Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 82.0%

Time: 18.0s

Alternatives: 16

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% 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: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((b * i) - (x * t))
	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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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 92.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 54.3%

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

      1. associate-*r* 54.3%

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

      2. neg-mul-1 54.3%

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

      3. cancel-sign-sub 54.3%

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

      4. +-commutative 54.3%

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

      5. mul-1-neg 54.3%

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

      6. unsub-neg 54.3%

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

      7. *-commutative 54.3%

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

   4. Simplified 54.3%

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

4. Final simplification 84.7%

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

Alternative 2: 28.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-197}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* c (* t j))) (t_3 (* t (* x (- a)))))
   (if (<= y -8.6e+203)
     (* j (* y (- i)))
     (if (<= y -5.3e+38)
       t_2
       (if (<= y -3.15e-106)
         t_3
         (if (<= y -1.05e-142)
           t_1
           (if (<= y 1.05e-209)
             t_2
             (if (<= y 4.3e-197)
               (* c (* z (- b)))
               (if (<= y 6.2e-78)
                 (* i (* a b))
                 (if (<= y 3.7e-7)
                   t_3
                   (if (<= y 1.15e+92) t_1 (* i (* y (- j))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = c * (t * j);
	double t_3 = t * (x * -a);
	double tmp;
	if (y <= -8.6e+203) {
		tmp = j * (y * -i);
	} else if (y <= -5.3e+38) {
		tmp = t_2;
	} else if (y <= -3.15e-106) {
		tmp = t_3;
	} else if (y <= -1.05e-142) {
		tmp = t_1;
	} else if (y <= 1.05e-209) {
		tmp = t_2;
	} else if (y <= 4.3e-197) {
		tmp = c * (z * -b);
	} else if (y <= 6.2e-78) {
		tmp = i * (a * b);
	} else if (y <= 3.7e-7) {
		tmp = t_3;
	} else if (y <= 1.15e+92) {
		tmp = t_1;
	} else {
		tmp = i * (y * -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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (b * i)
    t_2 = c * (t * j)
    t_3 = t * (x * -a)
    if (y <= (-8.6d+203)) then
        tmp = j * (y * -i)
    else if (y <= (-5.3d+38)) then
        tmp = t_2
    else if (y <= (-3.15d-106)) then
        tmp = t_3
    else if (y <= (-1.05d-142)) then
        tmp = t_1
    else if (y <= 1.05d-209) then
        tmp = t_2
    else if (y <= 4.3d-197) then
        tmp = c * (z * -b)
    else if (y <= 6.2d-78) then
        tmp = i * (a * b)
    else if (y <= 3.7d-7) then
        tmp = t_3
    else if (y <= 1.15d+92) then
        tmp = t_1
    else
        tmp = i * (y * -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 t_1 = a * (b * i);
	double t_2 = c * (t * j);
	double t_3 = t * (x * -a);
	double tmp;
	if (y <= -8.6e+203) {
		tmp = j * (y * -i);
	} else if (y <= -5.3e+38) {
		tmp = t_2;
	} else if (y <= -3.15e-106) {
		tmp = t_3;
	} else if (y <= -1.05e-142) {
		tmp = t_1;
	} else if (y <= 1.05e-209) {
		tmp = t_2;
	} else if (y <= 4.3e-197) {
		tmp = c * (z * -b);
	} else if (y <= 6.2e-78) {
		tmp = i * (a * b);
	} else if (y <= 3.7e-7) {
		tmp = t_3;
	} else if (y <= 1.15e+92) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = c * (t * j)
	t_3 = t * (x * -a)
	tmp = 0
	if y <= -8.6e+203:
		tmp = j * (y * -i)
	elif y <= -5.3e+38:
		tmp = t_2
	elif y <= -3.15e-106:
		tmp = t_3
	elif y <= -1.05e-142:
		tmp = t_1
	elif y <= 1.05e-209:
		tmp = t_2
	elif y <= 4.3e-197:
		tmp = c * (z * -b)
	elif y <= 6.2e-78:
		tmp = i * (a * b)
	elif y <= 3.7e-7:
		tmp = t_3
	elif y <= 1.15e+92:
		tmp = t_1
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(c * Float64(t * j))
	t_3 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (y <= -8.6e+203)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (y <= -5.3e+38)
		tmp = t_2;
	elseif (y <= -3.15e-106)
		tmp = t_3;
	elseif (y <= -1.05e-142)
		tmp = t_1;
	elseif (y <= 1.05e-209)
		tmp = t_2;
	elseif (y <= 4.3e-197)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (y <= 6.2e-78)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 3.7e-7)
		tmp = t_3;
	elseif (y <= 1.15e+92)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	t_2 = c * (t * j);
	t_3 = t * (x * -a);
	tmp = 0.0;
	if (y <= -8.6e+203)
		tmp = j * (y * -i);
	elseif (y <= -5.3e+38)
		tmp = t_2;
	elseif (y <= -3.15e-106)
		tmp = t_3;
	elseif (y <= -1.05e-142)
		tmp = t_1;
	elseif (y <= 1.05e-209)
		tmp = t_2;
	elseif (y <= 4.3e-197)
		tmp = c * (z * -b);
	elseif (y <= 6.2e-78)
		tmp = i * (a * b);
	elseif (y <= 3.7e-7)
		tmp = t_3;
	elseif (y <= 1.15e+92)
		tmp = t_1;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+203], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.3e+38], t$95$2, If[LessEqual[y, -3.15e-106], t$95$3, If[LessEqual[y, -1.05e-142], t$95$1, If[LessEqual[y, 1.05e-209], t$95$2, If[LessEqual[y, 4.3e-197], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-78], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-7], t$95$3, If[LessEqual[y, 1.15e+92], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.6e203

   1. Initial program 64.9%

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

   2. Taylor expanded in i around inf 46.7%

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

      1. cancel-sign-sub-inv 46.7%

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

      2. metadata-eval 46.7%

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

      3. *-lft-identity 46.7%

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

      4. +-commutative 46.7%

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

      5. mul-1-neg 46.7%

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

      6. unsub-neg 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in a around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. *-commutative 37.2%

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

      3. associate-*r* 50.9%

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

      4. distribute-rgt-neg-in 50.9%

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

      5. *-commutative 50.9%

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

      6. distribute-rgt-neg-in 50.9%

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

   7. Simplified 50.9%

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

   if -8.6e203 < y < -5.30000000000000024e38 or -1.05e-142 < y < 1.04999999999999998e-209

   1. Initial program 75.3%

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

   2. Taylor expanded in c around inf 58.9%

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

      1. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in j around inf 44.0%

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

      1. *-commutative 44.0%

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

   7. Simplified 44.0%

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

   if -5.30000000000000024e38 < y < -3.1500000000000002e-106 or 6.20000000000000035e-78 < y < 3.70000000000000004e-7

   1. Initial program 83.9%

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

   2. Taylor expanded in t around inf 39.1%

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

      1. +-commutative 39.1%

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

      2. mul-1-neg 39.1%

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

      3. unsub-neg 39.1%

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

      4. *-commutative 39.1%

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

      5. *-commutative 39.1%

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

   4. Simplified 39.1%

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

   5. Taylor expanded in j around 0 36.8%

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

      1. mul-1-neg 36.8%

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

      2. distribute-rgt-neg-in 36.8%

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

   7. Simplified 36.8%

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

   if -3.1500000000000002e-106 < y < -1.05e-142 or 3.70000000000000004e-7 < y < 1.14999999999999999e92

   1. Initial program 78.1%

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

   2. Taylor expanded in a around inf 60.2%

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

      1. associate-*r* 60.2%

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

      2. neg-mul-1 60.2%

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

      3. cancel-sign-sub 60.2%

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

      4. +-commutative 60.2%

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

      5. mul-1-neg 60.2%

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

      6. unsub-neg 60.2%

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

      7. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in i around inf 49.4%

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

   if 1.04999999999999998e-209 < y < 4.3e-197

   1. Initial program 75.0%

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

   2. Taylor expanded in c around inf 75.7%

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

      1. *-commutative 75.7%

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

   4. Simplified 75.7%

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

   5. Taylor expanded in j around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-rgt-neg-in 75.7%

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

   7. Simplified 75.7%

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

   if 4.3e-197 < y < 6.20000000000000035e-78

   1. Initial program 80.7%

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

   2. Taylor expanded in b around inf 49.9%

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

      1. *-commutative 49.9%

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

   4. Simplified 49.9%

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

   5. Taylor expanded in i around inf 41.4%

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

      1. *-commutative 41.4%

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

      2. associate-*l* 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in b around 0 41.4%

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

      1. *-commutative 41.4%

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

      2. *-commutative 41.4%

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

      3. associate-*r* 45.2%

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

      4. *-commutative 45.2%

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

   10. Simplified 45.2%

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

   if 1.14999999999999999e92 < y

   1. Initial program 54.8%

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

   2. Taylor expanded in y around inf 79.6%

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

   3. Taylor expanded in i around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. distribute-rgt-neg-in 60.3%

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

   5. Simplified 60.3%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-197}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-78}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 3: 62.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+261} \lor \neg \left(y \leq 3.8 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -2.5e+261) (not (<= y 3.8e+45)))
   (* y (- (* x z) (* i j)))
   (+ (* j (- (* t c) (* y i))) (* b (- (* a i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.5e+261) || !(y <= 3.8e+45)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-2.5d+261)) .or. (.not. (y <= 3.8d+45))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.5e+261) || !(y <= 3.8e+45)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -2.5e+261) or not (y <= 3.8e+45):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -2.5e+261) || !(y <= 3.8e+45))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -2.5e+261) || ~((y <= 3.8e+45)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -2.5e+261], N[Not[LessEqual[y, 3.8e+45]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e261 or 3.8000000000000002e45 < y

   1. Initial program 61.7%

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

   2. Taylor expanded in y around inf 75.6%

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

   if -2.5e261 < y < 3.8000000000000002e45

   1. Initial program 77.1%

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

   2. Taylor expanded in x around 0 65.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+261} \lor \neg \left(y \leq 3.8 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 69.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -310 \lor \neg \left(j \leq 2.6 \cdot 10^{-62}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (or (<= j -310.0) (not (<= j 2.6e-62)))
     (+ (* j (- (* t c) (* y i))) t_1)
     (+ (* x (- (* y z) (* t a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if ((j <= -310.0) || !(j <= 2.6e-62)) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if ((j <= (-310.0d0)) .or. (.not. (j <= 2.6d-62))) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else
        tmp = (x * ((y * z) - (t * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if ((j <= -310.0) || !(j <= 2.6e-62)) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if (j <= -310.0) or not (j <= 2.6e-62):
		tmp = (j * ((t * c) - (y * i))) + t_1
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if ((j <= -310.0) || !(j <= 2.6e-62))
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if ((j <= -310.0) || ~((j <= 2.6e-62)))
		tmp = (j * ((t * c) - (y * i))) + t_1;
	else
		tmp = (x * ((y * z) - (t * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[j, -310.0], N[Not[LessEqual[j, 2.6e-62]], $MachinePrecision]], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if j < -310 or 2.5999999999999999e-62 < j

   1. Initial program 72.8%

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

   2. Taylor expanded in x around 0 72.5%

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

   if -310 < j < 2.5999999999999999e-62

   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. Taylor expanded in j around 0 79.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -310 \lor \neg \left(j \leq 2.6 \cdot 10^{-62}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5: 45.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -130000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= x -130000.0)
     (* t (- (* c j) (* x a)))
     (if (<= x -8.2e-219)
       (* b (- (* a i) (* z c)))
       (if (<= x 5.6e-187)
         t_1
         (if (<= x 8.5e-67)
           (* c (- (* t j) (* z b)))
           (if (<= x 1.75e-32)
             t_1
             (if (<= x 100000000.0)
               (* z (- (* x y) (* b c)))
               (* a (- (* b i) (* x t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (x <= -130000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -8.2e-219) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.6e-187) {
		tmp = t_1;
	} else if (x <= 8.5e-67) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.75e-32) {
		tmp = t_1;
	} else if (x <= 100000000.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (x <= (-130000.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= (-8.2d-219)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 5.6d-187) then
        tmp = t_1
    else if (x <= 8.5d-67) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.75d-32) then
        tmp = t_1
    else if (x <= 100000000.0d0) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (x <= -130000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -8.2e-219) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.6e-187) {
		tmp = t_1;
	} else if (x <= 8.5e-67) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.75e-32) {
		tmp = t_1;
	} else if (x <= 100000000.0) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if x <= -130000.0:
		tmp = t * ((c * j) - (x * a))
	elif x <= -8.2e-219:
		tmp = b * ((a * i) - (z * c))
	elif x <= 5.6e-187:
		tmp = t_1
	elif x <= 8.5e-67:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.75e-32:
		tmp = t_1
	elif x <= 100000000.0:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (x <= -130000.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= -8.2e-219)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 5.6e-187)
		tmp = t_1;
	elseif (x <= 8.5e-67)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.75e-32)
		tmp = t_1;
	elseif (x <= 100000000.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (x <= -130000.0)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= -8.2e-219)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 5.6e-187)
		tmp = t_1;
	elseif (x <= 8.5e-67)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.75e-32)
		tmp = t_1;
	elseif (x <= 100000000.0)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -130000.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.2e-219], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e-187], t$95$1, If[LessEqual[x, 8.5e-67], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-32], t$95$1, If[LessEqual[x, 100000000.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.3e5

   1. Initial program 68.4%

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

   2. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

      5. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   if -1.3e5 < x < -8.2e-219

   1. Initial program 77.9%

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

   2. Taylor expanded in b around inf 54.2%

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

      1. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   if -8.2e-219 < x < 5.6e-187 or 8.49999999999999993e-67 < x < 1.7499999999999999e-32

   1. Initial program 69.1%

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

   2. Taylor expanded in i around inf 70.2%

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

      1. cancel-sign-sub-inv 70.2%

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

      2. metadata-eval 70.2%

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

      3. *-lft-identity 70.2%

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

      4. +-commutative 70.2%

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

      5. mul-1-neg 70.2%

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

      6. unsub-neg 70.2%

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

   4. Simplified 70.2%

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

   if 5.6e-187 < x < 8.49999999999999993e-67

   1. Initial program 74.1%

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

   2. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

   4. Simplified 78.9%

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

   if 1.7499999999999999e-32 < x < 1e8

   1. Initial program 75.0%

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

   2. Taylor expanded in z around inf 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

   4. Simplified 75.2%

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

   if 1e8 < x

   1. Initial program 76.9%

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

   2. Taylor expanded in a around inf 62.7%

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

      1. associate-*r* 62.7%

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

      2. neg-mul-1 62.7%

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

      3. cancel-sign-sub 62.7%

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

      4. +-commutative 62.7%

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

      5. mul-1-neg 62.7%

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

      6. unsub-neg 62.7%

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

      7. *-commutative 62.7%

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

   4. Simplified 62.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -130000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 100000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 6: 29.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;i \leq -0.068:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.16 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 10^{-181}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))) (t_3 (* x (* y z))))
   (if (<= i -0.068)
     t_2
     (if (<= i -2.16e-57)
       (* t (* c j))
       (if (<= i -3e-61)
         t_2
         (if (<= i -1.6e-117)
           t_3
           (if (<= i 5.6e-239)
             t_1
             (if (<= i 1e-181)
               t_3
               (if (<= i 2.4e+117) t_1 (* b (* a i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double t_3 = x * (y * z);
	double tmp;
	if (i <= -0.068) {
		tmp = t_2;
	} else if (i <= -2.16e-57) {
		tmp = t * (c * j);
	} else if (i <= -3e-61) {
		tmp = t_2;
	} else if (i <= -1.6e-117) {
		tmp = t_3;
	} else if (i <= 5.6e-239) {
		tmp = t_1;
	} else if (i <= 1e-181) {
		tmp = t_3;
	} else if (i <= 2.4e+117) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = a * (b * i)
    t_3 = x * (y * z)
    if (i <= (-0.068d0)) then
        tmp = t_2
    else if (i <= (-2.16d-57)) then
        tmp = t * (c * j)
    else if (i <= (-3d-61)) then
        tmp = t_2
    else if (i <= (-1.6d-117)) then
        tmp = t_3
    else if (i <= 5.6d-239) then
        tmp = t_1
    else if (i <= 1d-181) then
        tmp = t_3
    else if (i <= 2.4d+117) then
        tmp = t_1
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = a * (b * i);
	double t_3 = x * (y * z);
	double tmp;
	if (i <= -0.068) {
		tmp = t_2;
	} else if (i <= -2.16e-57) {
		tmp = t * (c * j);
	} else if (i <= -3e-61) {
		tmp = t_2;
	} else if (i <= -1.6e-117) {
		tmp = t_3;
	} else if (i <= 5.6e-239) {
		tmp = t_1;
	} else if (i <= 1e-181) {
		tmp = t_3;
	} else if (i <= 2.4e+117) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	t_3 = x * (y * z)
	tmp = 0
	if i <= -0.068:
		tmp = t_2
	elif i <= -2.16e-57:
		tmp = t * (c * j)
	elif i <= -3e-61:
		tmp = t_2
	elif i <= -1.6e-117:
		tmp = t_3
	elif i <= 5.6e-239:
		tmp = t_1
	elif i <= 1e-181:
		tmp = t_3
	elif i <= 2.4e+117:
		tmp = t_1
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (i <= -0.068)
		tmp = t_2;
	elseif (i <= -2.16e-57)
		tmp = Float64(t * Float64(c * j));
	elseif (i <= -3e-61)
		tmp = t_2;
	elseif (i <= -1.6e-117)
		tmp = t_3;
	elseif (i <= 5.6e-239)
		tmp = t_1;
	elseif (i <= 1e-181)
		tmp = t_3;
	elseif (i <= 2.4e+117)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = a * (b * i);
	t_3 = x * (y * z);
	tmp = 0.0;
	if (i <= -0.068)
		tmp = t_2;
	elseif (i <= -2.16e-57)
		tmp = t * (c * j);
	elseif (i <= -3e-61)
		tmp = t_2;
	elseif (i <= -1.6e-117)
		tmp = t_3;
	elseif (i <= 5.6e-239)
		tmp = t_1;
	elseif (i <= 1e-181)
		tmp = t_3;
	elseif (i <= 2.4e+117)
		tmp = t_1;
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -0.068], t$95$2, If[LessEqual[i, -2.16e-57], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3e-61], t$95$2, If[LessEqual[i, -1.6e-117], t$95$3, If[LessEqual[i, 5.6e-239], t$95$1, If[LessEqual[i, 1e-181], t$95$3, If[LessEqual[i, 2.4e+117], t$95$1, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -0.068000000000000005 or -2.1599999999999999e-57 < i < -3.00000000000000012e-61

   1. Initial program 65.0%

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

   2. Taylor expanded in a around inf 58.6%

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

      1. associate-*r* 58.6%

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

      2. neg-mul-1 58.6%

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

      3. cancel-sign-sub 58.6%

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

      4. +-commutative 58.6%

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

      5. mul-1-neg 58.6%

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

      6. unsub-neg 58.6%

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

      7. *-commutative 58.6%

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

   4. Simplified 58.6%

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

   5. Taylor expanded in i around inf 53.7%

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

   if -0.068000000000000005 < i < -2.1599999999999999e-57

   1. Initial program 73.3%

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

   2. Taylor expanded in c around inf 48.8%

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

      1. *-commutative 48.8%

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

   4. Simplified 48.8%

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

   5. Taylor expanded in j around inf 35.5%

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

      1. associate-*r* 41.4%

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

   7. Simplified 41.4%

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

   if -3.00000000000000012e-61 < i < -1.59999999999999998e-117 or 5.60000000000000025e-239 < i < 1.00000000000000005e-181

   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. Taylor expanded in y around inf 49.4%

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

   3. Taylor expanded in i around 0 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -1.59999999999999998e-117 < i < 5.60000000000000025e-239 or 1.00000000000000005e-181 < i < 2.3999999999999999e117

   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. Taylor expanded in c around inf 46.3%

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

      1. *-commutative 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in j around inf 31.9%

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

      1. *-commutative 31.9%

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

   7. Simplified 31.9%

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

   if 2.3999999999999999e117 < i

   1. Initial program 58.4%

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

   2. Taylor expanded in b around inf 59.2%

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

      1. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in i around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l* 50.1%

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

   7. Simplified 50.1%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -0.068:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.16 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 10^{-181}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+117}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 7: 45.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -155000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -155000.0)
   (* t (- (* c j) (* x a)))
   (if (<= x -9e-221)
     (* b (- (* a i) (* z c)))
     (if (<= x 5.5e-187)
       (* i (- (* a b) (* y j)))
       (if (<= x 4.4e-70)
         (* c (- (* t j) (* z b)))
         (* a (- (* b i) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -155000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -9e-221) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.5e-187) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 4.4e-70) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-155000.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= (-9d-221)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 5.5d-187) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 4.4d-70) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -155000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -9e-221) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.5e-187) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 4.4e-70) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -155000.0:
		tmp = t * ((c * j) - (x * a))
	elif x <= -9e-221:
		tmp = b * ((a * i) - (z * c))
	elif x <= 5.5e-187:
		tmp = i * ((a * b) - (y * j))
	elif x <= 4.4e-70:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -155000.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= -9e-221)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 5.5e-187)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 4.4e-70)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -155000.0)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= -9e-221)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 5.5e-187)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 4.4e-70)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -155000.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-221], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-187], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-70], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -155000

   1. Initial program 68.4%

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

   2. Taylor expanded in t around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

      5. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   if -155000 < x < -9.00000000000000052e-221

   1. Initial program 77.9%

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

   2. Taylor expanded in b around inf 54.2%

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

      1. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   if -9.00000000000000052e-221 < x < 5.50000000000000033e-187

   1. Initial program 66.2%

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

   2. Taylor expanded in i around inf 69.6%

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

      1. cancel-sign-sub-inv 69.6%

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

      2. metadata-eval 69.6%

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

      3. *-lft-identity 69.6%

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

      4. +-commutative 69.6%

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

      5. mul-1-neg 69.6%

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

      6. unsub-neg 69.6%

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

   4. Simplified 69.6%

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

   if 5.50000000000000033e-187 < x < 4.3999999999999998e-70

   1. Initial program 72.6%

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

   2. Taylor expanded in c around inf 77.8%

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

      1. *-commutative 77.8%

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

   4. Simplified 77.8%

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

   if 4.3999999999999998e-70 < x

   1. Initial program 77.8%

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

   2. Taylor expanded in a around inf 59.9%

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

      1. associate-*r* 59.9%

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

      2. neg-mul-1 59.9%

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

      3. cancel-sign-sub 59.9%

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

      4. +-commutative 59.9%

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

      5. mul-1-neg 59.9%

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

      6. unsub-neg 59.9%

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

      7. *-commutative 59.9%

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

   4. Simplified 59.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -155000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 8: 44.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 82:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= t -1.7e+53)
     t_1
     (if (<= t -1.4e-57)
       (* y (* i (- j)))
       (if (<= t 82.0) (* b (- (* a i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (t <= -1.7e+53) {
		tmp = t_1;
	} else if (t <= -1.4e-57) {
		tmp = y * (i * -j);
	} else if (t <= 82.0) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (t <= (-1.7d+53)) then
        tmp = t_1
    else if (t <= (-1.4d-57)) then
        tmp = y * (i * -j)
    else if (t <= 82.0d0) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (t <= -1.7e+53) {
		tmp = t_1;
	} else if (t <= -1.4e-57) {
		tmp = y * (i * -j);
	} else if (t <= 82.0) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if t <= -1.7e+53:
		tmp = t_1
	elif t <= -1.4e-57:
		tmp = y * (i * -j)
	elif t <= 82.0:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (t <= -1.7e+53)
		tmp = t_1;
	elseif (t <= -1.4e-57)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= 82.0)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (t <= -1.7e+53)
		tmp = t_1;
	elseif (t <= -1.4e-57)
		tmp = y * (i * -j);
	elseif (t <= 82.0)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+53], t$95$1, If[LessEqual[t, -1.4e-57], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 82.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.69999999999999999e53 or 82 < t

   1. Initial program 62.9%

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

   2. Taylor expanded in a around inf 56.3%

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

      1. associate-*r* 56.3%

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

      2. neg-mul-1 56.3%

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

      3. cancel-sign-sub 56.3%

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

      4. +-commutative 56.3%

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

      5. mul-1-neg 56.3%

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

      6. unsub-neg 56.3%

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

      7. *-commutative 56.3%

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

   4. Simplified 56.3%

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

   if -1.69999999999999999e53 < t < -1.4e-57

   1. Initial program 74.9%

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

   2. Taylor expanded in y around inf 65.4%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. neg-mul-1 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   5. Simplified 50.7%

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

   if -1.4e-57 < t < 82

   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. Taylor expanded in b around inf 50.2%

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

      1. *-commutative 50.2%

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

   4. Simplified 50.2%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 82:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 9: 30.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-136}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-218}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.45e+110)
   (* x (* y z))
   (if (<= y -3e-136)
     (* c (* z (- b)))
     (if (<= y 4.9e-218)
       (* c (* t j))
       (if (<= y 1.15e+86) (* b (* a i)) (* i (* y (- 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 (y <= -1.45e+110) {
		tmp = x * (y * z);
	} else if (y <= -3e-136) {
		tmp = c * (z * -b);
	} else if (y <= 4.9e-218) {
		tmp = c * (t * j);
	} else if (y <= 1.15e+86) {
		tmp = b * (a * i);
	} else {
		tmp = i * (y * -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 (y <= (-1.45d+110)) then
        tmp = x * (y * z)
    else if (y <= (-3d-136)) then
        tmp = c * (z * -b)
    else if (y <= 4.9d-218) then
        tmp = c * (t * j)
    else if (y <= 1.15d+86) then
        tmp = b * (a * i)
    else
        tmp = i * (y * -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 (y <= -1.45e+110) {
		tmp = x * (y * z);
	} else if (y <= -3e-136) {
		tmp = c * (z * -b);
	} else if (y <= 4.9e-218) {
		tmp = c * (t * j);
	} else if (y <= 1.15e+86) {
		tmp = b * (a * i);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.45e+110:
		tmp = x * (y * z)
	elif y <= -3e-136:
		tmp = c * (z * -b)
	elif y <= 4.9e-218:
		tmp = c * (t * j)
	elif y <= 1.15e+86:
		tmp = b * (a * i)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.45e+110)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3e-136)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (y <= 4.9e-218)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 1.15e+86)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.45e+110)
		tmp = x * (y * z);
	elseif (y <= -3e-136)
		tmp = c * (z * -b);
	elseif (y <= 4.9e-218)
		tmp = c * (t * j);
	elseif (y <= 1.15e+86)
		tmp = b * (a * i);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.45e+110], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-136], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-218], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+86], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.45e110

   1. Initial program 69.9%

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

   2. Taylor expanded in y around inf 53.3%

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

   3. Taylor expanded in i around 0 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   if -1.45e110 < y < -2.9999999999999998e-136

   1. Initial program 70.3%

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

   2. Taylor expanded in c around inf 41.9%

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

      1. *-commutative 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in j around 0 29.6%

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

      1. mul-1-neg 29.6%

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

      2. distribute-rgt-neg-in 29.6%

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

   7. Simplified 29.6%

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

   if -2.9999999999999998e-136 < y < 4.89999999999999978e-218

   1. Initial program 82.6%

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

   2. Taylor expanded in c around inf 58.8%

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

      1. *-commutative 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in j around inf 45.6%

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

      1. *-commutative 45.6%

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

   7. Simplified 45.6%

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

   if 4.89999999999999978e-218 < y < 1.14999999999999995e86

   1. Initial program 81.3%

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

   2. Taylor expanded in b around inf 52.4%

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

      1. *-commutative 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in i around inf 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l* 39.7%

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

   7. Simplified 39.7%

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

   if 1.14999999999999995e86 < y

   1. Initial program 54.8%

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

   2. Taylor expanded in y around inf 79.6%

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

   3. Taylor expanded in i around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. distribute-rgt-neg-in 60.3%

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

   5. Simplified 60.3%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-136}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-218}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 10: 27.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+132} \lor \neg \left(y \leq 1.12 \cdot 10^{+282}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.95e+210)
   (* x (* y z))
   (if (<= y 1.62e-217)
     (* c (* t j))
     (if (or (<= y 2.4e+132) (not (<= y 1.12e+282)))
       (* a (* b i))
       (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.95e+210) {
		tmp = x * (y * z);
	} else if (y <= 1.62e-217) {
		tmp = c * (t * j);
	} else if ((y <= 2.4e+132) || !(y <= 1.12e+282)) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.95d+210)) then
        tmp = x * (y * z)
    else if (y <= 1.62d-217) then
        tmp = c * (t * j)
    else if ((y <= 2.4d+132) .or. (.not. (y <= 1.12d+282))) then
        tmp = a * (b * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.95e+210) {
		tmp = x * (y * z);
	} else if (y <= 1.62e-217) {
		tmp = c * (t * j);
	} else if ((y <= 2.4e+132) || !(y <= 1.12e+282)) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.95e+210:
		tmp = x * (y * z)
	elif y <= 1.62e-217:
		tmp = c * (t * j)
	elif (y <= 2.4e+132) or not (y <= 1.12e+282):
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.95e+210)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 1.62e-217)
		tmp = Float64(c * Float64(t * j));
	elseif ((y <= 2.4e+132) || !(y <= 1.12e+282))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.95e+210)
		tmp = x * (y * z);
	elseif (y <= 1.62e-217)
		tmp = c * (t * j);
	elseif ((y <= 2.4e+132) || ~((y <= 1.12e+282)))
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.95e+210], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.62e-217], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.4e+132], N[Not[LessEqual[y, 1.12e+282]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.95e210

   1. Initial program 63.1%

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

   2. Taylor expanded in y around inf 74.2%

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

   3. Taylor expanded in i around 0 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   if -1.95e210 < y < 1.61999999999999998e-217

   1. Initial program 76.7%

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

   2. Taylor expanded in c around inf 49.3%

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

      1. *-commutative 49.3%

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

   4. Simplified 49.3%

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

   5. Taylor expanded in j around inf 33.3%

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

      1. *-commutative 33.3%

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

   7. Simplified 33.3%

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

   if 1.61999999999999998e-217 < y < 2.4000000000000001e132 or 1.12e282 < y

   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. Taylor expanded in a around inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. neg-mul-1 56.2%

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

      3. cancel-sign-sub 56.2%

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

      4. +-commutative 56.2%

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

      5. mul-1-neg 56.2%

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

      6. unsub-neg 56.2%

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

      7. *-commutative 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in i around inf 40.4%

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

   if 2.4000000000000001e132 < y < 1.12e282

   1. Initial program 53.7%

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

   2. Taylor expanded in y around inf 76.8%

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

   3. Taylor expanded in i around 0 34.9%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+132} \lor \neg \left(y \leq 1.12 \cdot 10^{+282}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 50.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+142} \lor \neg \left(c \leq 1.1 \cdot 10^{+86}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -6.5e+142) (not (<= c 1.1e+86)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -6.5e+142) || !(c <= 1.1e+86)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-6.5d+142)) .or. (.not. (c <= 1.1d+86))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -6.5e+142) || !(c <= 1.1e+86)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -6.5e+142) or not (c <= 1.1e+86):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -6.5e+142) || !(c <= 1.1e+86))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -6.5e+142) || ~((c <= 1.1e+86)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -6.5e+142], N[Not[LessEqual[c, 1.1e+86]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.4999999999999997e142 or 1.10000000000000002e86 < c

   1. Initial program 68.3%

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

   2. Taylor expanded in c around inf 71.3%

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

      1. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   if -6.4999999999999997e142 < c < 1.10000000000000002e86

   1. Initial program 75.5%

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

   2. Taylor expanded in a around inf 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

      3. cancel-sign-sub 51.8%

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

      4. +-commutative 51.8%

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

      5. mul-1-neg 51.8%

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

      6. unsub-neg 51.8%

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

      7. *-commutative 51.8%

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

   4. Simplified 51.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+142} \lor \neg \left(c \leq 1.1 \cdot 10^{+86}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 12: 41.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.55e+144)
   (* t (* c j))
   (if (<= c 4.2e+95) (* a (- (* b i) (* x t))) (* 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 (c <= -1.55e+144) {
		tmp = t * (c * j);
	} else if (c <= 4.2e+95) {
		tmp = a * ((b * i) - (x * t));
	} 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 (c <= (-1.55d+144)) then
        tmp = t * (c * j)
    else if (c <= 4.2d+95) then
        tmp = a * ((b * i) - (x * t))
    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 (c <= -1.55e+144) {
		tmp = t * (c * j);
	} else if (c <= 4.2e+95) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.55e+144:
		tmp = t * (c * j)
	elif c <= 4.2e+95:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.55e+144)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 4.2e+95)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	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 (c <= -1.55e+144)
		tmp = t * (c * j);
	elseif (c <= 4.2e+95)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.55e+144], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e+95], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.5500000000000001e144

   1. Initial program 76.3%

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

   2. Taylor expanded in c around inf 65.1%

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

      1. *-commutative 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in j around inf 42.1%

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

      1. associate-*r* 46.0%

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

   7. Simplified 46.0%

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

   if -1.5500000000000001e144 < c < 4.2e95

   1. Initial program 75.5%

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

   2. Taylor expanded in a around inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

      3. cancel-sign-sub 51.2%

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

      4. +-commutative 51.2%

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

      5. mul-1-neg 51.2%

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

      6. unsub-neg 51.2%

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

      7. *-commutative 51.2%

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

   4. Simplified 51.2%

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

   if 4.2e95 < c

   1. Initial program 63.9%

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

   2. Taylor expanded in c around inf 75.8%

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

      1. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in j around inf 55.0%

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

      1. *-commutative 55.0%

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

   7. Simplified 55.0%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 13: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+118}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.4e+30)
   (* a (* b i))
   (if (<= i -5.2e-134)
     (* c (* z (- b)))
     (if (<= i 1.2e+118) (* c (* t j)) (* b (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.4e+30) {
		tmp = a * (b * i);
	} else if (i <= -5.2e-134) {
		tmp = c * (z * -b);
	} else if (i <= 1.2e+118) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.4d+30)) then
        tmp = a * (b * i)
    else if (i <= (-5.2d-134)) then
        tmp = c * (z * -b)
    else if (i <= 1.2d+118) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.4e+30) {
		tmp = a * (b * i);
	} else if (i <= -5.2e-134) {
		tmp = c * (z * -b);
	} else if (i <= 1.2e+118) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.4e+30:
		tmp = a * (b * i)
	elif i <= -5.2e-134:
		tmp = c * (z * -b)
	elif i <= 1.2e+118:
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.4e+30)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -5.2e-134)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 1.2e+118)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.4e+30)
		tmp = a * (b * i);
	elseif (i <= -5.2e-134)
		tmp = c * (z * -b);
	elseif (i <= 1.2e+118)
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.4e+30], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.2e-134], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e+118], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.4000000000000002e30

   1. Initial program 65.4%

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

   2. Taylor expanded in a around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. +-commutative 59.8%

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

      5. mul-1-neg 59.8%

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

      6. unsub-neg 59.8%

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

      7. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   5. Taylor expanded in i around inf 55.9%

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

   if -3.4000000000000002e30 < i < -5.20000000000000045e-134

   1. Initial program 75.8%

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

   2. Taylor expanded in c around inf 48.7%

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

      1. *-commutative 48.7%

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

   4. Simplified 48.7%

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

   5. Taylor expanded in j around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. distribute-rgt-neg-in 35.2%

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

   7. Simplified 35.2%

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

   if -5.20000000000000045e-134 < i < 1.2e118

   1. Initial program 80.5%

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

   2. Taylor expanded in c around inf 44.0%

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

      1. *-commutative 44.0%

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

   4. Simplified 44.0%

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

   5. Taylor expanded in j around inf 30.8%

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

      1. *-commutative 30.8%

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

   7. Simplified 30.8%

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

   if 1.2e118 < i

   1. Initial program 58.4%

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

   2. Taylor expanded in b around inf 59.2%

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

      1. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in i around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l* 50.1%

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

   7. Simplified 50.1%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+118}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 14: 29.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+96} \lor \neg \left(c \leq 4.2 \cdot 10^{+95}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.55e+96) (not (<= c 4.2e+95))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.55e+96) || !(c <= 4.2e+95)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.55d+96)) .or. (.not. (c <= 4.2d+95))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.55e+96) || !(c <= 4.2e+95)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.55e+96) or not (c <= 4.2e+95):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.55e+96) || !(c <= 4.2e+95))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.55e+96) || ~((c <= 4.2e+95)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.55e+96], N[Not[LessEqual[c, 4.2e+95]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.5499999999999999e96 or 4.2e95 < c

   1. Initial program 68.9%

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

   2. Taylor expanded in c around inf 69.7%

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

      1. *-commutative 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in j around inf 49.9%

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

      1. *-commutative 49.9%

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

   7. Simplified 49.9%

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

   if -1.5499999999999999e96 < c < 4.2e95

   1. Initial program 75.5%

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

   2. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. neg-mul-1 50.6%

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

      3. cancel-sign-sub 50.6%

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

      4. +-commutative 50.6%

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

      5. mul-1-neg 50.6%

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

      6. unsub-neg 50.6%

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

      7. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in i around inf 29.4%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+96} \lor \neg \left(c \leq 4.2 \cdot 10^{+95}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 15: 24.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.3e+209)
   (* x (* y z))
   (if (<= y 1.05e-216) (* 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 (y <= -1.3e+209) {
		tmp = x * (y * z);
	} else if (y <= 1.05e-216) {
		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 (y <= (-1.3d+209)) then
        tmp = x * (y * z)
    else if (y <= 1.05d-216) 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 (y <= -1.3e+209) {
		tmp = x * (y * z);
	} else if (y <= 1.05e-216) {
		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 y <= -1.3e+209:
		tmp = x * (y * z)
	elif y <= 1.05e-216:
		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 (y <= -1.3e+209)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 1.05e-216)
		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 (y <= -1.3e+209)
		tmp = x * (y * z);
	elseif (y <= 1.05e-216)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.3e+209], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-216], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e209

   1. Initial program 63.1%

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

   2. Taylor expanded in y around inf 74.2%

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

   3. Taylor expanded in i around 0 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   if -1.3e209 < y < 1.0500000000000001e-216

   1. Initial program 76.7%

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

   2. Taylor expanded in c around inf 49.3%

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

      1. *-commutative 49.3%

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

   4. Simplified 49.3%

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

   5. Taylor expanded in j around inf 33.3%

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

      1. *-commutative 33.3%

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

   7. Simplified 33.3%

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

   if 1.0500000000000001e-216 < y

   1. Initial program 71.3%

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

   2. Taylor expanded in a around inf 53.1%

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

      1. associate-*r* 53.1%

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

      2. neg-mul-1 53.1%

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

      3. cancel-sign-sub 53.1%

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

      4. +-commutative 53.1%

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

      5. mul-1-neg 53.1%

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

      6. unsub-neg 53.1%

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

      7. *-commutative 53.1%

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

   4. Simplified 53.1%

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

   5. Taylor expanded in i around inf 35.6%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 16: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.2%

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

2. Taylor expanded in a around inf 43.7%

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

   1. associate-*r* 43.7%

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

   2. neg-mul-1 43.7%

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

   3. cancel-sign-sub 43.7%

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

   4. +-commutative 43.7%

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

   5. mul-1-neg 43.7%

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

   6. unsub-neg 43.7%

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

   7. *-commutative 43.7%

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

4. Simplified 43.7%

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

5. Taylor expanded in i around inf 26.0%

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

6. Final simplification 26.0%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 69.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))