b -3.4e+34)
       t_1
       (if (<= b -5.3e-17)
         (- (* t (- (* c j) (* x a))) (* b (* z c)))
         (if (<= b -1.7e-70)
           (* y (- (* x z) (* i j)))
           (if (<= b 9.5e-21)
             t_1
             (if (<= b 3.3e+129)
               (* a (- (* b i) (* x t)))
               (* b (* i (- a (* c (/ z i)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (b <= -2.6e+110) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else if (b <= -3.4e+34) {
		tmp = t_1;
	} else if (b <= -5.3e-17) {
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	} else if (b <= -1.7e-70) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 9.5e-21) {
		tmp = t_1;
	} else if (b <= 3.3e+129) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    if (b <= (-2.6d+110)) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else if (b <= (-3.4d+34)) then
        tmp = t_1
    else if (b <= (-5.3d-17)) then
        tmp = (t * ((c * j) - (x * a))) - (b * (z * c))
    else if (b <= (-1.7d-70)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 9.5d-21) then
        tmp = t_1
    else if (b <= 3.3d+129) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = b * (i * (a - (c * (z / i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (b <= -2.6e+110) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else if (b <= -3.4e+34) {
		tmp = t_1;
	} else if (b <= -5.3e-17) {
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	} else if (b <= -1.7e-70) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 9.5e-21) {
		tmp = t_1;
	} else if (b <= 3.3e+129) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	tmp = 0
	if b <= -2.6e+110:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	elif b <= -3.4e+34:
		tmp = t_1
	elif b <= -5.3e-17:
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c))
	elif b <= -1.7e-70:
		tmp = y * ((x * z) - (i * j))
	elif b <= 9.5e-21:
		tmp = t_1
	elif b <= 3.3e+129:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = b * (i * (a - (c * (z / i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (b <= -2.6e+110)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= -3.4e+34)
		tmp = t_1;
	elseif (b <= -5.3e-17)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(z * c)));
	elseif (b <= -1.7e-70)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 9.5e-21)
		tmp = t_1;
	elseif (b <= 3.3e+129)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (b <= -2.6e+110)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	elseif (b <= -3.4e+34)
		tmp = t_1;
	elseif (b <= -5.3e-17)
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	elseif (b <= -1.7e-70)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 9.5e-21)
		tmp = t_1;
	elseif (b <= 3.3e+129)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = b * (i * (a - (c * (z / i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+110], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e+34], t$95$1, If[LessEqual[b, -5.3e-17], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-70], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-21], t$95$1, If[LessEqual[b, 3.3e+129], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.6e110

   1. Initial program 71.4%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-*l* 76.3%

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

      6. mul-1-neg 76.3%

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

      7. associate-*r* 73.9%

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

      8. *-commutative 73.9%

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

      9. associate-*l* 71.6%

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

      10. distribute-rgt-neg-in 71.6%

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

      11. mul-1-neg 71.6%

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

      12. distribute-lft-in 71.6%

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

      13. mul-1-neg 71.6%

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

      14. unsub-neg 71.6%

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

      15. *-commutative 71.6%

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

      16. *-commutative 71.6%

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

      17. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in j around inf 78.8%

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

      1. associate-*r* 78.8%

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

      2. *-commutative 78.8%

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

      3. *-commutative 78.8%

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

      4. *-commutative 78.8%

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

   8. Simplified 78.8%

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

   if -2.6e110 < b < -3.3999999999999999e34 or -1.69999999999999998e-70 < b < 9.4999999999999994e-21

   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 72.2%

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

   if -3.3999999999999999e34 < b < -5.2999999999999998e-17

   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 0 85.1%

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

      1. +-commutative 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*r* 85.1%

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

      4. *-commutative 85.1%

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

      5. associate-*l* 85.1%

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

      6. mul-1-neg 85.1%

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

      7. associate-*r* 67.8%

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

      8. *-commutative 67.8%

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

      9. associate-*l* 85.3%

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

      10. distribute-rgt-neg-in 85.3%

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

      11. mul-1-neg 85.3%

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

      12. distribute-lft-in 85.3%

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

      13. mul-1-neg 85.3%

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

      14. unsub-neg 85.3%

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

      15. *-commutative 85.3%

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

      16. *-commutative 85.3%

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

      17. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in z around inf 76.2%

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

   if -5.2999999999999998e-17 < b < -1.69999999999999998e-70

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

   5. Simplified 63.7%

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

   if 9.4999999999999994e-21 < b < 3.2999999999999999e129

   1. Initial program 81.1%

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

   3. Taylor expanded in y around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r* 74.4%

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

      4. *-commutative 74.4%

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

      5. associate-*l* 77.3%

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

      6. mul-1-neg 77.3%

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

      7. associate-*r* 68.3%

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

      8. *-commutative 68.3%

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

      9. associate-*l* 74.6%

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

      10. distribute-rgt-neg-in 74.6%

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

      11. mul-1-neg 74.6%

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

      12. distribute-lft-in 77.8%

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

      13. mul-1-neg 77.8%

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

      14. unsub-neg 77.8%

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

      15. *-commutative 77.8%

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

      16. *-commutative 77.8%

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

      17. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in c around 0 68.1%

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

      1. associate-*r* 68.1%

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

      2. neg-mul-1 68.1%

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

      3. cancel-sign-sub 68.1%

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

      4. mul-1-neg 68.1%

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

      5. distribute-rgt-neg-in 68.1%

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

      6. mul-1-neg 68.1%

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

      7. distribute-lft-in 71.3%

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

      8. +-commutative 71.3%

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

      9. mul-1-neg 71.3%

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

      10. unsub-neg 71.3%

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

   8. Simplified 71.3%

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

   if 3.2999999999999999e129 < b

   1. Initial program 66.8%

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

   3. Taylor expanded in b around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in i around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

      3. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x (- z (* i (/ j x)))))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= y -4e+173)
     t_1
     (if (<= y -1e-34)
       (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))
       (if (<= y -1.25e-92)
         (+ (* y (- (* x z) (* i j))) t_2)
         (if (<= y 3.6e+73) (+ (* t (- (* c j) (* x a))) 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 = y * (x * (z - (i * (j / x))));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -4e+173) {
		tmp = t_1;
	} else if (y <= -1e-34) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -1.25e-92) {
		tmp = (y * ((x * z) - (i * j))) + t_2;
	} else if (y <= 3.6e+73) {
		tmp = (t * ((c * j) - (x * a))) + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * (z - (i * (j / x))))
    t_2 = b * ((a * i) - (z * c))
    if (y <= (-4d+173)) then
        tmp = t_1
    else if (y <= (-1d-34)) then
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (y <= (-1.25d-92)) then
        tmp = (y * ((x * z) - (i * j))) + t_2
    else if (y <= 3.6d+73) then
        tmp = (t * ((c * j) - (x * a))) + t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * (z - (i * (j / x))));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -4e+173) {
		tmp = t_1;
	} else if (y <= -1e-34) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (y <= -1.25e-92) {
		tmp = (y * ((x * z) - (i * j))) + t_2;
	} else if (y <= 3.6e+73) {
		tmp = (t * ((c * j) - (x * a))) + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * (z - (i * (j / x))))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -4e+173:
		tmp = t_1
	elif y <= -1e-34:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif y <= -1.25e-92:
		tmp = (y * ((x * z) - (i * j))) + t_2
	elif y <= 3.6e+73:
		tmp = (t * ((c * j) - (x * a))) + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -4e+173)
		tmp = t_1;
	elseif (y <= -1e-34)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (y <= -1.25e-92)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_2);
	elseif (y <= 3.6e+73)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * (z - (i * (j / x))));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (y <= -4e+173)
		tmp = t_1;
	elseif (y <= -1e-34)
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (y <= -1.25e-92)
		tmp = (y * ((x * z) - (i * j))) + t_2;
	elseif (y <= 3.6e+73)
		tmp = (t * ((c * j) - (x * a))) + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+173], t$95$1, If[LessEqual[y, -1e-34], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-92], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, 3.6e+73], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.0000000000000001e173 or 3.5999999999999999e73 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in x around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

      3. associate-/l* 77.2%

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

   8. Simplified 77.2%

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

   if -4.0000000000000001e173 < y < -9.99999999999999928e-35

   1. Initial program 65.4%

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

   3. Taylor expanded in b around 0 76.1%

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

   if -9.99999999999999928e-35 < y < -1.25000000000000003e-92

   1. Initial program 92.7%

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

   3. Taylor expanded in t around 0 92.8%

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

      1. associate-*r* 86.1%

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

      2. associate-*r* 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-*r* 79.0%

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

      5. distribute-rgt-in 79.0%

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

      6. +-commutative 79.0%

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

      7. mul-1-neg 79.0%

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

      8. unsub-neg 79.0%

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

      9. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -1.25000000000000003e-92 < y < 3.5999999999999999e73

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-*r* 81.1%

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

      4. *-commutative 81.1%

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

      5. associate-*l* 81.7%

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

      6. mul-1-neg 81.7%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 81.1%

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

      10. distribute-rgt-neg-in 81.1%

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

      11. mul-1-neg 81.1%

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

      12. distribute-lft-in 82.6%

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

      13. mul-1-neg 82.6%

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

      14. unsub-neg 82.6%

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

      15. *-commutative 82.6%

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

      16. *-commutative 82.6%

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

      17. *-commutative 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.08e-7)
   (* y (- (* x z) (* i j)))
   (if (<= y 1.45e-304)
     (- (* t (- (* c j) (* x a))) (* b (* z c)))
     (if (<= y 1.05e-278)
       (- (* a (* b i)) (* a (* x t)))
       (if (<= y 9.5e+73)
         (+ (* t (* c j)) (* b (- (* a i) (* z c))))
         (* y (* x (- z (* i (/ j x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.08e-7) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 1.45e-304) {
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	} else if (y <= 1.05e-278) {
		tmp = (a * (b * i)) - (a * (x * t));
	} else if (y <= 9.5e+73) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.08d-7)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= 1.45d-304) then
        tmp = (t * ((c * j) - (x * a))) - (b * (z * c))
    else if (y <= 1.05d-278) then
        tmp = (a * (b * i)) - (a * (x * t))
    else if (y <= 9.5d+73) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else
        tmp = y * (x * (z - (i * (j / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.08e-7) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 1.45e-304) {
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	} else if (y <= 1.05e-278) {
		tmp = (a * (b * i)) - (a * (x * t));
	} else if (y <= 9.5e+73) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.08e-7:
		tmp = y * ((x * z) - (i * j))
	elif y <= 1.45e-304:
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c))
	elif y <= 1.05e-278:
		tmp = (a * (b * i)) - (a * (x * t))
	elif y <= 9.5e+73:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	else:
		tmp = y * (x * (z - (i * (j / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.08e-7)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= 1.45e-304)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(z * c)));
	elseif (y <= 1.05e-278)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(a * Float64(x * t)));
	elseif (y <= 9.5e+73)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.08e-7)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= 1.45e-304)
		tmp = (t * ((c * j) - (x * a))) - (b * (z * c));
	elseif (y <= 1.05e-278)
		tmp = (a * (b * i)) - (a * (x * t));
	elseif (y <= 9.5e+73)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	else
		tmp = y * (x * (z - (i * (j / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.08e-7], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-304], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-278], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+73], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.08000000000000001e-7

   1. Initial program 59.8%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   5. Simplified 75.3%

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

   if -1.08000000000000001e-7 < y < 1.45e-304

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 68.7%

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

      4. *-commutative 68.7%

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

      5. associate-*l* 70.3%

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

      6. mul-1-neg 70.3%

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

      7. associate-*r* 70.4%

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

      8. *-commutative 70.4%

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

      9. associate-*l* 72.3%

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

      10. distribute-rgt-neg-in 72.3%

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

      11. mul-1-neg 72.3%

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

      12. distribute-lft-in 72.3%

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

      13. mul-1-neg 72.3%

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

      14. unsub-neg 72.3%

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

      15. *-commutative 72.3%

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

      16. *-commutative 72.3%

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

      17. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in z around inf 70.1%

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

   if 1.45e-304 < y < 1.05000000000000007e-278

   1. Initial program 71.4%

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

   3. Taylor expanded in t around -inf 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in a around -inf 85.9%

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

      1. associate-*r* 85.9%

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

      2. *-commutative 85.9%

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

      3. +-commutative 85.9%

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

      4. mul-1-neg 85.9%

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

      5. unsub-neg 85.9%

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

      6. associate-/l* 86.0%

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

   8. Simplified 86.0%

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

   9. Taylor expanded in t around 0 86.1%

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

   if 1.05000000000000007e-278 < y < 9.4999999999999996e73

   1. Initial program 85.0%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 82.2%

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

      4. *-commutative 82.2%

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

      5. associate-*l* 83.1%

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

      6. mul-1-neg 83.1%

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

      7. associate-*r* 77.9%

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

      8. *-commutative 77.9%

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

      9. associate-*l* 82.2%

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

      10. distribute-rgt-neg-in 82.2%

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

      11. mul-1-neg 82.2%

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

      12. distribute-lft-in 84.3%

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

      13. mul-1-neg 84.3%

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

      14. unsub-neg 84.3%

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

      15. *-commutative 84.3%

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

      16. *-commutative 84.3%

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

      17. *-commutative 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in j around inf 68.7%

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

      1. associate-*r* 69.7%

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

      2. *-commutative 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

   8. Simplified 69.7%

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

   if 9.4999999999999996e73 < y

   1. Initial program 48.5%

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

   3. Taylor expanded in y around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in x around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

      3. associate-/l* 71.4%

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

   8. Simplified 71.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -0.000135:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (* c j)) (* b (- (* a i) (* z c))))))
   (if (<= y -0.000135)
     (* y (- (* x z) (* i j)))
     (if (<= y 1.15e-22)
       t_1
       (if (<= y 1.85e-6)
         (* a (- (* b i) (* x t)))
         (if (<= y 8.4e+74) t_1 (* y (* x (- z (* i (/ j x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (y <= -0.000135) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 1.15e-22) {
		tmp = t_1;
	} else if (y <= 1.85e-6) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 8.4e+74) {
		tmp = t_1;
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)))
    if (y <= (-0.000135d0)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= 1.15d-22) then
        tmp = t_1
    else if (y <= 1.85d-6) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 8.4d+74) then
        tmp = t_1
    else
        tmp = y * (x * (z - (i * (j / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (y <= -0.000135) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 1.15e-22) {
		tmp = t_1;
	} else if (y <= 1.85e-6) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 8.4e+74) {
		tmp = t_1;
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)))
	tmp = 0
	if y <= -0.000135:
		tmp = y * ((x * z) - (i * j))
	elif y <= 1.15e-22:
		tmp = t_1
	elif y <= 1.85e-6:
		tmp = a * ((b * i) - (x * t))
	elif y <= 8.4e+74:
		tmp = t_1
	else:
		tmp = y * (x * (z - (i * (j / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (y <= -0.000135)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= 1.15e-22)
		tmp = t_1;
	elseif (y <= 1.85e-6)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 8.4e+74)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (y <= -0.000135)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= 1.15e-22)
		tmp = t_1;
	elseif (y <= 1.85e-6)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 8.4e+74)
		tmp = t_1;
	else
		tmp = y * (x * (z - (i * (j / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.000135], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-22], t$95$1, If[LessEqual[y, 1.85e-6], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+74], t$95$1, N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000002e-4

   1. Initial program 59.2%

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

   3. Taylor expanded in y around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if -1.35000000000000002e-4 < y < 1.1499999999999999e-22 or 1.8500000000000001e-6 < y < 8.3999999999999995e74

   1. Initial program 85.0%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 77.2%

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

      4. *-commutative 77.2%

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

      5. associate-*l* 77.7%

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

      6. mul-1-neg 77.7%

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

      7. associate-*r* 75.0%

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

      8. *-commutative 75.0%

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

      9. associate-*l* 78.5%

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

      10. distribute-rgt-neg-in 78.5%

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

      11. mul-1-neg 78.5%

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

      12. distribute-lft-in 79.1%

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

      13. mul-1-neg 79.1%

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

      14. unsub-neg 79.1%

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

      15. *-commutative 79.1%

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

      16. *-commutative 79.1%

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

      17. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in j around inf 68.6%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

      3. *-commutative 67.7%

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

      4. *-commutative 67.7%

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

   8. Simplified 67.7%

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

   if 1.1499999999999999e-22 < y < 1.8500000000000001e-6

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-*l* 75.8%

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

      6. mul-1-neg 75.8%

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

      7. associate-*r* 64.7%

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

      8. *-commutative 64.7%

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

      9. associate-*l* 64.7%

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

      10. distribute-rgt-neg-in 64.7%

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

      11. mul-1-neg 64.7%

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

      12. distribute-lft-in 77.2%

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

      13. mul-1-neg 77.2%

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

      14. unsub-neg 77.2%

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

      15. *-commutative 77.2%

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

      16. *-commutative 77.2%

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

      17. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in c around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. cancel-sign-sub 100.0%

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

      4. mul-1-neg 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-in 100.0%

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

      8. +-commutative 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

   8. Simplified 100.0%

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

   if 8.3999999999999995e74 < y

   1. Initial program 48.5%

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

   3. Taylor expanded in y around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in x around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

      3. associate-/l* 71.4%

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

   8. Simplified 71.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000135:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.95e+179)
   (* x (- (* y z) (* t a)))
   (if (<= z -4.5e-115)
     (* b (* i (- a (* c (/ z i)))))
     (if (<= z 3.1e-281)
       (* i (- (* a b) (* y j)))
       (if (<= z 4e-240)
         (* t (- (* c j) (* x a)))
         (if (<= z 1.55e-77)
           (* a (- (* b i) (* x t)))
           (* z (- (* x y) (* b c)))))))))

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 <= -1.95e+179) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -4.5e-115) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (z <= 3.1e-281) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 4e-240) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.55e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.95d+179)) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= (-4.5d-115)) then
        tmp = b * (i * (a - (c * (z / i))))
    else if (z <= 3.1d-281) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 4d-240) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 1.55d-77) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.95e+179) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -4.5e-115) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (z <= 3.1e-281) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 4e-240) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.55e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.95e+179:
		tmp = x * ((y * z) - (t * a))
	elif z <= -4.5e-115:
		tmp = b * (i * (a - (c * (z / i))))
	elif z <= 3.1e-281:
		tmp = i * ((a * b) - (y * j))
	elif z <= 4e-240:
		tmp = t * ((c * j) - (x * a))
	elif z <= 1.55e-77:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.95e+179)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= -4.5e-115)
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	elseif (z <= 3.1e-281)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 4e-240)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 1.55e-77)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.95e+179)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= -4.5e-115)
		tmp = b * (i * (a - (c * (z / i))));
	elseif (z <= 3.1e-281)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 4e-240)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 1.55e-77)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.95e+179], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-115], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-281], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-240], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-77], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.94999999999999987e179

   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. Step-by-step derivation

      1. +-commutative 66.9%

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

      2. fma-define 66.9%

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

      3. *-commutative 66.9%

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

      4. *-commutative 66.9%

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

      5. cancel-sign-sub-inv 66.9%

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

      6. cancel-sign-sub 66.9%

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

      7. sub-neg 66.9%

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

      8. sub-neg 66.9%

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

      9. *-commutative 66.9%

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

      10. fma-neg 66.9%

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

      11. *-commutative 66.9%

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

      12. distribute-rgt-neg-out 66.9%

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

      13. remove-double-neg 66.9%

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

      14. *-commutative 66.9%

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

      15. *-commutative 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in x around inf 81.8%

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

   if -1.94999999999999987e179 < z < -4.50000000000000023e-115

   1. Initial program 70.1%

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

   3. Taylor expanded in b around inf 56.8%

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

      1. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in i around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

      3. associate-/l* 61.1%

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

   8. Simplified 61.1%

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

   if -4.50000000000000023e-115 < z < 3.1000000000000002e-281

   1. Initial program 79.7%

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

   3. Taylor expanded in i around inf 67.7%

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

      1. distribute-lft-out-- 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if 3.1000000000000002e-281 < z < 3.9999999999999999e-240

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. mul-1-neg 99.7%

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

      3. unsub-neg 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if 3.9999999999999999e-240 < z < 1.55000000000000004e-77

   1. Initial program 85.3%

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

   3. Taylor expanded in y around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-*l* 73.7%

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

      6. mul-1-neg 73.7%

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

      7. associate-*r* 70.6%

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

      8. *-commutative 70.6%

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

      9. associate-*l* 67.8%

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

      10. distribute-rgt-neg-in 67.8%

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

      11. mul-1-neg 67.8%

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

      12. distribute-lft-in 67.8%

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

      13. mul-1-neg 67.8%

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

      14. unsub-neg 67.8%

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

      15. *-commutative 67.8%

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

      16. *-commutative 67.8%

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

      17. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around 0 54.4%

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

      1. associate-*r* 54.4%

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

      2. neg-mul-1 54.4%

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

      3. cancel-sign-sub 54.4%

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

      4. mul-1-neg 54.4%

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

      5. distribute-rgt-neg-in 54.4%

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

      6. mul-1-neg 54.4%

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

      7. distribute-lft-in 54.4%

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

      8. +-commutative 54.4%

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

      9. mul-1-neg 54.4%

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

      10. unsub-neg 54.4%

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

   8. Simplified 54.4%

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

   if 1.55000000000000004e-77 < z

   1. Initial program 66.6%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. *-commutative 71.5%

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

   5. Simplified 71.5%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.45e+185)
   (* y (- (* x z) (* i j)))
   (if (<= z -3.8e-115)
     (* b (* i (- a (* c (/ z i)))))
     (if (<= z 3.1e-281)
       (* i (- (* a b) (* y j)))
       (if (<= z 1.25e-239)
         (* t (- (* c j) (* x a)))
         (if (<= z 1.55e-77)
           (* a (- (* b i) (* x t)))
           (* z (- (* x y) (* b c)))))))))

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 <= -1.45e+185) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -3.8e-115) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (z <= 3.1e-281) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.25e-239) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.55e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.45d+185)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-3.8d-115)) then
        tmp = b * (i * (a - (c * (z / i))))
    else if (z <= 3.1d-281) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 1.25d-239) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 1.55d-77) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.45e+185) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -3.8e-115) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (z <= 3.1e-281) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.25e-239) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 1.55e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.45e+185:
		tmp = y * ((x * z) - (i * j))
	elif z <= -3.8e-115:
		tmp = b * (i * (a - (c * (z / i))))
	elif z <= 3.1e-281:
		tmp = i * ((a * b) - (y * j))
	elif z <= 1.25e-239:
		tmp = t * ((c * j) - (x * a))
	elif z <= 1.55e-77:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.45e+185)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -3.8e-115)
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	elseif (z <= 3.1e-281)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 1.25e-239)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 1.55e-77)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.45e+185)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -3.8e-115)
		tmp = b * (i * (a - (c * (z / i))));
	elseif (z <= 3.1e-281)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 1.25e-239)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 1.55e-77)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.45e+185], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-115], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-281], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-239], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-77], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.44999999999999994e185

   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 y around inf 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

   5. Simplified 74.7%

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

   if -1.44999999999999994e185 < z < -3.79999999999999992e-115

   1. Initial program 70.1%

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

   3. Taylor expanded in b around inf 56.8%

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

      1. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in i around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

      3. associate-/l* 61.1%

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

   8. Simplified 61.1%

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

   if -3.79999999999999992e-115 < z < 3.1000000000000002e-281

   1. Initial program 79.7%

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

   3. Taylor expanded in i around inf 67.7%

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

      1. distribute-lft-out-- 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if 3.1000000000000002e-281 < z < 1.25e-239

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. mul-1-neg 99.7%

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

      3. unsub-neg 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if 1.25e-239 < z < 1.55000000000000004e-77

   1. Initial program 85.3%

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

   3. Taylor expanded in y around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-*l* 73.7%

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

      6. mul-1-neg 73.7%

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

      7. associate-*r* 70.6%

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

      8. *-commutative 70.6%

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

      9. associate-*l* 67.8%

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

      10. distribute-rgt-neg-in 67.8%

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

      11. mul-1-neg 67.8%

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

      12. distribute-lft-in 67.8%

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

      13. mul-1-neg 67.8%

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

      14. unsub-neg 67.8%

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

      15. *-commutative 67.8%

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

      16. *-commutative 67.8%

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

      17. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around 0 54.4%

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

      1. associate-*r* 54.4%

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

      2. neg-mul-1 54.4%

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

      3. cancel-sign-sub 54.4%

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

      4. mul-1-neg 54.4%

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

      5. distribute-rgt-neg-in 54.4%

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

      6. mul-1-neg 54.4%

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

      7. distribute-lft-in 54.4%

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

      8. +-commutative 54.4%

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

      9. mul-1-neg 54.4%

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

      10. unsub-neg 54.4%

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

   8. Simplified 54.4%

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

   if 1.55000000000000004e-77 < z

   1. Initial program 66.6%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. *-commutative 71.5%

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

   5. Simplified 71.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 700000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1.15e+159)
     t_2
     (if (<= c -3e-23)
       t_1
       (if (<= c -2.05e-100)
         (* j (- (* t c) (* y i)))
         (if (<= c 700000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.15e+159) {
		tmp = t_2;
	} else if (c <= -3e-23) {
		tmp = t_1;
	} else if (c <= -2.05e-100) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 700000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.15d+159)) then
        tmp = t_2
    else if (c <= (-3d-23)) then
        tmp = t_1
    else if (c <= (-2.05d-100)) then
        tmp = j * ((t * c) - (y * i))
    else if (c <= 700000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.15e+159) {
		tmp = t_2;
	} else if (c <= -3e-23) {
		tmp = t_1;
	} else if (c <= -2.05e-100) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 700000.0) {
		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 <= -1.15e+159:
		tmp = t_2
	elif c <= -3e-23:
		tmp = t_1
	elif c <= -2.05e-100:
		tmp = j * ((t * c) - (y * i))
	elif c <= 700000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.15e+159)
		tmp = t_2;
	elseif (c <= -3e-23)
		tmp = t_1;
	elseif (c <= -2.05e-100)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (c <= 700000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.15e+159)
		tmp = t_2;
	elseif (c <= -3e-23)
		tmp = t_1;
	elseif (c <= -2.05e-100)
		tmp = j * ((t * c) - (y * i));
	elseif (c <= 700000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(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, -1.15e+159], t$95$2, If[LessEqual[c, -3e-23], t$95$1, If[LessEqual[c, -2.05e-100], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 700000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.14999999999999998e159 or 7e5 < c

   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 c around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -1.14999999999999998e159 < c < -3.00000000000000003e-23 or -2.0499999999999999e-100 < c < 7e5

   1. Initial program 75.9%

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

   3. Taylor expanded in y around 0 62.5%

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

      1. +-commutative 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 62.5%

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

      4. *-commutative 62.5%

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

      5. associate-*l* 62.5%

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

      6. mul-1-neg 62.5%

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

      7. associate-*r* 55.6%

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

      8. *-commutative 55.6%

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

      9. associate-*l* 57.1%

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

      10. distribute-rgt-neg-in 57.1%

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

      11. mul-1-neg 57.1%

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

      12. distribute-lft-in 57.9%

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

      13. mul-1-neg 57.9%

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

      14. unsub-neg 57.9%

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

      15. *-commutative 57.9%

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

      16. *-commutative 57.9%

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

      17. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in c around 0 53.8%

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

      1. associate-*r* 53.8%

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

      2. neg-mul-1 53.8%

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

      3. cancel-sign-sub 53.8%

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

      4. mul-1-neg 53.8%

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

      5. distribute-rgt-neg-in 53.8%

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

      6. mul-1-neg 53.8%

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

      7. distribute-lft-in 56.3%

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

      8. +-commutative 56.3%

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

      9. mul-1-neg 56.3%

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

      10. unsub-neg 56.3%

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

   8. Simplified 56.3%

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

   if -3.00000000000000003e-23 < c < -2.0499999999999999e-100

   1. Initial program 84.5%

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

   3. Taylor expanded in j around inf 65.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 700000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= z -3e+192)
     (* y (* x z))
     (if (<= z -6e-28)
       t_1
       (if (<= z 1.7e-160)
         (* a (- (* b i) (* x t)))
         (if (<= z 2.4e+169) t_1 (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (z <= -3e+192) {
		tmp = y * (x * z);
	} else if (z <= -6e-28) {
		tmp = t_1;
	} else if (z <= 1.7e-160) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 2.4e+169) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (z <= (-3d+192)) then
        tmp = y * (x * z)
    else if (z <= (-6d-28)) then
        tmp = t_1
    else if (z <= 1.7d-160) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 2.4d+169) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (z <= -3e+192) {
		tmp = y * (x * z);
	} else if (z <= -6e-28) {
		tmp = t_1;
	} else if (z <= 1.7e-160) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 2.4e+169) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if z <= -3e+192:
		tmp = y * (x * z)
	elif z <= -6e-28:
		tmp = t_1
	elif z <= 1.7e-160:
		tmp = a * ((b * i) - (x * t))
	elif z <= 2.4e+169:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (z <= -3e+192)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -6e-28)
		tmp = t_1;
	elseif (z <= 1.7e-160)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 2.4e+169)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (z <= -3e+192)
		tmp = y * (x * z);
	elseif (z <= -6e-28)
		tmp = t_1;
	elseif (z <= 1.7e-160)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 2.4e+169)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+192], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-28], t$95$1, If[LessEqual[z, 1.7e-160], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+169], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3e192

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 80.5%

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

      1. +-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in x around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*l* 68.8%

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

   8. Simplified 68.8%

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

   if -3e192 < z < -6.00000000000000005e-28 or 1.70000000000000011e-160 < z < 2.3999999999999998e169

   1. Initial program 71.2%

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

   3. Taylor expanded in b around inf 51.8%

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

      1. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   if -6.00000000000000005e-28 < z < 1.70000000000000011e-160

   1. Initial program 80.0%

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

   3. Taylor expanded in y around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r* 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-*l* 67.1%

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

      6. mul-1-neg 67.1%

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

      7. associate-*r* 61.7%

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

      8. *-commutative 61.7%

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

      9. associate-*l* 63.8%

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

      10. distribute-rgt-neg-in 63.8%

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

      11. mul-1-neg 63.8%

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

      12. distribute-lft-in 65.0%

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

      13. mul-1-neg 65.0%

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

      14. unsub-neg 65.0%

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

      15. *-commutative 65.0%

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

      16. *-commutative 65.0%

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

      17. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in c around 0 53.7%

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

      1. associate-*r* 53.7%

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

      2. neg-mul-1 53.7%

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

      3. cancel-sign-sub 53.7%

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

      4. mul-1-neg 53.7%

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

      5. distribute-rgt-neg-in 53.7%

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

      6. mul-1-neg 53.7%

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

      7. distribute-lft-in 54.8%

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

      8. +-commutative 54.8%

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

      9. mul-1-neg 54.8%

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

      10. unsub-neg 54.8%

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

   8. Simplified 54.8%

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

   if 2.3999999999999998e169 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in t around 0 70.0%

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

      1. associate-*r* 70.0%

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

      2. associate-*r* 70.0%

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

      3. *-commutative 70.0%

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

      4. associate-*r* 86.4%

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

      5. distribute-rgt-in 93.3%

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

      6. +-commutative 93.3%

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

      7. mul-1-neg 93.3%

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

      8. unsub-neg 93.3%

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

      9. *-commutative 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in x around inf 57.7%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* z c)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.2e-121)
     t_2
     (if (<= a -1.8e-230)
       t_1
       (if (<= a 6.2e-233) (* y (* x z)) (if (<= a 2.8e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * -(z * c);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.2e-121) {
		tmp = t_2;
	} else if (a <= -1.8e-230) {
		tmp = t_1;
	} else if (a <= 6.2e-233) {
		tmp = y * (x * z);
	} else if (a <= 2.8e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * -(z * c)
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1.2d-121)) then
        tmp = t_2
    else if (a <= (-1.8d-230)) then
        tmp = t_1
    else if (a <= 6.2d-233) then
        tmp = y * (x * z)
    else if (a <= 2.8d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * -(z * c);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.2e-121) {
		tmp = t_2;
	} else if (a <= -1.8e-230) {
		tmp = t_1;
	} else if (a <= 6.2e-233) {
		tmp = y * (x * z);
	} else if (a <= 2.8e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * -(z * c)
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.2e-121:
		tmp = t_2
	elif a <= -1.8e-230:
		tmp = t_1
	elif a <= 6.2e-233:
		tmp = y * (x * z)
	elif a <= 2.8e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(-Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.2e-121)
		tmp = t_2;
	elseif (a <= -1.8e-230)
		tmp = t_1;
	elseif (a <= 6.2e-233)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 2.8e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * -(z * c);
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.2e-121)
		tmp = t_2;
	elseif (a <= -1.8e-230)
		tmp = t_1;
	elseif (a <= 6.2e-233)
		tmp = y * (x * z);
	elseif (a <= 2.8e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-121], t$95$2, If[LessEqual[a, -1.8e-230], t$95$1, If[LessEqual[a, 6.2e-233], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.20000000000000002e-121 or 2.8e29 < a

   1. Initial program 67.1%

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

   3. Taylor expanded in y around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 67.0%

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

      4. *-commutative 67.0%

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

      5. associate-*l* 67.7%

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

      6. mul-1-neg 67.7%

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

      7. associate-*r* 60.5%

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

      8. *-commutative 60.5%

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

      9. associate-*l* 65.1%

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

      10. distribute-rgt-neg-in 65.1%

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

      11. mul-1-neg 65.1%

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

      12. distribute-lft-in 66.5%

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

      13. mul-1-neg 66.5%

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

      14. unsub-neg 66.5%

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

      15. *-commutative 66.5%

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

      16. *-commutative 66.5%

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

      17. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in c around 0 59.2%

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

      1. associate-*r* 59.2%

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

      2. neg-mul-1 59.2%

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

      3. cancel-sign-sub 59.2%

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

      4. mul-1-neg 59.2%

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

      5. distribute-rgt-neg-in 59.2%

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

      6. mul-1-neg 59.2%

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

      7. distribute-lft-in 61.9%

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

      8. +-commutative 61.9%

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

      9. mul-1-neg 61.9%

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

      10. unsub-neg 61.9%

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

   8. Simplified 61.9%

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

   if -1.20000000000000002e-121 < a < -1.7999999999999999e-230 or 6.2000000000000003e-233 < a < 2.8e29

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf 47.2%

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

      1. *-commutative 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in a around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. *-commutative 45.5%

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

      3. distribute-rgt-neg-in 45.5%

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

      4. *-commutative 45.5%

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

      5. distribute-rgt-neg-in 45.5%

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

   8. Simplified 45.5%

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

   if -1.7999999999999999e-230 < a < 6.2000000000000003e-233

   1. Initial program 80.8%

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

   3. Taylor expanded in y around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in x around inf 33.8%

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

      1. *-commutative 33.8%

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

      2. associate-*l* 36.5%

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

   8. Simplified 36.5%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-230}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.5e-5)
   (* y (- (* x z) (* i j)))
   (if (<= y 5.2e+75)
     (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))
     (* y (* x (- z (* i (/ j x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.5e-5) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 5.2e+75) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-5.5d-5)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= 5.2d+75) then
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = y * (x * (z - (i * (j / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.5e-5) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 5.2e+75) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = y * (x * (z - (i * (j / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.5e-5:
		tmp = y * ((x * z) - (i * j))
	elif y <= 5.2e+75:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = y * (x * (z - (i * (j / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.5e-5)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= 5.2e+75)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5.5e-5)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= 5.2e+75)
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = y * (x * (z - (i * (j / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.5e-5], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+75], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000002e-5

   1. Initial program 59.2%

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

   3. Taylor expanded in y around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if -5.5000000000000002e-5 < y < 5.1999999999999997e75

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-*l* 77.6%

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

      6. mul-1-neg 77.6%

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

      7. associate-*r* 74.5%

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

      8. *-commutative 74.5%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot a\right)} \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. associate-*l* 77.7%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 77.7%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 77.7%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 79.0%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 79.0%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 79.0%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 79.0%

          \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 79.0%

          \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      17. *-commutative 79.0%

          \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 79.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   if 5.1999999999999997e75 < y

   1. Initial program 48.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 71.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 71.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 71.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 71.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 71.1%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(z + -1 \cdot \frac{i \cdot j}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 71.1%

         \[\leadsto y \cdot \left(x \cdot \left(z + \color{blue}{\left(-\frac{i \cdot j}{x}\right)}\right)\right) \]

      2. unsub-neg 71.1%

         \[\leadsto y \cdot \left(x \cdot \color{blue}{\left(z - \frac{i \cdot j}{x}\right)}\right) \]

      3. associate-/l* 71.4%

         \[\leadsto y \cdot \left(x \cdot \left(z - \color{blue}{i \cdot \frac{j}{x}}\right)\right) \]

   8. Simplified 71.4%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -8.6 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= i -8.6e+99)
     t_1
     (if (<= i 1.3e-206)
       (* a (* t (- x)))
       (if (<= i 1.95e-78)
         (* y (* x z))
         (if (<= i 8e+131) (* z (* b (- c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (i <= -8.6e+99) {
		tmp = t_1;
	} else if (i <= 1.3e-206) {
		tmp = a * (t * -x);
	} else if (i <= 1.95e-78) {
		tmp = y * (x * z);
	} else if (i <= 8e+131) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (i <= (-8.6d+99)) then
        tmp = t_1
    else if (i <= 1.3d-206) then
        tmp = a * (t * -x)
    else if (i <= 1.95d-78) then
        tmp = y * (x * z)
    else if (i <= 8d+131) then
        tmp = z * (b * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (i <= -8.6e+99) {
		tmp = t_1;
	} else if (i <= 1.3e-206) {
		tmp = a * (t * -x);
	} else if (i <= 1.95e-78) {
		tmp = y * (x * z);
	} else if (i <= 8e+131) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if i <= -8.6e+99:
		tmp = t_1
	elif i <= 1.3e-206:
		tmp = a * (t * -x)
	elif i <= 1.95e-78:
		tmp = y * (x * z)
	elif i <= 8e+131:
		tmp = z * (b * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -8.6e+99)
		tmp = t_1;
	elseif (i <= 1.3e-206)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 1.95e-78)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 8e+131)
		tmp = Float64(z * Float64(b * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (i <= -8.6e+99)
		tmp = t_1;
	elseif (i <= 1.3e-206)
		tmp = a * (t * -x);
	elseif (i <= 1.95e-78)
		tmp = y * (x * z);
	elseif (i <= 8e+131)
		tmp = z * (b * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.6e+99], t$95$1, If[LessEqual[i, 1.3e-206], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.95e-78], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e+131], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.6000000000000003e99 or 7.9999999999999993e131 < i

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 59.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 50.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -8.6000000000000003e99 < i < 1.3e-206

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 72.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in x around inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot \left(a - \frac{y \cdot z}{t}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto \color{blue}{-t \cdot \left(x \cdot \left(a - \frac{y \cdot z}{t}\right)\right)} \]

      2. associate-*r* 46.0%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot \left(a - \frac{y \cdot z}{t}\right)} \]

      3. distribute-rgt-neg-in 46.0%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-\left(a - \frac{y \cdot z}{t}\right)\right)} \]

      4. mul-1-neg 46.0%

         \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(-1 \cdot \left(a - \frac{y \cdot z}{t}\right)\right)} \]

      5. distribute-lft-out-- 46.0%

         \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(-1 \cdot a - -1 \cdot \frac{y \cdot z}{t}\right)} \]

      6. cancel-sign-sub-inv 46.0%

         \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(-1 \cdot a + \left(--1\right) \cdot \frac{y \cdot z}{t}\right)} \]

      7. metadata-eval 46.0%

         \[\leadsto \left(t \cdot x\right) \cdot \left(-1 \cdot a + \color{blue}{1} \cdot \frac{y \cdot z}{t}\right) \]

      8. *-lft-identity 46.0%

         \[\leadsto \left(t \cdot x\right) \cdot \left(-1 \cdot a + \color{blue}{\frac{y \cdot z}{t}}\right) \]

      9. +-commutative 46.0%

         \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(\frac{y \cdot z}{t} + -1 \cdot a\right)} \]

      10. mul-1-neg 46.0%

          \[\leadsto \left(t \cdot x\right) \cdot \left(\frac{y \cdot z}{t} + \color{blue}{\left(-a\right)}\right) \]

      11. unsub-neg 46.0%

          \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(\frac{y \cdot z}{t} - a\right)} \]

      12. associate-/l* 45.9%

          \[\leadsto \left(t \cdot x\right) \cdot \left(\color{blue}{y \cdot \frac{z}{t}} - a\right) \]

   8. Simplified 45.9%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(y \cdot \frac{z}{t} - a\right)} \]

   9. Taylor expanded in y around 0 35.0%

      \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(-1 \cdot a\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 35.0%

          \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(-a\right)} \]

   11. Simplified 35.0%

       \[\leadsto \left(t \cdot x\right) \cdot \color{blue}{\left(-a\right)} \]

   if 1.3e-206 < i < 1.9500000000000001e-78

   1. Initial program 65.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 43.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 43.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 43.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 31.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 43.2%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 43.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.9500000000000001e-78 < i < 7.9999999999999993e131

   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 57.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   5. Simplified 57.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   6. Taylor expanded in x around 0 47.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 47.0%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-lft-neg-in 47.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(-b\right) \cdot c\right)} \]

      3. *-commutative 47.0%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   8. Simplified 47.0%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+99}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-z \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* z c)))) (t_2 (* b (* a i))))
   (if (<= a -1.8e-121)
     t_2
     (if (<= a -1.25e-228)
       t_1
       (if (<= a 1.5e-87) (* z (* x y)) (if (<= a 2.1e+30) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * -(z * c);
	double t_2 = b * (a * i);
	double tmp;
	if (a <= -1.8e-121) {
		tmp = t_2;
	} else if (a <= -1.25e-228) {
		tmp = t_1;
	} else if (a <= 1.5e-87) {
		tmp = z * (x * y);
	} else if (a <= 2.1e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * -(z * c)
    t_2 = b * (a * i)
    if (a <= (-1.8d-121)) then
        tmp = t_2
    else if (a <= (-1.25d-228)) then
        tmp = t_1
    else if (a <= 1.5d-87) then
        tmp = z * (x * y)
    else if (a <= 2.1d+30) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * -(z * c);
	double t_2 = b * (a * i);
	double tmp;
	if (a <= -1.8e-121) {
		tmp = t_2;
	} else if (a <= -1.25e-228) {
		tmp = t_1;
	} else if (a <= 1.5e-87) {
		tmp = z * (x * y);
	} else if (a <= 2.1e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * -(z * c)
	t_2 = b * (a * i)
	tmp = 0
	if a <= -1.8e-121:
		tmp = t_2
	elif a <= -1.25e-228:
		tmp = t_1
	elif a <= 1.5e-87:
		tmp = z * (x * y)
	elif a <= 2.1e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(-Float64(z * c)))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -1.8e-121)
		tmp = t_2;
	elseif (a <= -1.25e-228)
		tmp = t_1;
	elseif (a <= 1.5e-87)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 2.1e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * -(z * c);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (a <= -1.8e-121)
		tmp = t_2;
	elseif (a <= -1.25e-228)
		tmp = t_1;
	elseif (a <= 1.5e-87)
		tmp = z * (x * y);
	elseif (a <= 2.1e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e-121], t$95$2, If[LessEqual[a, -1.25e-228], t$95$1, If[LessEqual[a, 1.5e-87], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.79999999999999992e-121 or 2.1e30 < a

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 46.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 46.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 40.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -1.79999999999999992e-121 < a < -1.24999999999999993e-228 or 1.50000000000000008e-87 < a < 2.1e30

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 53.6%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around 0 51.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 51.3%

         \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

      3. distribute-rgt-neg-in 51.3%

         \[\leadsto \color{blue}{b \cdot \left(-z \cdot c\right)} \]

      4. *-commutative 51.3%

         \[\leadsto b \cdot \left(-\color{blue}{c \cdot z}\right) \]

      5. distribute-rgt-neg-in 51.3%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]

   if -1.24999999999999993e-228 < a < 1.50000000000000008e-87

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 68.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 68.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 68.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 68.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 70.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 70.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 70.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 70.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 70.1%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 70.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 33.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 35.0%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   8. Simplified 35.0%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-121}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -7.5e+187)
   (* y (- (* x z) (* i j)))
   (if (<= z -1.3e-28)
     (* b (* i (- a (* c (/ z i)))))
     (if (<= z 1.55e-77)
       (* a (- (* b i) (* x t)))
       (* z (- (* x y) (* b c)))))))

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 <= -7.5e+187) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.3e-28) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (z <= 1.55e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-7.5d+187)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-1.3d-28)) then
        tmp = b * (i * (a - (c * (z / i))))
    else if (z <= 1.55d-77) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.5e+187) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.3e-28) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (z <= 1.55e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -7.5e+187:
		tmp = y * ((x * z) - (i * j))
	elif z <= -1.3e-28:
		tmp = b * (i * (a - (c * (z / i))))
	elif z <= 1.55e-77:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -7.5e+187)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -1.3e-28)
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	elseif (z <= 1.55e-77)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -7.5e+187)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -1.3e-28)
		tmp = b * (i * (a - (c * (z / i))));
	elseif (z <= 1.55e-77)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -7.5e+187], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-28], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-77], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000002e187

   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 y around inf 77.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 77.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 77.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 77.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   if -7.5000000000000002e187 < z < -1.3e-28

   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 b around inf 63.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.2%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in i around inf 67.2%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.2%

         \[\leadsto b \cdot \left(i \cdot \left(a + \color{blue}{\left(-\frac{c \cdot z}{i}\right)}\right)\right) \]

      2. unsub-neg 67.2%

         \[\leadsto b \cdot \left(i \cdot \color{blue}{\left(a - \frac{c \cdot z}{i}\right)}\right) \]

      3. associate-/l* 67.2%

         \[\leadsto b \cdot \left(i \cdot \left(a - \color{blue}{c \cdot \frac{z}{i}}\right)\right) \]

   8. Simplified 67.2%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)} \]

   if -1.3e-28 < z < 1.55000000000000004e-77

   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 y around 0 69.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 69.5%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 68.5%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 68.5%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 69.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 69.1%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. associate-*r* 63.6%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. *-commutative 63.6%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot a\right)} \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. associate-*l* 66.3%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 66.3%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 66.3%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 67.3%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 67.3%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 67.3%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 67.3%

          \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 67.3%

          \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      17. *-commutative 67.3%

          \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in c around 0 52.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 52.9%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. neg-mul-1 52.9%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \color{blue}{\left(-a\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub 52.9%

         \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. mul-1-neg 52.9%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. distribute-rgt-neg-in 52.9%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} + a \cdot \left(b \cdot i\right) \]

      6. mul-1-neg 52.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} + a \cdot \left(b \cdot i\right) \]

      7. distribute-lft-in 53.9%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      8. +-commutative 53.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 53.9%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 53.9%

          \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if 1.55000000000000004e-77 < z

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 71.5%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   5. Simplified 71.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+191}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.4e+191)
   (* y (- (* x z) (* i j)))
   (if (<= z -5.4e-29)
     (* b (- (* a i) (* z c)))
     (if (<= z 1.25e-77)
       (* a (- (* b i) (* x t)))
       (* z (- (* x y) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.4e+191) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -5.4e-29) {
		tmp = b * ((a * i) - (z * c));
	} else if (z <= 1.25e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.4d+191)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-5.4d-29)) then
        tmp = b * ((a * i) - (z * c))
    else if (z <= 1.25d-77) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.4e+191) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -5.4e-29) {
		tmp = b * ((a * i) - (z * c));
	} else if (z <= 1.25e-77) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.4e+191:
		tmp = y * ((x * z) - (i * j))
	elif z <= -5.4e-29:
		tmp = b * ((a * i) - (z * c))
	elif z <= 1.25e-77:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.4e+191)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -5.4e-29)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (z <= 1.25e-77)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.4e+191)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -5.4e-29)
		tmp = b * ((a * i) - (z * c));
	elseif (z <= 1.25e-77)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.4e+191], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.4e-29], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-77], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.39999999999999986e191

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 80.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 80.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 80.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 80.5%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   if -2.39999999999999986e191 < z < -5.40000000000000045e-29

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 62.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 62.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -5.40000000000000045e-29 < z < 1.24999999999999991e-77

   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 y around 0 69.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 69.5%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 68.5%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 68.5%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 69.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 69.1%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. associate-*r* 63.6%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. *-commutative 63.6%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot a\right)} \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. associate-*l* 66.3%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 66.3%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 66.3%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 67.3%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 67.3%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 67.3%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 67.3%

          \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 67.3%

          \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      17. *-commutative 67.3%

          \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in c around 0 52.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 52.9%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. neg-mul-1 52.9%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \color{blue}{\left(-a\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub 52.9%

         \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. mul-1-neg 52.9%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. distribute-rgt-neg-in 52.9%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} + a \cdot \left(b \cdot i\right) \]

      6. mul-1-neg 52.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} + a \cdot \left(b \cdot i\right) \]

      7. distribute-lft-in 53.9%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      8. +-commutative 53.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 53.9%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 53.9%

          \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if 1.24999999999999991e-77 < z

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 71.5%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   5. Simplified 71.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+191}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-121} \lor \neg \left(a \leq 3.5 \cdot 10^{+31}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.7e+122)
   (* x (* t (- a)))
   (if (or (<= a -1.8e-121) (not (<= a 3.5e+31)))
     (* b (* a i))
     (* b (- (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.7e+122) {
		tmp = x * (t * -a);
	} else if ((a <= -1.8e-121) || !(a <= 3.5e+31)) {
		tmp = b * (a * i);
	} else {
		tmp = b * -(z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.7d+122)) then
        tmp = x * (t * -a)
    else if ((a <= (-1.8d-121)) .or. (.not. (a <= 3.5d+31))) then
        tmp = b * (a * i)
    else
        tmp = b * -(z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.7e+122) {
		tmp = x * (t * -a);
	} else if ((a <= -1.8e-121) || !(a <= 3.5e+31)) {
		tmp = b * (a * i);
	} else {
		tmp = b * -(z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.7e+122:
		tmp = x * (t * -a)
	elif (a <= -1.8e-121) or not (a <= 3.5e+31):
		tmp = b * (a * i)
	else:
		tmp = b * -(z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.7e+122)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif ((a <= -1.8e-121) || !(a <= 3.5e+31))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(b * Float64(-Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.7e+122)
		tmp = x * (t * -a);
	elseif ((a <= -1.8e-121) || ~((a <= 3.5e+31)))
		tmp = b * (a * i);
	else
		tmp = b * -(z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.7e+122], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.8e-121], N[Not[LessEqual[a, 3.5e+31]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6999999999999998e122

   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. Step-by-step derivation

      1. +-commutative 65.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 70.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 70.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 70.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 70.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 70.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 70.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 70.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 70.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 70.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 70.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 70.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 55.4%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around inf 46.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 49.0%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-lft-neg-out 49.0%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} \]

      4. *-commutative 49.0%

         \[\leadsto \color{blue}{x \cdot \left(-a \cdot t\right)} \]

      5. *-commutative 49.0%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      6. distribute-rgt-neg-in 49.0%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-a\right)\right)} \]

   if -2.6999999999999998e122 < a < -1.79999999999999992e-121 or 3.5e31 < a

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 41.1%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -1.79999999999999992e-121 < a < 3.5e31

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around 0 38.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 38.7%

         \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

      3. distribute-rgt-neg-in 38.7%

         \[\leadsto \color{blue}{b \cdot \left(-z \cdot c\right)} \]

      4. *-commutative 38.7%

         \[\leadsto b \cdot \left(-\color{blue}{c \cdot z}\right) \]

      5. distribute-rgt-neg-in 38.7%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   8. Simplified 38.7%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-121} \lor \neg \left(a \leq 3.5 \cdot 10^{+31}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+158} \lor \neg \left(c \leq 3500000\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8.2e+158) (not (<= c 3500000.0)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8.2e+158) || !(c <= 3500000.0)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-8.2d+158)) .or. (.not. (c <= 3500000.0d0))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8.2e+158) || !(c <= 3500000.0)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -8.2e+158) or not (c <= 3500000.0):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -8.2e+158) || !(c <= 3500000.0))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -8.2e+158) || ~((c <= 3500000.0)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -8.2e+158], N[Not[LessEqual[c, 3500000.0]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.20000000000000008e158 or 3.5e6 < c

   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 c around inf 65.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 65.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 65.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 65.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -8.20000000000000008e158 < c < 3.5e6

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 60.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. +-commutative 60.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 60.9%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 61.5%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 61.5%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 61.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 61.5%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. associate-*r* 54.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. *-commutative 54.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot a\right)} \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. associate-*l* 56.8%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 56.8%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 56.8%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 57.5%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 57.5%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 57.5%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 57.5%

          \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 57.5%

          \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      17. *-commutative 57.5%

          \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 57.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in c around 0 50.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.8%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. neg-mul-1 50.8%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \color{blue}{\left(-a\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub 50.8%

         \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. mul-1-neg 50.8%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. distribute-rgt-neg-in 50.8%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} + a \cdot \left(b \cdot i\right) \]

      6. mul-1-neg 50.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} + a \cdot \left(b \cdot i\right) \]

      7. distribute-lft-in 52.9%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      8. +-commutative 52.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 52.9%

          \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+158} \lor \neg \left(c \leq 3500000\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+125} \lor \neg \left(z \leq 1.55 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -9.5e+125) (not (<= z 1.55e-11))) (* y (* x z)) (* b (* a 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+125) || !(z <= 1.55e-11)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * 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+125)) .or. (.not. (z <= 1.55d-11))) then
        tmp = y * (x * z)
    else
        tmp = b * (a * 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+125) || !(z <= 1.55e-11)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -9.5e+125) or not (z <= 1.55e-11):
		tmp = y * (x * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -9.5e+125) || !(z <= 1.55e-11))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(a * 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+125) || ~((z <= 1.55e-11)))
		tmp = y * (x * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -9.5e+125], N[Not[LessEqual[z, 1.55e-11]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000041e125 or 1.55000000000000014e-11 < z

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 58.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 58.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 43.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 47.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 47.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -9.50000000000000041e125 < z < 1.55000000000000014e-11

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 31.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+125} \lor \neg \left(z \leq 1.55 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+197} \lor \neg \left(z \leq 4.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.4e+197) (not (<= z 4.4e-13))) (* x (* y z)) (* b (* a 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 <= -1.4e+197) || !(z <= 4.4e-13)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * 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 <= (-1.4d+197)) .or. (.not. (z <= 4.4d-13))) then
        tmp = x * (y * z)
    else
        tmp = b * (a * 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 <= -1.4e+197) || !(z <= 4.4e-13)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -1.4e+197) or not (z <= 4.4e-13):
		tmp = x * (y * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.4e+197) || !(z <= 4.4e-13))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -1.4e+197) || ~((z <= 4.4e-13)))
		tmp = x * (y * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -1.4e+197], N[Not[LessEqual[z, 4.4e-13]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e197 or 4.39999999999999993e-13 < z

   1. Initial program 65.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.4%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around 0 48.3%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Simplified 48.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -1.3999999999999999e197 < z < 4.39999999999999993e-13

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 44.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 30.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+197} \lor \neg \left(z \leq 4.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+106} \lor \neg \left(c \leq 920000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4.2e+106) (not (<= c 920000.0))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.2e+106) || !(c <= 920000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-4.2d+106)) .or. (.not. (c <= 920000.0d0))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.2e+106) || !(c <= 920000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -4.2e+106) or not (c <= 920000.0):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -4.2e+106) || !(c <= 920000.0))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -4.2e+106) || ~((c <= 920000.0)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -4.2e+106], N[Not[LessEqual[c, 920000.0]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.2000000000000001e106 or 9.2e5 < c

   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 t around inf 43.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 43.0%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 43.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 43.0%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 43.0%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 43.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 35.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 35.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.2000000000000001e106 < c < 9.2e5

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 33.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+106} \lor \neg \left(c \leq 920000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -9e+125)
   (* y (* x z))
   (if (<= z 2.05e-11) (* b (* a i)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9e+125) {
		tmp = y * (x * z);
	} else if (z <= 2.05e-11) {
		tmp = b * (a * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-9d+125)) then
        tmp = y * (x * z)
    else if (z <= 2.05d-11) then
        tmp = b * (a * i)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9e+125) {
		tmp = y * (x * z);
	} else if (z <= 2.05e-11) {
		tmp = b * (a * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -9e+125:
		tmp = y * (x * z)
	elif z <= 2.05e-11:
		tmp = b * (a * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -9e+125)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 2.05e-11)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -9e+125)
		tmp = y * (x * z);
	elseif (z <= 2.05e-11)
		tmp = b * (a * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -9e+125], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-11], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.0000000000000001e125

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 64.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 64.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 64.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 53.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 55.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 55.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -9.0000000000000001e125 < z < 2.05e-11

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 31.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 2.05e-11 < z

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 64.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 64.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 64.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 68.7%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 73.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 73.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 73.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 73.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 73.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 38.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 44.9%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   8. Simplified 44.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = b * (a * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. 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%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 44.4%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 26.2%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
7. Add Preprocessing

Alternative 26: 22.1% 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 72.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. 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%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 44.4%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 24.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Add Preprocessing

Developer target: 69.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024103 
(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)))))