Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 82.5%

Time: 16.3s

Alternatives: 19

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: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(b * N[(a - N[(j * N[(y / b), $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 92.2%

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

   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 i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in b around inf 54.8%

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

      1. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

      1. pow1 52.7%

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

      2. mul-1-neg 52.7%

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

   10. Applied egg-rr 52.7%

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

       1. unpow1 52.7%

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

       2. distribute-lft-neg-in 52.7%

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

   12. Simplified 52.7%

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

4. Final simplification 85.1%

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

Alternative 2: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;c \leq -850000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.9 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+58}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= c -850000.0)
     (* c (- (* t j) (* z b)))
     (if (<= c 4.4e-181)
       t_2
       (if (<= c 1.65e-155)
         t_1
         (if (<= c 7.9e-109)
           (* b (- (* a i) (* z c)))
           (if (<= c 1.7e-61)
             t_1
             (if (<= c 1.55e-22)
               t_2
               (if (<= c 9.2e+58)
                 (* (* x y) (- z (* a (/ t y))))
                 (- (* j (* t c)) (* 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 t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (c <= -850000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= 4.4e-181) {
		tmp = t_2;
	} else if (c <= 1.65e-155) {
		tmp = t_1;
	} else if (c <= 7.9e-109) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 1.7e-61) {
		tmp = t_1;
	} else if (c <= 1.55e-22) {
		tmp = t_2;
	} else if (c <= 9.2e+58) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else {
		tmp = (j * (t * c)) - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((a * b) - (y * j))
    if (c <= (-850000.0d0)) then
        tmp = c * ((t * j) - (z * b))
    else if (c <= 4.4d-181) then
        tmp = t_2
    else if (c <= 1.65d-155) then
        tmp = t_1
    else if (c <= 7.9d-109) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 1.7d-61) then
        tmp = t_1
    else if (c <= 1.55d-22) then
        tmp = t_2
    else if (c <= 9.2d+58) then
        tmp = (x * y) * (z - (a * (t / y)))
    else
        tmp = (j * (t * c)) - (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 t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (c <= -850000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= 4.4e-181) {
		tmp = t_2;
	} else if (c <= 1.65e-155) {
		tmp = t_1;
	} else if (c <= 7.9e-109) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 1.7e-61) {
		tmp = t_1;
	} else if (c <= 1.55e-22) {
		tmp = t_2;
	} else if (c <= 9.2e+58) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else {
		tmp = (j * (t * c)) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if c <= -850000.0:
		tmp = c * ((t * j) - (z * b))
	elif c <= 4.4e-181:
		tmp = t_2
	elif c <= 1.65e-155:
		tmp = t_1
	elif c <= 7.9e-109:
		tmp = b * ((a * i) - (z * c))
	elif c <= 1.7e-61:
		tmp = t_1
	elif c <= 1.55e-22:
		tmp = t_2
	elif c <= 9.2e+58:
		tmp = (x * y) * (z - (a * (t / y)))
	else:
		tmp = (j * (t * c)) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (c <= -850000.0)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (c <= 4.4e-181)
		tmp = t_2;
	elseif (c <= 1.65e-155)
		tmp = t_1;
	elseif (c <= 7.9e-109)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 1.7e-61)
		tmp = t_1;
	elseif (c <= 1.55e-22)
		tmp = t_2;
	elseif (c <= 9.2e+58)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	else
		tmp = Float64(Float64(j * Float64(t * c)) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (c <= -850000.0)
		tmp = c * ((t * j) - (z * b));
	elseif (c <= 4.4e-181)
		tmp = t_2;
	elseif (c <= 1.65e-155)
		tmp = t_1;
	elseif (c <= 7.9e-109)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 1.7e-61)
		tmp = t_1;
	elseif (c <= 1.55e-22)
		tmp = t_2;
	elseif (c <= 9.2e+58)
		tmp = (x * y) * (z - (a * (t / y)));
	else
		tmp = (j * (t * c)) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -850000.0], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.4e-181], t$95$2, If[LessEqual[c, 1.65e-155], t$95$1, If[LessEqual[c, 7.9e-109], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-61], t$95$1, If[LessEqual[c, 1.55e-22], t$95$2, If[LessEqual[c, 9.2e+58], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -8.5e5

   1. Initial program 73.7%

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

   3. Taylor expanded in c around inf 77.1%

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

      1. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   if -8.5e5 < c < 4.39999999999999994e-181 or 1.6999999999999999e-61 < c < 1.55000000000000006e-22

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.0%

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

      2. fma-define 75.1%

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

      3. *-commutative 75.1%

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

      4. *-commutative 75.1%

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

      5. cancel-sign-sub-inv 75.1%

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

      6. cancel-sign-sub 75.1%

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

      7. sub-neg 75.1%

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

      8. sub-neg 75.1%

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

      9. *-commutative 75.1%

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

      10. fma-neg 75.1%

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

      11. *-commutative 75.1%

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

      12. distribute-rgt-neg-out 75.1%

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

      13. remove-double-neg 75.1%

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

      14. *-commutative 75.1%

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

      15. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in b around inf 75.1%

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

      1. fma-define 76.2%

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

      2. associate-/l* 71.0%

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

      3. +-commutative 71.0%

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

      4. mul-1-neg 71.0%

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

      5. sub-neg 71.0%

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

      6. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in i around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. *-commutative 67.1%

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

      3. mul-1-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. unsub-neg 67.1%

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

      6. *-commutative 67.1%

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

   10. Simplified 67.1%

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

   if 4.39999999999999994e-181 < c < 1.64999999999999993e-155 or 7.8999999999999997e-109 < c < 1.6999999999999999e-61

   1. Initial program 93.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 93.7%

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

      2. fma-define 93.7%

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

      3. *-commutative 93.7%

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

      4. *-commutative 93.7%

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

      5. cancel-sign-sub-inv 93.7%

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

      6. cancel-sign-sub 93.7%

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

      7. sub-neg 93.7%

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

      8. sub-neg 93.7%

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

      9. *-commutative 93.7%

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

      10. fma-neg 93.7%

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

      11. *-commutative 93.7%

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

      12. distribute-rgt-neg-out 93.7%

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

      13. remove-double-neg 93.7%

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

      14. *-commutative 93.7%

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

      15. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf 72.0%

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

   if 1.64999999999999993e-155 < c < 7.8999999999999997e-109

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if 1.55000000000000006e-22 < c < 9.2000000000000001e58

   1. Initial program 82.6%

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

   3. Taylor expanded in y around -inf 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in x around inf 65.6%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. mul-1-neg 71.1%

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

      4. unsub-neg 71.1%

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

      5. associate-/l* 71.1%

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

   8. Simplified 71.1%

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

   if 9.2000000000000001e58 < c

   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 71.4%

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

   4. Taylor expanded in a around 0 64.7%

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

      1. *-commutative 64.7%

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

      2. associate-*r* 62.1%

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

      3. *-commutative 62.1%

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

      4. *-commutative 62.1%

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

   6. Simplified 62.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -850000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-181}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 7.9 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+58}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -38000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.36 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -38000.0)
     t_3
     (if (<= c 4e-181)
       t_2
       (if (<= c 1.55e-155)
         t_1
         (if (<= c 4.5e-107)
           (* b (- (* a i) (* z c)))
           (if (<= c 2.6e-65)
             t_1
             (if (<= c 1.36e-20)
               t_2
               (if (<= c 9e+99) (* z (- (* x y) (* b c))) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -38000.0) {
		tmp = t_3;
	} else if (c <= 4e-181) {
		tmp = t_2;
	} else if (c <= 1.55e-155) {
		tmp = t_1;
	} else if (c <= 4.5e-107) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 2.6e-65) {
		tmp = t_1;
	} else if (c <= 1.36e-20) {
		tmp = t_2;
	} else if (c <= 9e+99) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((a * b) - (y * j))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-38000.0d0)) then
        tmp = t_3
    else if (c <= 4d-181) then
        tmp = t_2
    else if (c <= 1.55d-155) then
        tmp = t_1
    else if (c <= 4.5d-107) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 2.6d-65) then
        tmp = t_1
    else if (c <= 1.36d-20) then
        tmp = t_2
    else if (c <= 9d+99) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -38000.0) {
		tmp = t_3;
	} else if (c <= 4e-181) {
		tmp = t_2;
	} else if (c <= 1.55e-155) {
		tmp = t_1;
	} else if (c <= 4.5e-107) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 2.6e-65) {
		tmp = t_1;
	} else if (c <= 1.36e-20) {
		tmp = t_2;
	} else if (c <= 9e+99) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((a * b) - (y * j))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -38000.0:
		tmp = t_3
	elif c <= 4e-181:
		tmp = t_2
	elif c <= 1.55e-155:
		tmp = t_1
	elif c <= 4.5e-107:
		tmp = b * ((a * i) - (z * c))
	elif c <= 2.6e-65:
		tmp = t_1
	elif c <= 1.36e-20:
		tmp = t_2
	elif c <= 9e+99:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -38000.0)
		tmp = t_3;
	elseif (c <= 4e-181)
		tmp = t_2;
	elseif (c <= 1.55e-155)
		tmp = t_1;
	elseif (c <= 4.5e-107)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 2.6e-65)
		tmp = t_1;
	elseif (c <= 1.36e-20)
		tmp = t_2;
	elseif (c <= 9e+99)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((a * b) - (y * j));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -38000.0)
		tmp = t_3;
	elseif (c <= 4e-181)
		tmp = t_2;
	elseif (c <= 1.55e-155)
		tmp = t_1;
	elseif (c <= 4.5e-107)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 2.6e-65)
		tmp = t_1;
	elseif (c <= 1.36e-20)
		tmp = t_2;
	elseif (c <= 9e+99)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -38000.0], t$95$3, If[LessEqual[c, 4e-181], t$95$2, If[LessEqual[c, 1.55e-155], t$95$1, If[LessEqual[c, 4.5e-107], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e-65], t$95$1, If[LessEqual[c, 1.36e-20], t$95$2, If[LessEqual[c, 9e+99], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -38000 or 8.9999999999999999e99 < c

   1. Initial program 71.6%

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

   3. Taylor expanded in c around inf 70.8%

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

      1. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   if -38000 < c < 4.00000000000000019e-181 or 2.6000000000000001e-65 < c < 1.36e-20

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.0%

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

      2. fma-define 75.1%

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

      3. *-commutative 75.1%

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

      4. *-commutative 75.1%

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

      5. cancel-sign-sub-inv 75.1%

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

      6. cancel-sign-sub 75.1%

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

      7. sub-neg 75.1%

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

      8. sub-neg 75.1%

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

      9. *-commutative 75.1%

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

      10. fma-neg 75.1%

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

      11. *-commutative 75.1%

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

      12. distribute-rgt-neg-out 75.1%

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

      13. remove-double-neg 75.1%

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

      14. *-commutative 75.1%

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

      15. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in b around inf 75.1%

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

      1. fma-define 76.2%

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

      2. associate-/l* 71.0%

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

      3. +-commutative 71.0%

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

      4. mul-1-neg 71.0%

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

      5. sub-neg 71.0%

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

      6. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in i around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. *-commutative 67.1%

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

      3. mul-1-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. unsub-neg 67.1%

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

      6. *-commutative 67.1%

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

   10. Simplified 67.1%

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

   if 4.00000000000000019e-181 < c < 1.55e-155 or 4.50000000000000016e-107 < c < 2.6000000000000001e-65

   1. Initial program 93.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 93.7%

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

      2. fma-define 93.7%

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

      3. *-commutative 93.7%

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

      4. *-commutative 93.7%

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

      5. cancel-sign-sub-inv 93.7%

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

      6. cancel-sign-sub 93.7%

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

      7. sub-neg 93.7%

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

      8. sub-neg 93.7%

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

      9. *-commutative 93.7%

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

      10. fma-neg 93.7%

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

      11. *-commutative 93.7%

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

      12. distribute-rgt-neg-out 93.7%

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

      13. remove-double-neg 93.7%

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

      14. *-commutative 93.7%

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

      15. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf 72.0%

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

   if 1.55e-155 < c < 4.50000000000000016e-107

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if 1.36e-20 < c < 8.9999999999999999e99

   1. Initial program 84.1%

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

   3. Taylor expanded in z around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -38000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-181}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.36 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot \left(z - a \cdot \frac{t}{y}\right)\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* b (- (* a i) (* z c)))))
        (t_2 (* x (* y (- z (* a (/ t y)))))))
   (if (<= x -7.2e+202)
     t_2
     (if (<= x -4.6e+143)
       t_1
       (if (<= x -6.6e+97)
         t_2
         (if (<= x 3.7e+140) t_1 (* x (- (* y z) (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	double t_2 = x * (y * (z - (a * (t / y))));
	double tmp;
	if (x <= -7.2e+202) {
		tmp = t_2;
	} else if (x <= -4.6e+143) {
		tmp = t_1;
	} else if (x <= -6.6e+97) {
		tmp = t_2;
	} else if (x <= 3.7e+140) {
		tmp = t_1;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
    t_2 = x * (y * (z - (a * (t / y))))
    if (x <= (-7.2d+202)) then
        tmp = t_2
    else if (x <= (-4.6d+143)) then
        tmp = t_1
    else if (x <= (-6.6d+97)) then
        tmp = t_2
    else if (x <= 3.7d+140) then
        tmp = t_1
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	double t_2 = x * (y * (z - (a * (t / y))));
	double tmp;
	if (x <= -7.2e+202) {
		tmp = t_2;
	} else if (x <= -4.6e+143) {
		tmp = t_1;
	} else if (x <= -6.6e+97) {
		tmp = t_2;
	} else if (x <= 3.7e+140) {
		tmp = t_1;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
	t_2 = x * (y * (z - (a * (t / y))))
	tmp = 0
	if x <= -7.2e+202:
		tmp = t_2
	elif x <= -4.6e+143:
		tmp = t_1
	elif x <= -6.6e+97:
		tmp = t_2
	elif x <= 3.7e+140:
		tmp = t_1
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(x * Float64(y * Float64(z - Float64(a * Float64(t / y)))))
	tmp = 0.0
	if (x <= -7.2e+202)
		tmp = t_2;
	elseif (x <= -4.6e+143)
		tmp = t_1;
	elseif (x <= -6.6e+97)
		tmp = t_2;
	elseif (x <= 3.7e+140)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	t_2 = x * (y * (z - (a * (t / y))));
	tmp = 0.0;
	if (x <= -7.2e+202)
		tmp = t_2;
	elseif (x <= -4.6e+143)
		tmp = t_1;
	elseif (x <= -6.6e+97)
		tmp = t_2;
	elseif (x <= 3.7e+140)
		tmp = t_1;
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+202], t$95$2, If[LessEqual[x, -4.6e+143], t$95$1, If[LessEqual[x, -6.6e+97], t$95$2, If[LessEqual[x, 3.7e+140], t$95$1, N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.20000000000000016e202 or -4.5999999999999999e143 < x < -6.6000000000000003e97

   1. Initial program 83.3%

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

   3. Taylor expanded in y around -inf 64.1%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. associate-/l* 84.1%

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

   8. Simplified 84.1%

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

   if -7.20000000000000016e202 < x < -4.5999999999999999e143 or -6.6000000000000003e97 < x < 3.70000000000000003e140

   1. Initial program 74.8%

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

   3. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if 3.70000000000000003e140 < x

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.7%

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

      2. fma-define 78.9%

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

      3. *-commutative 78.9%

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

      4. *-commutative 78.9%

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

      5. cancel-sign-sub-inv 78.9%

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

      6. cancel-sign-sub 78.9%

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

      7. sub-neg 78.9%

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

      8. sub-neg 78.9%

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

      9. *-commutative 78.9%

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

      10. fma-neg 78.9%

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

      11. *-commutative 78.9%

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

      12. distribute-rgt-neg-out 78.9%

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

      13. remove-double-neg 78.9%

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

      14. *-commutative 78.9%

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

      15. *-commutative 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around inf 76.5%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - a \cdot \frac{t}{y}\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - a \cdot \frac{t}{y}\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+140}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;c \leq -1350000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(y \cdot \left(\frac{b \cdot i}{y} - t \cdot \frac{x}{y}\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= c -1350000.0)
     (* c (- (* t j) (* z b)))
     (if (<= c 4.3e-188)
       t_1
       (if (<= c 2.25e-63)
         (* a (* y (- (/ (* b i) y) (* t (/ x y)))))
         (if (<= c 1.75e-21)
           t_1
           (if (<= c 6.6e+59)
             (* (* x y) (- z (* a (/ t y))))
             (- (* j (* t c)) (* 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 t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (c <= -1350000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= 4.3e-188) {
		tmp = t_1;
	} else if (c <= 2.25e-63) {
		tmp = a * (y * (((b * i) / y) - (t * (x / y))));
	} else if (c <= 1.75e-21) {
		tmp = t_1;
	} else if (c <= 6.6e+59) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else {
		tmp = (j * (t * c)) - (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) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (c <= (-1350000.0d0)) then
        tmp = c * ((t * j) - (z * b))
    else if (c <= 4.3d-188) then
        tmp = t_1
    else if (c <= 2.25d-63) then
        tmp = a * (y * (((b * i) / y) - (t * (x / y))))
    else if (c <= 1.75d-21) then
        tmp = t_1
    else if (c <= 6.6d+59) then
        tmp = (x * y) * (z - (a * (t / y)))
    else
        tmp = (j * (t * c)) - (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 t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (c <= -1350000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= 4.3e-188) {
		tmp = t_1;
	} else if (c <= 2.25e-63) {
		tmp = a * (y * (((b * i) / y) - (t * (x / y))));
	} else if (c <= 1.75e-21) {
		tmp = t_1;
	} else if (c <= 6.6e+59) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else {
		tmp = (j * (t * c)) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if c <= -1350000.0:
		tmp = c * ((t * j) - (z * b))
	elif c <= 4.3e-188:
		tmp = t_1
	elif c <= 2.25e-63:
		tmp = a * (y * (((b * i) / y) - (t * (x / y))))
	elif c <= 1.75e-21:
		tmp = t_1
	elif c <= 6.6e+59:
		tmp = (x * y) * (z - (a * (t / y)))
	else:
		tmp = (j * (t * c)) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (c <= -1350000.0)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (c <= 4.3e-188)
		tmp = t_1;
	elseif (c <= 2.25e-63)
		tmp = Float64(a * Float64(y * Float64(Float64(Float64(b * i) / y) - Float64(t * Float64(x / y)))));
	elseif (c <= 1.75e-21)
		tmp = t_1;
	elseif (c <= 6.6e+59)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	else
		tmp = Float64(Float64(j * Float64(t * c)) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (c <= -1350000.0)
		tmp = c * ((t * j) - (z * b));
	elseif (c <= 4.3e-188)
		tmp = t_1;
	elseif (c <= 2.25e-63)
		tmp = a * (y * (((b * i) / y) - (t * (x / y))));
	elseif (c <= 1.75e-21)
		tmp = t_1;
	elseif (c <= 6.6e+59)
		tmp = (x * y) * (z - (a * (t / y)));
	else
		tmp = (j * (t * c)) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1350000.0], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.3e-188], t$95$1, If[LessEqual[c, 2.25e-63], N[(a * N[(y * N[(N[(N[(b * i), $MachinePrecision] / y), $MachinePrecision] - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-21], t$95$1, If[LessEqual[c, 6.6e+59], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.35e6

   1. Initial program 73.7%

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

   3. Taylor expanded in c around inf 77.1%

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

      1. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   if -1.35e6 < c < 4.29999999999999988e-188 or 2.25e-63 < c < 1.7500000000000002e-21

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.5%

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

      2. fma-define 74.5%

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

      3. *-commutative 74.5%

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

      4. *-commutative 74.5%

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

      5. cancel-sign-sub-inv 74.5%

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

      6. cancel-sign-sub 74.5%

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

      7. sub-neg 74.5%

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

      8. sub-neg 74.5%

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

      9. *-commutative 74.5%

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

      10. fma-neg 74.5%

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

      11. *-commutative 74.5%

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

      12. distribute-rgt-neg-out 74.5%

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

      13. remove-double-neg 74.5%

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

      14. *-commutative 74.5%

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

      15. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in b around inf 74.6%

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

      1. fma-define 75.7%

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

      2. associate-/l* 72.5%

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

      3. +-commutative 72.5%

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

      4. mul-1-neg 72.5%

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

      5. sub-neg 72.5%

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

      6. *-commutative 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in i around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. mul-1-neg 67.4%

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

      4. *-commutative 67.4%

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

      5. unsub-neg 67.4%

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

      6. *-commutative 67.4%

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

   10. Simplified 67.4%

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

   if 4.29999999999999988e-188 < c < 2.25e-63

   1. Initial program 89.8%

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

   3. Taylor expanded in y around -inf 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in a around -inf 52.9%

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

      1. associate-/l* 52.9%

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

   8. Simplified 52.9%

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

   if 1.7500000000000002e-21 < c < 6.5999999999999999e59

   1. Initial program 82.6%

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

   3. Taylor expanded in y around -inf 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in x around inf 65.6%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. mul-1-neg 71.1%

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

      4. unsub-neg 71.1%

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

      5. associate-/l* 71.1%

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

   8. Simplified 71.1%

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

   if 6.5999999999999999e59 < c

   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 71.4%

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

   4. Taylor expanded in a around 0 64.7%

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

      1. *-commutative 64.7%

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

      2. associate-*r* 62.1%

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

      3. *-commutative 62.1%

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

      4. *-commutative 62.1%

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

   6. Simplified 62.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1350000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-188}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(y \cdot \left(\frac{b \cdot i}{y} - t \cdot \frac{x}{y}\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -25:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* t (* c j))))
   (if (<= c -2.45e+60)
     t_2
     (if (<= c -25.0)
       (* b (* z (- c)))
       (if (<= c -2.2e-112)
         t_1
         (if (<= c 3.5e-108)
           (* i (* a b))
           (if (<= c 2.65e-8)
             (* t (* x (- a)))
             (if (<= c 5.5e+61) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -2.45e+60) {
		tmp = t_2;
	} else if (c <= -25.0) {
		tmp = b * (z * -c);
	} else if (c <= -2.2e-112) {
		tmp = t_1;
	} else if (c <= 3.5e-108) {
		tmp = i * (a * b);
	} else if (c <= 2.65e-8) {
		tmp = t * (x * -a);
	} else if (c <= 5.5e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = t * (c * j)
    if (c <= (-2.45d+60)) then
        tmp = t_2
    else if (c <= (-25.0d0)) then
        tmp = b * (z * -c)
    else if (c <= (-2.2d-112)) then
        tmp = t_1
    else if (c <= 3.5d-108) then
        tmp = i * (a * b)
    else if (c <= 2.65d-8) then
        tmp = t * (x * -a)
    else if (c <= 5.5d+61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -2.45e+60) {
		tmp = t_2;
	} else if (c <= -25.0) {
		tmp = b * (z * -c);
	} else if (c <= -2.2e-112) {
		tmp = t_1;
	} else if (c <= 3.5e-108) {
		tmp = i * (a * b);
	} else if (c <= 2.65e-8) {
		tmp = t * (x * -a);
	} else if (c <= 5.5e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = t * (c * j)
	tmp = 0
	if c <= -2.45e+60:
		tmp = t_2
	elif c <= -25.0:
		tmp = b * (z * -c)
	elif c <= -2.2e-112:
		tmp = t_1
	elif c <= 3.5e-108:
		tmp = i * (a * b)
	elif c <= 2.65e-8:
		tmp = t * (x * -a)
	elif c <= 5.5e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -2.45e+60)
		tmp = t_2;
	elseif (c <= -25.0)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -2.2e-112)
		tmp = t_1;
	elseif (c <= 3.5e-108)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 2.65e-8)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 5.5e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = t * (c * j);
	tmp = 0.0;
	if (c <= -2.45e+60)
		tmp = t_2;
	elseif (c <= -25.0)
		tmp = b * (z * -c);
	elseif (c <= -2.2e-112)
		tmp = t_1;
	elseif (c <= 3.5e-108)
		tmp = i * (a * b);
	elseif (c <= 2.65e-8)
		tmp = t * (x * -a);
	elseif (c <= 5.5e+61)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.45e+60], t$95$2, If[LessEqual[c, -25.0], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.2e-112], t$95$1, If[LessEqual[c, 3.5e-108], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.65e-8], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e+61], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.4500000000000001e60 or 5.50000000000000036e61 < c

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in j around inf 47.1%

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

   if -2.4500000000000001e60 < c < -25

   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 85.5%

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

      1. *-commutative 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in i around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. *-commutative 71.6%

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

   8. Simplified 71.6%

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

   if -25 < c < -2.20000000000000021e-112 or 2.6499999999999999e-8 < c < 5.50000000000000036e61

   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 69.7%

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

      1. *-commutative 69.7%

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

      2. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in y around inf 53.7%

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

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if -2.20000000000000021e-112 < c < 3.4999999999999999e-108

   1. Initial program 80.6%

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

   3. Taylor expanded in i around inf 61.7%

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

      1. distribute-lft-out-- 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in b around inf 59.6%

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

      1. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

      1. pow1 58.4%

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

      2. mul-1-neg 58.4%

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

   10. Applied egg-rr 58.4%

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

       1. unpow1 58.4%

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

       2. distribute-lft-neg-in 58.4%

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

   12. Simplified 58.4%

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

   13. Taylor expanded in b around inf 36.5%

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

       1. *-commutative 36.5%

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

       2. *-commutative 36.5%

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

       3. associate-*r* 39.8%

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

   15. Simplified 39.8%

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

   if 3.4999999999999999e-108 < c < 2.6499999999999999e-8

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in j around 0 37.4%

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

      1. neg-mul-1 37.4%

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

      2. *-commutative 37.4%

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

      3. distribute-rgt-neg-in 37.4%

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

   8. Simplified 37.4%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -25:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-112}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -7000000.0)
     t_2
     (if (<= c 1.1e-105)
       t_1
       (if (<= c 1.35e-65)
         (* t (- (* c j) (* x a)))
         (if (<= c 4.2e-21)
           t_1
           (if (<= c 3.9e+100) (* z (- (* x y) (* b c))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -7000000.0) {
		tmp = t_2;
	} else if (c <= 1.1e-105) {
		tmp = t_1;
	} else if (c <= 1.35e-65) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 4.2e-21) {
		tmp = t_1;
	} else if (c <= 3.9e+100) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-7000000.0d0)) then
        tmp = t_2
    else if (c <= 1.1d-105) then
        tmp = t_1
    else if (c <= 1.35d-65) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 4.2d-21) then
        tmp = t_1
    else if (c <= 3.9d+100) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -7000000.0) {
		tmp = t_2;
	} else if (c <= 1.1e-105) {
		tmp = t_1;
	} else if (c <= 1.35e-65) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 4.2e-21) {
		tmp = t_1;
	} else if (c <= 3.9e+100) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -7000000.0:
		tmp = t_2
	elif c <= 1.1e-105:
		tmp = t_1
	elif c <= 1.35e-65:
		tmp = t * ((c * j) - (x * a))
	elif c <= 4.2e-21:
		tmp = t_1
	elif c <= 3.9e+100:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7000000.0)
		tmp = t_2;
	elseif (c <= 1.1e-105)
		tmp = t_1;
	elseif (c <= 1.35e-65)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 4.2e-21)
		tmp = t_1;
	elseif (c <= 3.9e+100)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -7000000.0)
		tmp = t_2;
	elseif (c <= 1.1e-105)
		tmp = t_1;
	elseif (c <= 1.35e-65)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 4.2e-21)
		tmp = t_1;
	elseif (c <= 3.9e+100)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7000000.0], t$95$2, If[LessEqual[c, 1.1e-105], t$95$1, If[LessEqual[c, 1.35e-65], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e-21], t$95$1, If[LessEqual[c, 3.9e+100], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7e6 or 3.9e100 < c

   1. Initial program 71.6%

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

   3. Taylor expanded in c around inf 70.8%

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

      1. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   if -7e6 < c < 1.10000000000000002e-105 or 1.3499999999999999e-65 < c < 4.20000000000000025e-21

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.3%

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

      2. fma-define 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

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

      5. cancel-sign-sub-inv 77.2%

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

      6. cancel-sign-sub 77.2%

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

      7. sub-neg 77.2%

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

      8. sub-neg 77.2%

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

      9. *-commutative 77.2%

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

      10. fma-neg 77.2%

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

      11. *-commutative 77.2%

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

      12. distribute-rgt-neg-out 77.2%

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

      13. remove-double-neg 77.2%

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

      14. *-commutative 77.2%

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

      15. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in b around inf 76.4%

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

      1. fma-define 77.4%

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

      2. associate-/l* 72.1%

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

      3. +-commutative 72.1%

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

      4. mul-1-neg 72.1%

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

      5. sub-neg 72.1%

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

      6. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in i around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. *-commutative 62.7%

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

      3. mul-1-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. unsub-neg 62.7%

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

      6. *-commutative 62.7%

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

   10. Simplified 62.7%

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

   if 1.10000000000000002e-105 < c < 1.3499999999999999e-65

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if 4.20000000000000025e-21 < c < 3.9e100

   1. Initial program 84.1%

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

   3. Taylor expanded in z around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-21}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+100}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -29000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -29000000.0)
     t_2
     (if (<= c 2.65e-107)
       t_1
       (if (<= c 5e-67)
         (* t (- (* c j) (* x a)))
         (if (<= c 1.85e-26)
           t_1
           (if (<= c 8e+58) (* y (- (* x z) (* i j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -29000000.0) {
		tmp = t_2;
	} else if (c <= 2.65e-107) {
		tmp = t_1;
	} else if (c <= 5e-67) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 1.85e-26) {
		tmp = t_1;
	} else if (c <= 8e+58) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-29000000.0d0)) then
        tmp = t_2
    else if (c <= 2.65d-107) then
        tmp = t_1
    else if (c <= 5d-67) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 1.85d-26) then
        tmp = t_1
    else if (c <= 8d+58) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -29000000.0) {
		tmp = t_2;
	} else if (c <= 2.65e-107) {
		tmp = t_1;
	} else if (c <= 5e-67) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 1.85e-26) {
		tmp = t_1;
	} else if (c <= 8e+58) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -29000000.0:
		tmp = t_2
	elif c <= 2.65e-107:
		tmp = t_1
	elif c <= 5e-67:
		tmp = t * ((c * j) - (x * a))
	elif c <= 1.85e-26:
		tmp = t_1
	elif c <= 8e+58:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -29000000.0)
		tmp = t_2;
	elseif (c <= 2.65e-107)
		tmp = t_1;
	elseif (c <= 5e-67)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 1.85e-26)
		tmp = t_1;
	elseif (c <= 8e+58)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -29000000.0)
		tmp = t_2;
	elseif (c <= 2.65e-107)
		tmp = t_1;
	elseif (c <= 5e-67)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 1.85e-26)
		tmp = t_1;
	elseif (c <= 8e+58)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -29000000.0], t$95$2, If[LessEqual[c, 2.65e-107], t$95$1, If[LessEqual[c, 5e-67], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e-26], t$95$1, If[LessEqual[c, 8e+58], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.9e7 or 7.99999999999999955e58 < c

   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 c around inf 70.1%

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

      1. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -2.9e7 < c < 2.65e-107 or 4.9999999999999999e-67 < c < 1.8499999999999999e-26

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.3%

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

      2. fma-define 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

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

      5. cancel-sign-sub-inv 77.2%

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

      6. cancel-sign-sub 77.2%

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

      7. sub-neg 77.2%

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

      8. sub-neg 77.2%

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

      9. *-commutative 77.2%

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

      10. fma-neg 77.2%

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

      11. *-commutative 77.2%

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

      12. distribute-rgt-neg-out 77.2%

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

      13. remove-double-neg 77.2%

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

      14. *-commutative 77.2%

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

      15. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in b around inf 76.4%

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

      1. fma-define 77.4%

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

      2. associate-/l* 72.1%

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

      3. +-commutative 72.1%

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

      4. mul-1-neg 72.1%

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

      5. sub-neg 72.1%

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

      6. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in i around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. *-commutative 62.7%

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

      3. mul-1-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. unsub-neg 62.7%

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

      6. *-commutative 62.7%

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

   10. Simplified 62.7%

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

   if 2.65e-107 < c < 4.9999999999999999e-67

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if 1.8499999999999999e-26 < c < 7.99999999999999955e58

   1. Initial program 82.6%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

   5. Simplified 54.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -29000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -36000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -36000.0)
     t_2
     (if (<= c 1.3e-105)
       t_1
       (if (<= c 1.65e-66)
         (* t (- (* c j) (* x a)))
         (if (<= c 2.05e-25) t_1 (if (<= c 7.8e+58) (* z (* x y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -36000.0) {
		tmp = t_2;
	} else if (c <= 1.3e-105) {
		tmp = t_1;
	} else if (c <= 1.65e-66) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 2.05e-25) {
		tmp = t_1;
	} else if (c <= 7.8e+58) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-36000.0d0)) then
        tmp = t_2
    else if (c <= 1.3d-105) then
        tmp = t_1
    else if (c <= 1.65d-66) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 2.05d-25) then
        tmp = t_1
    else if (c <= 7.8d+58) then
        tmp = z * (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -36000.0) {
		tmp = t_2;
	} else if (c <= 1.3e-105) {
		tmp = t_1;
	} else if (c <= 1.65e-66) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 2.05e-25) {
		tmp = t_1;
	} else if (c <= 7.8e+58) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -36000.0:
		tmp = t_2
	elif c <= 1.3e-105:
		tmp = t_1
	elif c <= 1.65e-66:
		tmp = t * ((c * j) - (x * a))
	elif c <= 2.05e-25:
		tmp = t_1
	elif c <= 7.8e+58:
		tmp = z * (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -36000.0)
		tmp = t_2;
	elseif (c <= 1.3e-105)
		tmp = t_1;
	elseif (c <= 1.65e-66)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 2.05e-25)
		tmp = t_1;
	elseif (c <= 7.8e+58)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -36000.0)
		tmp = t_2;
	elseif (c <= 1.3e-105)
		tmp = t_1;
	elseif (c <= 1.65e-66)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 2.05e-25)
		tmp = t_1;
	elseif (c <= 7.8e+58)
		tmp = z * (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -36000.0], t$95$2, If[LessEqual[c, 1.3e-105], t$95$1, If[LessEqual[c, 1.65e-66], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.05e-25], t$95$1, If[LessEqual[c, 7.8e+58], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -36000 or 7.8000000000000002e58 < c

   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 c around inf 70.1%

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

      1. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -36000 < c < 1.2999999999999999e-105 or 1.6499999999999999e-66 < c < 2.04999999999999994e-25

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.3%

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

      2. fma-define 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

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

      5. cancel-sign-sub-inv 77.2%

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

      6. cancel-sign-sub 77.2%

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

      7. sub-neg 77.2%

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

      8. sub-neg 77.2%

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

      9. *-commutative 77.2%

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

      10. fma-neg 77.2%

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

      11. *-commutative 77.2%

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

      12. distribute-rgt-neg-out 77.2%

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

      13. remove-double-neg 77.2%

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

      14. *-commutative 77.2%

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

      15. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in b around inf 76.4%

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

      1. fma-define 77.4%

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

      2. associate-/l* 72.1%

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

      3. +-commutative 72.1%

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

      4. mul-1-neg 72.1%

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

      5. sub-neg 72.1%

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

      6. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in i around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. *-commutative 62.7%

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

      3. mul-1-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. unsub-neg 62.7%

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

      6. *-commutative 62.7%

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

   10. Simplified 62.7%

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

   if 1.2999999999999999e-105 < c < 1.6499999999999999e-66

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if 2.04999999999999994e-25 < c < 7.8000000000000002e58

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -36000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-105}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-16}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -2.5e+30)
     t_1
     (if (<= c 2.05e-107)
       (* b (- (* a i) (* z c)))
       (if (<= c 1.3e-65)
         (* t (* x (- a)))
         (if (<= c 8.8e-16)
           (* i (* y (- j)))
           (if (<= c 8e+58) (* z (* x y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.5e+30) {
		tmp = t_1;
	} else if (c <= 2.05e-107) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 1.3e-65) {
		tmp = t * (x * -a);
	} else if (c <= 8.8e-16) {
		tmp = i * (y * -j);
	} else if (c <= 8e+58) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-2.5d+30)) then
        tmp = t_1
    else if (c <= 2.05d-107) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 1.3d-65) then
        tmp = t * (x * -a)
    else if (c <= 8.8d-16) then
        tmp = i * (y * -j)
    else if (c <= 8d+58) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.5e+30) {
		tmp = t_1;
	} else if (c <= 2.05e-107) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 1.3e-65) {
		tmp = t * (x * -a);
	} else if (c <= 8.8e-16) {
		tmp = i * (y * -j);
	} else if (c <= 8e+58) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.5e+30:
		tmp = t_1
	elif c <= 2.05e-107:
		tmp = b * ((a * i) - (z * c))
	elif c <= 1.3e-65:
		tmp = t * (x * -a)
	elif c <= 8.8e-16:
		tmp = i * (y * -j)
	elif c <= 8e+58:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.5e+30)
		tmp = t_1;
	elseif (c <= 2.05e-107)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 1.3e-65)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 8.8e-16)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 8e+58)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.5e+30)
		tmp = t_1;
	elseif (c <= 2.05e-107)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 1.3e-65)
		tmp = t * (x * -a);
	elseif (c <= 8.8e-16)
		tmp = i * (y * -j);
	elseif (c <= 8e+58)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+30], t$95$1, If[LessEqual[c, 2.05e-107], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-65], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e-16], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e+58], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.4999999999999999e30 or 7.99999999999999955e58 < c

   1. Initial program 72.2%

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

   3. Taylor expanded in c around inf 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   if -2.4999999999999999e30 < c < 2.05e-107

   1. Initial program 77.4%

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

   3. Taylor expanded in b around inf 45.0%

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

      1. *-commutative 45.0%

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

   5. Simplified 45.0%

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

   if 2.05e-107 < c < 1.30000000000000005e-65

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in j around 0 52.0%

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

      1. neg-mul-1 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

   8. Simplified 52.0%

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

   if 1.30000000000000005e-65 < c < 8.80000000000000001e-16

   1. Initial program 68.2%

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

   3. Taylor expanded in i around inf 83.1%

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

      1. distribute-lft-out-- 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in j around inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. mul-1-neg 51.4%

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

      3. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   if 8.80000000000000001e-16 < c < 7.99999999999999955e58

   1. Initial program 81.5%

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

   3. Taylor expanded in z around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf 57.1%

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

      1. *-commutative 57.1%

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

   8. Simplified 57.1%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-16}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -31.5:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* t (* c j))))
   (if (<= c -2e+48)
     t_2
     (if (<= c -31.5)
       (* b (* z (- c)))
       (if (<= c -3.1e-112)
         t_1
         (if (<= c 1.4e-80) (* i (* a b)) (if (<= c 4e+61) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -2e+48) {
		tmp = t_2;
	} else if (c <= -31.5) {
		tmp = b * (z * -c);
	} else if (c <= -3.1e-112) {
		tmp = t_1;
	} else if (c <= 1.4e-80) {
		tmp = i * (a * b);
	} else if (c <= 4e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = t * (c * j)
    if (c <= (-2d+48)) then
        tmp = t_2
    else if (c <= (-31.5d0)) then
        tmp = b * (z * -c)
    else if (c <= (-3.1d-112)) then
        tmp = t_1
    else if (c <= 1.4d-80) then
        tmp = i * (a * b)
    else if (c <= 4d+61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -2e+48) {
		tmp = t_2;
	} else if (c <= -31.5) {
		tmp = b * (z * -c);
	} else if (c <= -3.1e-112) {
		tmp = t_1;
	} else if (c <= 1.4e-80) {
		tmp = i * (a * b);
	} else if (c <= 4e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = t * (c * j)
	tmp = 0
	if c <= -2e+48:
		tmp = t_2
	elif c <= -31.5:
		tmp = b * (z * -c)
	elif c <= -3.1e-112:
		tmp = t_1
	elif c <= 1.4e-80:
		tmp = i * (a * b)
	elif c <= 4e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -2e+48)
		tmp = t_2;
	elseif (c <= -31.5)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -3.1e-112)
		tmp = t_1;
	elseif (c <= 1.4e-80)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 4e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = t * (c * j);
	tmp = 0.0;
	if (c <= -2e+48)
		tmp = t_2;
	elseif (c <= -31.5)
		tmp = b * (z * -c);
	elseif (c <= -3.1e-112)
		tmp = t_1;
	elseif (c <= 1.4e-80)
		tmp = i * (a * b);
	elseif (c <= 4e+61)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+48], t$95$2, If[LessEqual[c, -31.5], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.1e-112], t$95$1, If[LessEqual[c, 1.4e-80], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e+61], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.00000000000000009e48 or 3.9999999999999998e61 < c

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in j around inf 47.1%

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

   if -2.00000000000000009e48 < c < -31.5

   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 85.5%

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

      1. *-commutative 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in i around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. *-commutative 71.6%

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

   8. Simplified 71.6%

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

   if -31.5 < c < -3.0999999999999998e-112 or 1.39999999999999995e-80 < c < 3.9999999999999998e61

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if -3.0999999999999998e-112 < c < 1.39999999999999995e-80

   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 i around inf 59.0%

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

      1. distribute-lft-out-- 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in b around inf 57.0%

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

      1. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

      1. pow1 55.9%

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

      2. mul-1-neg 55.9%

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

   10. Applied egg-rr 55.9%

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

       1. unpow1 55.9%

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

       2. distribute-lft-neg-in 55.9%

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

   12. Simplified 55.9%

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

   13. Taylor expanded in b around inf 34.2%

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

       1. *-commutative 34.2%

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

       2. *-commutative 34.2%

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

       3. associate-*r* 37.3%

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

   15. Simplified 37.3%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -31.5:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-112}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -70000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -70000.0)
     t_1
     (if (<= c 1.08e-19)
       (* i (- (* a b) (* y j)))
       (if (<= c 7.8e+58) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -70000.0) {
		tmp = t_1;
	} else if (c <= 1.08e-19) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 7.8e+58) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-70000.0d0)) then
        tmp = t_1
    else if (c <= 1.08d-19) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 7.8d+58) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -70000.0) {
		tmp = t_1;
	} else if (c <= 1.08e-19) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 7.8e+58) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -70000.0:
		tmp = t_1
	elif c <= 1.08e-19:
		tmp = i * ((a * b) - (y * j))
	elif c <= 7.8e+58:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -70000.0)
		tmp = t_1;
	elseif (c <= 1.08e-19)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 7.8e+58)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -70000.0)
		tmp = t_1;
	elseif (c <= 1.08e-19)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 7.8e+58)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -70000.0], t$95$1, If[LessEqual[c, 1.08e-19], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.8e+58], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7e4 or 7.8000000000000002e58 < c

   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 c around inf 70.1%

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

      1. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -7e4 < c < 1.08e-19

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.4%

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

      2. fma-define 78.3%

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

      3. *-commutative 78.3%

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

      4. *-commutative 78.3%

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

      5. cancel-sign-sub-inv 78.3%

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

      6. cancel-sign-sub 78.3%

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

      7. sub-neg 78.3%

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

      8. sub-neg 78.3%

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

      9. *-commutative 78.3%

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

      10. fma-neg 78.3%

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

      11. *-commutative 78.3%

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

      12. distribute-rgt-neg-out 78.3%

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

      13. remove-double-neg 78.3%

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

      14. *-commutative 78.3%

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

      15. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 76.0%

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

      1. fma-define 76.9%

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

      2. associate-/l* 72.1%

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

      3. +-commutative 72.1%

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

      4. mul-1-neg 72.1%

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

      5. sub-neg 72.1%

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

      6. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in i around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. mul-1-neg 58.6%

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

      4. *-commutative 58.6%

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

      5. unsub-neg 58.6%

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

      6. *-commutative 58.6%

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

   10. Simplified 58.6%

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

   if 1.08e-19 < c < 7.8000000000000002e58

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -70000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -6.8e+33)
     t_1
     (if (<= c 1.65e-80) (* i (* a b)) (if (<= c 4e+61) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -6.8e+33) {
		tmp = t_1;
	} else if (c <= 1.65e-80) {
		tmp = i * (a * b);
	} else if (c <= 4e+61) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-6.8d+33)) then
        tmp = t_1
    else if (c <= 1.65d-80) then
        tmp = i * (a * b)
    else if (c <= 4d+61) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -6.8e+33) {
		tmp = t_1;
	} else if (c <= 1.65e-80) {
		tmp = i * (a * b);
	} else if (c <= 4e+61) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -6.8e+33:
		tmp = t_1
	elif c <= 1.65e-80:
		tmp = i * (a * b)
	elif c <= 4e+61:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -6.8e+33)
		tmp = t_1;
	elseif (c <= 1.65e-80)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 4e+61)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -6.8e+33)
		tmp = t_1;
	elseif (c <= 1.65e-80)
		tmp = i * (a * b);
	elseif (c <= 4e+61)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e+33], t$95$1, If[LessEqual[c, 1.65e-80], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e+61], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.7999999999999999e33 or 3.9999999999999998e61 < c

   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 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in j around inf 46.3%

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

   if -6.7999999999999999e33 < c < 1.65e-80

   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 i around inf 57.4%

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

      1. distribute-lft-out-- 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in b around inf 55.9%

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

      1. associate-/l* 55.0%

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

   8. Simplified 55.0%

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

      1. pow1 55.0%

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

      2. mul-1-neg 55.0%

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

   10. Applied egg-rr 55.0%

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

       1. unpow1 55.0%

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

       2. distribute-lft-neg-in 55.0%

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

   12. Simplified 55.0%

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

   13. Taylor expanded in b around inf 33.5%

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

       1. *-commutative 33.5%

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

       2. *-commutative 33.5%

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

       3. associate-*r* 36.0%

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

   15. Simplified 36.0%

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

   if 1.65e-80 < c < 3.9999999999999998e61

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around inf 40.6%

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

      1. *-commutative 40.6%

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

   8. Simplified 40.6%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.52 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -2.5e+35)
     t_1
     (if (<= c 1.52e-80)
       (* i (* a b))
       (if (<= c 7.5e+61) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -2.5e+35) {
		tmp = t_1;
	} else if (c <= 1.52e-80) {
		tmp = i * (a * b);
	} else if (c <= 7.5e+61) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-2.5d+35)) then
        tmp = t_1
    else if (c <= 1.52d-80) then
        tmp = i * (a * b)
    else if (c <= 7.5d+61) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -2.5e+35) {
		tmp = t_1;
	} else if (c <= 1.52e-80) {
		tmp = i * (a * b);
	} else if (c <= 7.5e+61) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -2.5e+35:
		tmp = t_1
	elif c <= 1.52e-80:
		tmp = i * (a * b)
	elif c <= 7.5e+61:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -2.5e+35)
		tmp = t_1;
	elseif (c <= 1.52e-80)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 7.5e+61)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -2.5e+35)
		tmp = t_1;
	elseif (c <= 1.52e-80)
		tmp = i * (a * b);
	elseif (c <= 7.5e+61)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+35], t$95$1, If[LessEqual[c, 1.52e-80], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+61], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.50000000000000011e35 or 7.5e61 < c

   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 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in j around inf 46.3%

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

   if -2.50000000000000011e35 < c < 1.5199999999999999e-80

   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 i around inf 57.4%

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

      1. distribute-lft-out-- 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in b around inf 55.9%

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

      1. associate-/l* 55.0%

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

   8. Simplified 55.0%

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

      1. pow1 55.0%

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

      2. mul-1-neg 55.0%

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

   10. Applied egg-rr 55.0%

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

       1. unpow1 55.0%

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

       2. distribute-lft-neg-in 55.0%

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

   12. Simplified 55.0%

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

   13. Taylor expanded in b around inf 33.5%

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

       1. *-commutative 33.5%

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

       2. *-commutative 33.5%

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

       3. associate-*r* 36.0%

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

   15. Simplified 36.0%

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

   if 1.5199999999999999e-80 < c < 7.5e61

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around inf 37.3%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.52 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+245}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.2e+245)
   (* j (* t c))
   (if (<= t 2.25e+52) (* b (- (* a i) (* z c))) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.2e+245) {
		tmp = j * (t * c);
	} else if (t <= 2.25e+52) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-2.2d+245)) then
        tmp = j * (t * c)
    else if (t <= 2.25d+52) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.2e+245) {
		tmp = j * (t * c);
	} else if (t <= 2.25e+52) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.2e+245:
		tmp = j * (t * c)
	elif t <= 2.25e+52:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.2e+245)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 2.25e+52)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.2e+245)
		tmp = j * (t * c);
	elseif (t <= 2.25e+52)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.2e+245], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+52], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2000000000000001e245

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 82.9%

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

      1. +-commutative 82.9%

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

      2. mul-1-neg 82.9%

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

      3. unsub-neg 82.9%

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

      4. *-commutative 82.9%

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

      5. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in j around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*r* 91.2%

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

      3. *-commutative 91.2%

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

   8. Simplified 91.2%

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

   if -2.2000000000000001e245 < t < 2.25e52

   1. Initial program 78.6%

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

   3. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

   5. Simplified 47.8%

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

   if 2.25e52 < t

   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 t around inf 66.9%

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

      1. +-commutative 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

      4. *-commutative 66.9%

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

      5. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in j around inf 55.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+245}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+34} \lor \neg \left(c \leq 6 \cdot 10^{+62}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2e+34) (not (<= c 6e+62))) (* t (* c j)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2e+34) || !(c <= 6e+62)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2d+34)) .or. (.not. (c <= 6d+62))) then
        tmp = t * (c * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2e+34) || !(c <= 6e+62)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2e+34) or not (c <= 6e+62):
		tmp = t * (c * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2e+34) || !(c <= 6e+62))
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2e+34) || ~((c <= 6e+62)))
		tmp = t * (c * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2e+34], N[Not[LessEqual[c, 6e+62]], $MachinePrecision]], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.99999999999999989e34 or 6e62 < c

   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 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in j around inf 46.3%

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

   if -1.99999999999999989e34 < c < 6e62

   1. Initial program 78.8%

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

   3. Taylor expanded in i around inf 52.8%

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

      1. distribute-lft-out-- 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in b around inf 52.2%

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

      1. associate-/l* 52.2%

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

   8. Simplified 52.2%

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

      1. pow1 52.2%

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

      2. mul-1-neg 52.2%

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

   10. Applied egg-rr 52.2%

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

       1. unpow1 52.2%

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

       2. distribute-lft-neg-in 52.2%

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

   12. Simplified 52.2%

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

   13. Taylor expanded in b around inf 30.1%

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

       1. *-commutative 30.1%

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

       2. *-commutative 30.1%

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

       3. associate-*r* 32.1%

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

   15. Simplified 32.1%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+34} \lor \neg \left(c \leq 6 \cdot 10^{+62}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.05 \cdot 10^{+34} \lor \neg \left(c \leq 1.35 \cdot 10^{+64}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.05e+34) (not (<= c 1.35e+64))) (* c (* t j)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.05e+34) || !(c <= 1.35e+64)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.05d+34)) .or. (.not. (c <= 1.35d+64))) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.05e+34) || !(c <= 1.35e+64)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.05e+34) or not (c <= 1.35e+64):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.05e+34) || !(c <= 1.35e+64))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.05e+34) || ~((c <= 1.35e+64)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.05e+34], N[Not[LessEqual[c, 1.35e+64]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.04999999999999998e34 or 1.35e64 < c

   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 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in j around inf 42.9%

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

   if -3.04999999999999998e34 < c < 1.35e64

   1. Initial program 78.8%

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

   3. Taylor expanded in i around inf 52.8%

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

      1. distribute-lft-out-- 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in b around inf 52.2%

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

      1. associate-/l* 52.2%

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

   8. Simplified 52.2%

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

      1. pow1 52.2%

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

      2. mul-1-neg 52.2%

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

   10. Applied egg-rr 52.2%

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

       1. unpow1 52.2%

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

       2. distribute-lft-neg-in 52.2%

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

   12. Simplified 52.2%

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

   13. Taylor expanded in b around inf 30.1%

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

       1. *-commutative 30.1%

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

       2. *-commutative 30.1%

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

       3. associate-*r* 32.1%

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

   15. Simplified 32.1%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.05 \cdot 10^{+34} \lor \neg \left(c \leq 1.35 \cdot 10^{+64}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+32} \lor \neg \left(c \leq 8.6 \cdot 10^{+63}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -6.2e+32) (not (<= c 8.6e+63))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -6.2e+32) || !(c <= 8.6e+63)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-6.2d+32)) .or. (.not. (c <= 8.6d+63))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -6.2e+32) || !(c <= 8.6e+63)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -6.2e+32) or not (c <= 8.6e+63):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -6.2e+32) || !(c <= 8.6e+63))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -6.2e+32) || ~((c <= 8.6e+63)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -6.2e+32], N[Not[LessEqual[c, 8.6e+63]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.19999999999999986e32 or 8.6000000000000001e63 < c

   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 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in j around inf 42.9%

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

   if -6.19999999999999986e32 < c < 8.6000000000000001e63

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf 41.3%

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

      1. *-commutative 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in i around inf 29.4%

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

   7. Taylor expanded in b around 0 30.1%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+32} \lor \neg \left(c \leq 8.6 \cdot 10^{+63}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.4% 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 75.6%

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

3. Taylor expanded in b around inf 42.5%

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

   1. *-commutative 42.5%

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

5. Simplified 42.5%

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

6. Taylor expanded in i around inf 21.8%

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

7. Taylor expanded in b around 0 23.3%

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

Developer target: 68.3% 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 2024100 
(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)))))