Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.3% → 82.4%

Time: 17.5s

Alternatives: 18

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = 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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(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 95.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 58.5%

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

      1. distribute-lft-out-- 58.5%

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

      2. *-commutative 58.5%

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

   5. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

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

Alternative 2: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.18 \cdot 10^{-26}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.22 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+173} \lor \neg \left(j \leq 8 \cdot 10^{+202}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -1.18e-26)
     t_3
     (if (<= j -1.7e-99)
       t_2
       (if (<= j -1.4e-255)
         t_1
         (if (<= j 1.22e-200)
           (* a (- (* b i) (* x t)))
           (if (<= j 3.4e-101)
             t_1
             (if (<= j 7e+34)
               t_2
               (if (or (<= j 2.1e+173) (not (<= j 8e+202))) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.18e-26) {
		tmp = t_3;
	} else if (j <= -1.7e-99) {
		tmp = t_2;
	} else if (j <= -1.4e-255) {
		tmp = t_1;
	} else if (j <= 1.22e-200) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 3.4e-101) {
		tmp = t_1;
	} else if (j <= 7e+34) {
		tmp = t_2;
	} else if ((j <= 2.1e+173) || !(j <= 8e+202)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-1.18d-26)) then
        tmp = t_3
    else if (j <= (-1.7d-99)) then
        tmp = t_2
    else if (j <= (-1.4d-255)) then
        tmp = t_1
    else if (j <= 1.22d-200) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= 3.4d-101) then
        tmp = t_1
    else if (j <= 7d+34) then
        tmp = t_2
    else if ((j <= 2.1d+173) .or. (.not. (j <= 8d+202))) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.18e-26) {
		tmp = t_3;
	} else if (j <= -1.7e-99) {
		tmp = t_2;
	} else if (j <= -1.4e-255) {
		tmp = t_1;
	} else if (j <= 1.22e-200) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 3.4e-101) {
		tmp = t_1;
	} else if (j <= 7e+34) {
		tmp = t_2;
	} else if ((j <= 2.1e+173) || !(j <= 8e+202)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.18e-26:
		tmp = t_3
	elif j <= -1.7e-99:
		tmp = t_2
	elif j <= -1.4e-255:
		tmp = t_1
	elif j <= 1.22e-200:
		tmp = a * ((b * i) - (x * t))
	elif j <= 3.4e-101:
		tmp = t_1
	elif j <= 7e+34:
		tmp = t_2
	elif (j <= 2.1e+173) or not (j <= 8e+202):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.18e-26)
		tmp = t_3;
	elseif (j <= -1.7e-99)
		tmp = t_2;
	elseif (j <= -1.4e-255)
		tmp = t_1;
	elseif (j <= 1.22e-200)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= 3.4e-101)
		tmp = t_1;
	elseif (j <= 7e+34)
		tmp = t_2;
	elseif ((j <= 2.1e+173) || !(j <= 8e+202))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.18e-26)
		tmp = t_3;
	elseif (j <= -1.7e-99)
		tmp = t_2;
	elseif (j <= -1.4e-255)
		tmp = t_1;
	elseif (j <= 1.22e-200)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= 3.4e-101)
		tmp = t_1;
	elseif (j <= 7e+34)
		tmp = t_2;
	elseif ((j <= 2.1e+173) || ~((j <= 8e+202)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.18e-26], t$95$3, If[LessEqual[j, -1.7e-99], t$95$2, If[LessEqual[j, -1.4e-255], t$95$1, If[LessEqual[j, 1.22e-200], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e-101], t$95$1, If[LessEqual[j, 7e+34], t$95$2, If[Or[LessEqual[j, 2.1e+173], N[Not[LessEqual[j, 8e+202]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.17999999999999996e-26 or 6.99999999999999996e34 < j < 2.1e173 or 7.9999999999999992e202 < j

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-in 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in a around 0 69.3%

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

   if -1.17999999999999996e-26 < j < -1.70000000000000003e-99 or 3.39999999999999989e-101 < j < 6.99999999999999996e34

   1. Initial program 79.1%

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

   3. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -1.70000000000000003e-99 < j < -1.40000000000000006e-255 or 1.22000000000000005e-200 < j < 3.39999999999999989e-101 or 2.1e173 < j < 7.9999999999999992e202

   1. Initial program 75.8%

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

   3. Taylor expanded in x around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -1.40000000000000006e-255 < j < 1.22000000000000005e-200

   1. Initial program 59.2%

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

   3. Taylor expanded in a around inf 67.5%

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

      1. distribute-lft-out-- 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.18 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.22 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+173} \lor \neg \left(j \leq 8 \cdot 10^{+202}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{-26}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-12} \lor \neg \left(j \leq 1.8 \cdot 10^{+171}\right) \land j \leq 8 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -7e-26)
     t_3
     (if (<= j -6.6e-99)
       t_2
       (if (<= j -7e-256)
         t_1
         (if (<= j 4.6e-197)
           t_2
           (if (or (<= j 1.8e-12) (and (not (<= j 1.8e+171)) (<= j 8e+202)))
             t_1
             t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7e-26) {
		tmp = t_3;
	} else if (j <= -6.6e-99) {
		tmp = t_2;
	} else if (j <= -7e-256) {
		tmp = t_1;
	} else if (j <= 4.6e-197) {
		tmp = t_2;
	} else if ((j <= 1.8e-12) || (!(j <= 1.8e+171) && (j <= 8e+202))) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-7d-26)) then
        tmp = t_3
    else if (j <= (-6.6d-99)) then
        tmp = t_2
    else if (j <= (-7d-256)) then
        tmp = t_1
    else if (j <= 4.6d-197) then
        tmp = t_2
    else if ((j <= 1.8d-12) .or. (.not. (j <= 1.8d+171)) .and. (j <= 8d+202)) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7e-26) {
		tmp = t_3;
	} else if (j <= -6.6e-99) {
		tmp = t_2;
	} else if (j <= -7e-256) {
		tmp = t_1;
	} else if (j <= 4.6e-197) {
		tmp = t_2;
	} else if ((j <= 1.8e-12) || (!(j <= 1.8e+171) && (j <= 8e+202))) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -7e-26:
		tmp = t_3
	elif j <= -6.6e-99:
		tmp = t_2
	elif j <= -7e-256:
		tmp = t_1
	elif j <= 4.6e-197:
		tmp = t_2
	elif (j <= 1.8e-12) or (not (j <= 1.8e+171) and (j <= 8e+202)):
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7e-26)
		tmp = t_3;
	elseif (j <= -6.6e-99)
		tmp = t_2;
	elseif (j <= -7e-256)
		tmp = t_1;
	elseif (j <= 4.6e-197)
		tmp = t_2;
	elseif ((j <= 1.8e-12) || (!(j <= 1.8e+171) && (j <= 8e+202)))
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -7e-26)
		tmp = t_3;
	elseif (j <= -6.6e-99)
		tmp = t_2;
	elseif (j <= -7e-256)
		tmp = t_1;
	elseif (j <= 4.6e-197)
		tmp = t_2;
	elseif ((j <= 1.8e-12) || (~((j <= 1.8e+171)) && (j <= 8e+202)))
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e-26], t$95$3, If[LessEqual[j, -6.6e-99], t$95$2, If[LessEqual[j, -7e-256], t$95$1, If[LessEqual[j, 4.6e-197], t$95$2, If[Or[LessEqual[j, 1.8e-12], And[N[Not[LessEqual[j, 1.8e+171]], $MachinePrecision], LessEqual[j, 8e+202]]], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.9999999999999997e-26 or 1.8e-12 < j < 1.80000000000000009e171 or 7.9999999999999992e202 < j

   1. Initial program 77.4%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

      3. distribute-rgt-neg-in 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in a around 0 68.8%

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

   if -6.9999999999999997e-26 < j < -6.59999999999999973e-99 or -7.00000000000000028e-256 < j < 4.6000000000000001e-197

   1. Initial program 65.8%

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

   3. Taylor expanded in b around inf 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -6.59999999999999973e-99 < j < -7.00000000000000028e-256 or 4.6000000000000001e-197 < j < 1.8e-12 or 1.80000000000000009e171 < j < 7.9999999999999992e202

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 66.8%

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

      1. *-commutative 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-12} \lor \neg \left(j \leq 1.8 \cdot 10^{+171}\right) \land j \leq 8 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 30.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -8.5e+53)
     t_1
     (if (<= j -9e-256)
       (* y (* x z))
       (if (<= j 1.25e-200)
         (* a (* b i))
         (if (<= j 1.16e-116)
           (* z (* x y))
           (if (<= j 1.48e+29)
             (* b (* a i))
             (if (<= j 4.5e+240) 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 = c * (t * j);
	double tmp;
	if (j <= -8.5e+53) {
		tmp = t_1;
	} else if (j <= -9e-256) {
		tmp = y * (x * z);
	} else if (j <= 1.25e-200) {
		tmp = a * (b * i);
	} else if (j <= 1.16e-116) {
		tmp = z * (x * y);
	} else if (j <= 1.48e+29) {
		tmp = b * (a * i);
	} else if (j <= 4.5e+240) {
		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) :: tmp
    t_1 = c * (t * j)
    if (j <= (-8.5d+53)) then
        tmp = t_1
    else if (j <= (-9d-256)) then
        tmp = y * (x * z)
    else if (j <= 1.25d-200) then
        tmp = a * (b * i)
    else if (j <= 1.16d-116) then
        tmp = z * (x * y)
    else if (j <= 1.48d+29) then
        tmp = b * (a * i)
    else if (j <= 4.5d+240) 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 = c * (t * j);
	double tmp;
	if (j <= -8.5e+53) {
		tmp = t_1;
	} else if (j <= -9e-256) {
		tmp = y * (x * z);
	} else if (j <= 1.25e-200) {
		tmp = a * (b * i);
	} else if (j <= 1.16e-116) {
		tmp = z * (x * y);
	} else if (j <= 1.48e+29) {
		tmp = b * (a * i);
	} else if (j <= 4.5e+240) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -8.5e+53:
		tmp = t_1
	elif j <= -9e-256:
		tmp = y * (x * z)
	elif j <= 1.25e-200:
		tmp = a * (b * i)
	elif j <= 1.16e-116:
		tmp = z * (x * y)
	elif j <= 1.48e+29:
		tmp = b * (a * i)
	elif j <= 4.5e+240:
		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(c * Float64(t * j))
	tmp = 0.0
	if (j <= -8.5e+53)
		tmp = t_1;
	elseif (j <= -9e-256)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.25e-200)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 1.16e-116)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 1.48e+29)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= 4.5e+240)
		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 = c * (t * j);
	tmp = 0.0;
	if (j <= -8.5e+53)
		tmp = t_1;
	elseif (j <= -9e-256)
		tmp = y * (x * z);
	elseif (j <= 1.25e-200)
		tmp = a * (b * i);
	elseif (j <= 1.16e-116)
		tmp = z * (x * y);
	elseif (j <= 1.48e+29)
		tmp = b * (a * i);
	elseif (j <= 4.5e+240)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.5e+53], t$95$1, If[LessEqual[j, -9e-256], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e-200], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e-116], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e+29], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e+240], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -8.5000000000000002e53 or 1.48e29 < j < 4.49999999999999979e240

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. distribute-rgt-neg-in 70.1%

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

      3. distribute-rgt-neg-in 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in c around inf 45.0%

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

      1. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   if -8.5000000000000002e53 < j < -9.0000000000000005e-256

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around inf 39.8%

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

   if -9.0000000000000005e-256 < j < 1.24999999999999998e-200

   1. Initial program 59.2%

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

   3. Taylor expanded in b around inf 66.5%

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

      1. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in i around inf 54.9%

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

   if 1.24999999999999998e-200 < j < 1.16e-116

   1. Initial program 44.2%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around inf 51.1%

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

      1. associate-*r* 51.2%

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

      2. *-commutative 51.2%

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

   8. Simplified 51.2%

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

   if 1.16e-116 < j < 1.48e29

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in i around inf 41.2%

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

   if 4.49999999999999979e240 < j

   1. Initial program 70.7%

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

   3. Taylor expanded in t around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-rgt-neg-in 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in t around 0 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

      3. *-commutative 54.2%

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

   8. Simplified 54.2%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+240}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+229}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -1.14 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-90}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-257}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= x -1.9e+229)
     (* a (* x (- t)))
     (if (<= x -6.9e+167)
       (* x (* y z))
       (if (<= x -1.14e+136)
         t_1
         (if (<= x -2.7e-90)
           (* c (* t j))
           (if (<= x -4.7e-257)
             (* z (* b (- c)))
             (if (<= x 5.8e+38) t_1 (* 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 t_1 = a * (b * i);
	double tmp;
	if (x <= -1.9e+229) {
		tmp = a * (x * -t);
	} else if (x <= -6.9e+167) {
		tmp = x * (y * z);
	} else if (x <= -1.14e+136) {
		tmp = t_1;
	} else if (x <= -2.7e-90) {
		tmp = c * (t * j);
	} else if (x <= -4.7e-257) {
		tmp = z * (b * -c);
	} else if (x <= 5.8e+38) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (x <= (-1.9d+229)) then
        tmp = a * (x * -t)
    else if (x <= (-6.9d+167)) then
        tmp = x * (y * z)
    else if (x <= (-1.14d+136)) then
        tmp = t_1
    else if (x <= (-2.7d-90)) then
        tmp = c * (t * j)
    else if (x <= (-4.7d-257)) then
        tmp = z * (b * -c)
    else if (x <= 5.8d+38) then
        tmp = t_1
    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 t_1 = a * (b * i);
	double tmp;
	if (x <= -1.9e+229) {
		tmp = a * (x * -t);
	} else if (x <= -6.9e+167) {
		tmp = x * (y * z);
	} else if (x <= -1.14e+136) {
		tmp = t_1;
	} else if (x <= -2.7e-90) {
		tmp = c * (t * j);
	} else if (x <= -4.7e-257) {
		tmp = z * (b * -c);
	} else if (x <= 5.8e+38) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if x <= -1.9e+229:
		tmp = a * (x * -t)
	elif x <= -6.9e+167:
		tmp = x * (y * z)
	elif x <= -1.14e+136:
		tmp = t_1
	elif x <= -2.7e-90:
		tmp = c * (t * j)
	elif x <= -4.7e-257:
		tmp = z * (b * -c)
	elif x <= 5.8e+38:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (x <= -1.9e+229)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -6.9e+167)
		tmp = Float64(x * Float64(y * z));
	elseif (x <= -1.14e+136)
		tmp = t_1;
	elseif (x <= -2.7e-90)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= -4.7e-257)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (x <= 5.8e+38)
		tmp = t_1;
	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)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (x <= -1.9e+229)
		tmp = a * (x * -t);
	elseif (x <= -6.9e+167)
		tmp = x * (y * z);
	elseif (x <= -1.14e+136)
		tmp = t_1;
	elseif (x <= -2.7e-90)
		tmp = c * (t * j);
	elseif (x <= -4.7e-257)
		tmp = z * (b * -c);
	elseif (x <= 5.8e+38)
		tmp = t_1;
	else
		tmp = y * (x * z);
	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]}, If[LessEqual[x, -1.9e+229], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.9e+167], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.14e+136], t$95$1, If[LessEqual[x, -2.7e-90], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.7e-257], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+38], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.90000000000000009e229

   1. Initial program 84.1%

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

   3. Taylor expanded in x around inf 69.8%

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

      1. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in y around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-*r* 57.8%

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

      3. *-commutative 57.8%

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

      4. associate-*r* 57.8%

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

      5. neg-mul-1 57.8%

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

   8. Simplified 57.8%

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

   if -1.90000000000000009e229 < x < -6.90000000000000042e167

   1. Initial program 84.9%

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

   3. Taylor expanded in x around inf 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

   8. Simplified 48.6%

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

   if -6.90000000000000042e167 < x < -1.14e136 or -4.6999999999999998e-257 < x < 5.80000000000000013e38

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 48.3%

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

      1. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in i around inf 41.5%

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

   if -1.14e136 < x < -2.69999999999999996e-90

   1. Initial program 81.1%

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

   3. Taylor expanded in t around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-rgt-neg-in 53.8%

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

      3. distribute-rgt-neg-in 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in c around inf 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if -2.69999999999999996e-90 < x < -4.6999999999999998e-257

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf 47.4%

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

      1. *-commutative 47.4%

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

      2. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in y around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. *-commutative 45.3%

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

      3. distribute-rgt-neg-in 45.3%

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

   8. Simplified 45.3%

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

   if 5.80000000000000013e38 < x

   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. Add Preprocessing

   3. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in z around inf 52.8%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+229}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -1.14 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-90}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-257}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + y \cdot \left(x \cdot z\right)\\ t_3 := b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{+55}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* y (* x z))))
        (t_3 (* b (* c (- (* a (/ i c)) z)))))
   (if (<= b -8.8e+55)
     t_3
     (if (<= b 9.2e-243)
       t_2
       (if (<= b 1.8e-44)
         (- t_1 (* a (* x t)))
         (if (<= b 1.05e+121) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (y * (x * z));
	double t_3 = b * (c * ((a * (i / c)) - z));
	double tmp;
	if (b <= -8.8e+55) {
		tmp = t_3;
	} else if (b <= 9.2e-243) {
		tmp = t_2;
	} else if (b <= 1.8e-44) {
		tmp = t_1 - (a * (x * t));
	} else if (b <= 1.05e+121) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (y * (x * z))
    t_3 = b * (c * ((a * (i / c)) - z))
    if (b <= (-8.8d+55)) then
        tmp = t_3
    else if (b <= 9.2d-243) then
        tmp = t_2
    else if (b <= 1.8d-44) then
        tmp = t_1 - (a * (x * t))
    else if (b <= 1.05d+121) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (y * (x * z));
	double t_3 = b * (c * ((a * (i / c)) - z));
	double tmp;
	if (b <= -8.8e+55) {
		tmp = t_3;
	} else if (b <= 9.2e-243) {
		tmp = t_2;
	} else if (b <= 1.8e-44) {
		tmp = t_1 - (a * (x * t));
	} else if (b <= 1.05e+121) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (y * (x * z))
	t_3 = b * (c * ((a * (i / c)) - z))
	tmp = 0
	if b <= -8.8e+55:
		tmp = t_3
	elif b <= 9.2e-243:
		tmp = t_2
	elif b <= 1.8e-44:
		tmp = t_1 - (a * (x * t))
	elif b <= 1.05e+121:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(y * Float64(x * z)))
	t_3 = Float64(b * Float64(c * Float64(Float64(a * Float64(i / c)) - z)))
	tmp = 0.0
	if (b <= -8.8e+55)
		tmp = t_3;
	elseif (b <= 9.2e-243)
		tmp = t_2;
	elseif (b <= 1.8e-44)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (b <= 1.05e+121)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 + (y * (x * z));
	t_3 = b * (c * ((a * (i / c)) - z));
	tmp = 0.0;
	if (b <= -8.8e+55)
		tmp = t_3;
	elseif (b <= 9.2e-243)
		tmp = t_2;
	elseif (b <= 1.8e-44)
		tmp = t_1 - (a * (x * t));
	elseif (b <= 1.05e+121)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(c * N[(N[(a * N[(i / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e+55], t$95$3, If[LessEqual[b, 9.2e-243], t$95$2, If[LessEqual[b, 1.8e-44], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+121], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.80000000000000042e55 or 1.0500000000000001e121 < b

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around inf 65.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

   if -8.80000000000000042e55 < b < 9.20000000000000001e-243 or 1.7999999999999999e-44 < b < 1.0500000000000001e121

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 71.6%

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

   5. Simplified 71.6%

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

   if 9.20000000000000001e-243 < b < 1.7999999999999999e-44

   1. Initial program 70.7%

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

   3. Taylor expanded in t around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. distribute-rgt-neg-in 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-243}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{if}\;b \leq -9.4 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(i \cdot \left(c \cdot \frac{t}{i} - y\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* y (* x z))))
        (t_2 (* b (* c (- (* a (/ i c)) z)))))
   (if (<= b -9.4e+55)
     t_2
     (if (<= b 9.5e-244)
       t_1
       (if (<= b 8e-45)
         (- (* j (* i (- (* c (/ t i)) y))) (* a (* x t)))
         (if (<= b 3.3e+122) 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 = (j * ((t * c) - (y * i))) + (y * (x * z));
	double t_2 = b * (c * ((a * (i / c)) - z));
	double tmp;
	if (b <= -9.4e+55) {
		tmp = t_2;
	} else if (b <= 9.5e-244) {
		tmp = t_1;
	} else if (b <= 8e-45) {
		tmp = (j * (i * ((c * (t / i)) - y))) - (a * (x * t));
	} else if (b <= 3.3e+122) {
		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 = (j * ((t * c) - (y * i))) + (y * (x * z))
    t_2 = b * (c * ((a * (i / c)) - z))
    if (b <= (-9.4d+55)) then
        tmp = t_2
    else if (b <= 9.5d-244) then
        tmp = t_1
    else if (b <= 8d-45) then
        tmp = (j * (i * ((c * (t / i)) - y))) - (a * (x * t))
    else if (b <= 3.3d+122) 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 = (j * ((t * c) - (y * i))) + (y * (x * z));
	double t_2 = b * (c * ((a * (i / c)) - z));
	double tmp;
	if (b <= -9.4e+55) {
		tmp = t_2;
	} else if (b <= 9.5e-244) {
		tmp = t_1;
	} else if (b <= 8e-45) {
		tmp = (j * (i * ((c * (t / i)) - y))) - (a * (x * t));
	} else if (b <= 3.3e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (y * (x * z))
	t_2 = b * (c * ((a * (i / c)) - z))
	tmp = 0
	if b <= -9.4e+55:
		tmp = t_2
	elif b <= 9.5e-244:
		tmp = t_1
	elif b <= 8e-45:
		tmp = (j * (i * ((c * (t / i)) - y))) - (a * (x * t))
	elif b <= 3.3e+122:
		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(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(y * Float64(x * z)))
	t_2 = Float64(b * Float64(c * Float64(Float64(a * Float64(i / c)) - z)))
	tmp = 0.0
	if (b <= -9.4e+55)
		tmp = t_2;
	elseif (b <= 9.5e-244)
		tmp = t_1;
	elseif (b <= 8e-45)
		tmp = Float64(Float64(j * Float64(i * Float64(Float64(c * Float64(t / i)) - y))) - Float64(a * Float64(x * t)));
	elseif (b <= 3.3e+122)
		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 = (j * ((t * c) - (y * i))) + (y * (x * z));
	t_2 = b * (c * ((a * (i / c)) - z));
	tmp = 0.0;
	if (b <= -9.4e+55)
		tmp = t_2;
	elseif (b <= 9.5e-244)
		tmp = t_1;
	elseif (b <= 8e-45)
		tmp = (j * (i * ((c * (t / i)) - y))) - (a * (x * t));
	elseif (b <= 3.3e+122)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(c * N[(N[(a * N[(i / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.4e+55], t$95$2, If[LessEqual[b, 9.5e-244], t$95$1, If[LessEqual[b, 8e-45], N[(N[(j * N[(i * N[(N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+122], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.4000000000000001e55 or 3.2999999999999999e122 < b

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around inf 65.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

   if -9.4000000000000001e55 < b < 9.4999999999999995e-244 or 7.99999999999999987e-45 < b < 3.2999999999999999e122

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 71.6%

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

   5. Simplified 71.6%

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

   if 9.4999999999999995e-244 < b < 7.99999999999999987e-45

   1. Initial program 70.7%

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

   3. Taylor expanded in t around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. distribute-rgt-neg-in 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in i around inf 69.2%

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

      1. associate-/l* 66.8%

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

   8. Simplified 66.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-244}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(i \cdot \left(c \cdot \frac{t}{i} - y\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot \left(c - i \cdot \frac{y}{t}\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* y (* x z))))
        (t_2 (* b (* c (- (* a (/ i c)) z)))))
   (if (<= b -8.6e+55)
     t_2
     (if (<= b 2.9e-237)
       t_1
       (if (<= b 2.7e-44)
         (- (* j (* t (- c (* i (/ y t))))) (* a (* x t)))
         (if (<= b 2.55e+120) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (y * (x * z));
	double t_2 = b * (c * ((a * (i / c)) - z));
	double tmp;
	if (b <= -8.6e+55) {
		tmp = t_2;
	} else if (b <= 2.9e-237) {
		tmp = t_1;
	} else if (b <= 2.7e-44) {
		tmp = (j * (t * (c - (i * (y / t))))) - (a * (x * t));
	} else if (b <= 2.55e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (y * (x * z))
    t_2 = b * (c * ((a * (i / c)) - z))
    if (b <= (-8.6d+55)) then
        tmp = t_2
    else if (b <= 2.9d-237) then
        tmp = t_1
    else if (b <= 2.7d-44) then
        tmp = (j * (t * (c - (i * (y / t))))) - (a * (x * t))
    else if (b <= 2.55d+120) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (y * (x * z));
	double t_2 = b * (c * ((a * (i / c)) - z));
	double tmp;
	if (b <= -8.6e+55) {
		tmp = t_2;
	} else if (b <= 2.9e-237) {
		tmp = t_1;
	} else if (b <= 2.7e-44) {
		tmp = (j * (t * (c - (i * (y / t))))) - (a * (x * t));
	} else if (b <= 2.55e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (y * (x * z))
	t_2 = b * (c * ((a * (i / c)) - z))
	tmp = 0
	if b <= -8.6e+55:
		tmp = t_2
	elif b <= 2.9e-237:
		tmp = t_1
	elif b <= 2.7e-44:
		tmp = (j * (t * (c - (i * (y / t))))) - (a * (x * t))
	elif b <= 2.55e+120:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(y * Float64(x * z)))
	t_2 = Float64(b * Float64(c * Float64(Float64(a * Float64(i / c)) - z)))
	tmp = 0.0
	if (b <= -8.6e+55)
		tmp = t_2;
	elseif (b <= 2.9e-237)
		tmp = t_1;
	elseif (b <= 2.7e-44)
		tmp = Float64(Float64(j * Float64(t * Float64(c - Float64(i * Float64(y / t))))) - Float64(a * Float64(x * t)));
	elseif (b <= 2.55e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (y * (x * z));
	t_2 = b * (c * ((a * (i / c)) - z));
	tmp = 0.0;
	if (b <= -8.6e+55)
		tmp = t_2;
	elseif (b <= 2.9e-237)
		tmp = t_1;
	elseif (b <= 2.7e-44)
		tmp = (j * (t * (c - (i * (y / t))))) - (a * (x * t));
	elseif (b <= 2.55e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(c * N[(N[(a * N[(i / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.6e+55], t$95$2, If[LessEqual[b, 2.9e-237], t$95$1, If[LessEqual[b, 2.7e-44], N[(N[(j * N[(t * N[(c - N[(i * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+120], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5999999999999998e55 or 2.55000000000000014e120 < b

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around inf 65.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

   if -8.5999999999999998e55 < b < 2.90000000000000011e-237 or 2.6999999999999999e-44 < b < 2.55000000000000014e120

   1. Initial program 83.0%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-*r* 71.4%

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

   5. Simplified 71.4%

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

   if 2.90000000000000011e-237 < b < 2.6999999999999999e-44

   1. Initial program 69.3%

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

   3. Taylor expanded in t around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. distribute-rgt-neg-in 67.5%

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

      3. distribute-rgt-neg-in 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in t around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. associate-/l* 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-237}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot \left(c - i \cdot \frac{y}{t}\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -2.05e-17)
     t_1
     (if (<= j -7.5e-256)
       (* x (* y (- z (/ (* t a) y))))
       (if (<= j 1.7e-198)
         (* a (- (* b i) (* x t)))
         (if (<= j 5.4e-102)
           (* x (- (* y z) (* t a)))
           (if (<= j 6.4e+23) (* 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.05e-17) {
		tmp = t_1;
	} else if (j <= -7.5e-256) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else if (j <= 1.7e-198) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 5.4e-102) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 6.4e+23) {
		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 = j * ((t * c) - (y * i))
    if (j <= (-2.05d-17)) then
        tmp = t_1
    else if (j <= (-7.5d-256)) then
        tmp = x * (y * (z - ((t * a) / y)))
    else if (j <= 1.7d-198) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= 5.4d-102) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 6.4d+23) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.05e-17) {
		tmp = t_1;
	} else if (j <= -7.5e-256) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else if (j <= 1.7e-198) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 5.4e-102) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 6.4e+23) {
		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 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.05e-17:
		tmp = t_1
	elif j <= -7.5e-256:
		tmp = x * (y * (z - ((t * a) / y)))
	elif j <= 1.7e-198:
		tmp = a * ((b * i) - (x * t))
	elif j <= 5.4e-102:
		tmp = x * ((y * z) - (t * a))
	elif j <= 6.4e+23:
		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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.05e-17)
		tmp = t_1;
	elseif (j <= -7.5e-256)
		tmp = Float64(x * Float64(y * Float64(z - Float64(Float64(t * a) / y))));
	elseif (j <= 1.7e-198)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= 5.4e-102)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 6.4e+23)
		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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.05e-17)
		tmp = t_1;
	elseif (j <= -7.5e-256)
		tmp = x * (y * (z - ((t * a) / y)));
	elseif (j <= 1.7e-198)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= 5.4e-102)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 6.4e+23)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.05e-17], t$95$1, If[LessEqual[j, -7.5e-256], N[(x * N[(y * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-198], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e-102], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e+23], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.05e-17 or 6.4e23 < j

   1. Initial program 78.9%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-in 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in a around 0 67.1%

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

   if -2.05e-17 < j < -7.50000000000000005e-256

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in y around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   if -7.50000000000000005e-256 < j < 1.6999999999999999e-198

   1. Initial program 59.2%

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

   3. Taylor expanded in a around inf 67.5%

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

      1. distribute-lft-out-- 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if 1.6999999999999999e-198 < j < 5.4e-102

   1. Initial program 55.3%

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

   3. Taylor expanded in x around inf 70.4%

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

      1. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if 5.4e-102 < j < 6.4e23

   1. Initial program 81.1%

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

   3. Taylor expanded in b around inf 63.5%

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

      1. *-commutative 63.5%

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

   5. Simplified 63.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{-102}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -1080000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* c (* t j))))
   (if (<= j -1080000000000.0)
     t_2
     (if (<= j -7e-256)
       t_1
       (if (<= j 4e-200)
         (* a (* b i))
         (if (<= j 6.5e-113) t_1 (if (<= j 1.75e+20) (* b (* a i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -1080000000000.0) {
		tmp = t_2;
	} else if (j <= -7e-256) {
		tmp = t_1;
	} else if (j <= 4e-200) {
		tmp = a * (b * i);
	} else if (j <= 6.5e-113) {
		tmp = t_1;
	} else if (j <= 1.75e+20) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = c * (t * j)
    if (j <= (-1080000000000.0d0)) then
        tmp = t_2
    else if (j <= (-7d-256)) then
        tmp = t_1
    else if (j <= 4d-200) then
        tmp = a * (b * i)
    else if (j <= 6.5d-113) then
        tmp = t_1
    else if (j <= 1.75d+20) then
        tmp = b * (a * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -1080000000000.0) {
		tmp = t_2;
	} else if (j <= -7e-256) {
		tmp = t_1;
	} else if (j <= 4e-200) {
		tmp = a * (b * i);
	} else if (j <= 6.5e-113) {
		tmp = t_1;
	} else if (j <= 1.75e+20) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = c * (t * j)
	tmp = 0
	if j <= -1080000000000.0:
		tmp = t_2
	elif j <= -7e-256:
		tmp = t_1
	elif j <= 4e-200:
		tmp = a * (b * i)
	elif j <= 6.5e-113:
		tmp = t_1
	elif j <= 1.75e+20:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -1080000000000.0)
		tmp = t_2;
	elseif (j <= -7e-256)
		tmp = t_1;
	elseif (j <= 4e-200)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 6.5e-113)
		tmp = t_1;
	elseif (j <= 1.75e+20)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (j <= -1080000000000.0)
		tmp = t_2;
	elseif (j <= -7e-256)
		tmp = t_1;
	elseif (j <= 4e-200)
		tmp = a * (b * i);
	elseif (j <= 6.5e-113)
		tmp = t_1;
	elseif (j <= 1.75e+20)
		tmp = b * (a * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1080000000000.0], t$95$2, If[LessEqual[j, -7e-256], t$95$1, If[LessEqual[j, 4e-200], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e-113], t$95$1, If[LessEqual[j, 1.75e+20], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.08e12 or 1.75e20 < j

   1. Initial program 78.1%

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

   3. Taylor expanded in t around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. distribute-rgt-neg-in 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in c around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if -1.08e12 < j < -7.00000000000000028e-256 or 3.9999999999999999e-200 < j < 6.49999999999999979e-113

   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. Add Preprocessing

   3. Taylor expanded in x around inf 62.9%

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

      1. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around inf 41.9%

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

      1. *-commutative 41.9%

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

   8. Simplified 41.9%

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

   if -7.00000000000000028e-256 < j < 3.9999999999999999e-200

   1. Initial program 59.2%

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

   3. Taylor expanded in b around inf 66.5%

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

      1. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in i around inf 54.9%

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

   if 6.49999999999999979e-113 < j < 1.75e20

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in i around inf 41.2%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1080000000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -1.05e+54)
     t_1
     (if (<= j -1.25e-255)
       (* y (* x z))
       (if (<= j 2.3e-200)
         (* a (* b i))
         (if (<= j 2.8e-117)
           (* x (* y z))
           (if (<= j 2.6e+27) (* b (* a i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -1.05e+54) {
		tmp = t_1;
	} else if (j <= -1.25e-255) {
		tmp = y * (x * z);
	} else if (j <= 2.3e-200) {
		tmp = a * (b * i);
	} else if (j <= 2.8e-117) {
		tmp = x * (y * z);
	} else if (j <= 2.6e+27) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (j <= (-1.05d+54)) then
        tmp = t_1
    else if (j <= (-1.25d-255)) then
        tmp = y * (x * z)
    else if (j <= 2.3d-200) then
        tmp = a * (b * i)
    else if (j <= 2.8d-117) then
        tmp = x * (y * z)
    else if (j <= 2.6d+27) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -1.05e+54) {
		tmp = t_1;
	} else if (j <= -1.25e-255) {
		tmp = y * (x * z);
	} else if (j <= 2.3e-200) {
		tmp = a * (b * i);
	} else if (j <= 2.8e-117) {
		tmp = x * (y * z);
	} else if (j <= 2.6e+27) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -1.05e+54:
		tmp = t_1
	elif j <= -1.25e-255:
		tmp = y * (x * z)
	elif j <= 2.3e-200:
		tmp = a * (b * i)
	elif j <= 2.8e-117:
		tmp = x * (y * z)
	elif j <= 2.6e+27:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -1.05e+54)
		tmp = t_1;
	elseif (j <= -1.25e-255)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 2.3e-200)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 2.8e-117)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 2.6e+27)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (j <= -1.05e+54)
		tmp = t_1;
	elseif (j <= -1.25e-255)
		tmp = y * (x * z);
	elseif (j <= 2.3e-200)
		tmp = a * (b * i);
	elseif (j <= 2.8e-117)
		tmp = x * (y * z);
	elseif (j <= 2.6e+27)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.05e+54], t$95$1, If[LessEqual[j, -1.25e-255], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-200], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-117], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+27], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.04999999999999993e54 or 2.60000000000000009e27 < j

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-rgt-neg-in 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in c around inf 42.4%

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

      1. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -1.04999999999999993e54 < j < -1.2499999999999999e-255

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around inf 39.8%

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

   if -1.2499999999999999e-255 < j < 2.30000000000000007e-200

   1. Initial program 59.2%

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

   3. Taylor expanded in b around inf 66.5%

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

      1. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in i around inf 54.9%

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

   if 2.30000000000000007e-200 < j < 2.8e-117

   1. Initial program 44.2%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if 2.8e-117 < j < 2.60000000000000009e27

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in i around inf 41.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1500:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -5.2e+53)
     t_1
     (if (<= j -1.2e-254)
       (* y (* x z))
       (if (<= j 2.4e-198)
         (* a (* b i))
         (if (<= j 7.8e-119)
           (* z (* x y))
           (if (<= j 1500.0) (* b (* a i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -5.2e+53) {
		tmp = t_1;
	} else if (j <= -1.2e-254) {
		tmp = y * (x * z);
	} else if (j <= 2.4e-198) {
		tmp = a * (b * i);
	} else if (j <= 7.8e-119) {
		tmp = z * (x * y);
	} else if (j <= 1500.0) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (j <= (-5.2d+53)) then
        tmp = t_1
    else if (j <= (-1.2d-254)) then
        tmp = y * (x * z)
    else if (j <= 2.4d-198) then
        tmp = a * (b * i)
    else if (j <= 7.8d-119) then
        tmp = z * (x * y)
    else if (j <= 1500.0d0) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -5.2e+53) {
		tmp = t_1;
	} else if (j <= -1.2e-254) {
		tmp = y * (x * z);
	} else if (j <= 2.4e-198) {
		tmp = a * (b * i);
	} else if (j <= 7.8e-119) {
		tmp = z * (x * y);
	} else if (j <= 1500.0) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -5.2e+53:
		tmp = t_1
	elif j <= -1.2e-254:
		tmp = y * (x * z)
	elif j <= 2.4e-198:
		tmp = a * (b * i)
	elif j <= 7.8e-119:
		tmp = z * (x * y)
	elif j <= 1500.0:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -5.2e+53)
		tmp = t_1;
	elseif (j <= -1.2e-254)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 2.4e-198)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 7.8e-119)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 1500.0)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (j <= -5.2e+53)
		tmp = t_1;
	elseif (j <= -1.2e-254)
		tmp = y * (x * z);
	elseif (j <= 2.4e-198)
		tmp = a * (b * i);
	elseif (j <= 7.8e-119)
		tmp = z * (x * y);
	elseif (j <= 1500.0)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.2e+53], t$95$1, If[LessEqual[j, -1.2e-254], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e-198], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-119], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1500.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.19999999999999996e53 or 1500 < j

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-rgt-neg-in 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in c around inf 42.4%

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

      1. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -5.19999999999999996e53 < j < -1.20000000000000001e-254

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around inf 39.8%

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

   if -1.20000000000000001e-254 < j < 2.39999999999999986e-198

   1. Initial program 59.2%

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

   3. Taylor expanded in b around inf 66.5%

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

      1. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in i around inf 54.9%

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

   if 2.39999999999999986e-198 < j < 7.7999999999999998e-119

   1. Initial program 44.2%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around inf 51.1%

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

      1. associate-*r* 51.2%

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

      2. *-commutative 51.2%

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

   8. Simplified 51.2%

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

   if 7.7999999999999998e-119 < j < 1500

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in i around inf 41.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1500:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -6.4e-27)
     t_2
     (if (<= j -1.9e-99)
       t_1
       (if (<= j -5.4e-254) (* y (* x z)) (if (<= j 8.8e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.4e-27) {
		tmp = t_2;
	} else if (j <= -1.9e-99) {
		tmp = t_1;
	} else if (j <= -5.4e-254) {
		tmp = y * (x * z);
	} else if (j <= 8.8e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-6.4d-27)) then
        tmp = t_2
    else if (j <= (-1.9d-99)) then
        tmp = t_1
    else if (j <= (-5.4d-254)) then
        tmp = y * (x * z)
    else if (j <= 8.8d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.4e-27) {
		tmp = t_2;
	} else if (j <= -1.9e-99) {
		tmp = t_1;
	} else if (j <= -5.4e-254) {
		tmp = y * (x * z);
	} else if (j <= 8.8e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -6.4e-27:
		tmp = t_2
	elif j <= -1.9e-99:
		tmp = t_1
	elif j <= -5.4e-254:
		tmp = y * (x * z)
	elif j <= 8.8e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.4e-27)
		tmp = t_2;
	elseif (j <= -1.9e-99)
		tmp = t_1;
	elseif (j <= -5.4e-254)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 8.8e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -6.4e-27)
		tmp = t_2;
	elseif (j <= -1.9e-99)
		tmp = t_1;
	elseif (j <= -5.4e-254)
		tmp = y * (x * z);
	elseif (j <= 8.8e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.4e-27], t$95$2, If[LessEqual[j, -1.9e-99], t$95$1, If[LessEqual[j, -5.4e-254], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.8e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.39999999999999982e-27 or 8.7999999999999995e27 < j

   1. Initial program 78.7%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-rgt-neg-in 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in a around 0 66.4%

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

   if -6.39999999999999982e-27 < j < -1.8999999999999998e-99 or -5.40000000000000013e-254 < j < 8.7999999999999995e27

   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. Add Preprocessing

   3. Taylor expanded in b around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   if -1.8999999999999998e-99 < j < -5.40000000000000013e-254

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 50.2%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+56} \lor \neg \left(b \leq 3.7 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.05e+56) (not (<= b 3.7e+120)))
   (* b (* c (- (* a (/ i c)) z)))
   (+ (* j (- (* t c) (* y 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 ((b <= -1.05e+56) || !(b <= 3.7e+120)) {
		tmp = b * (c * ((a * (i / c)) - z));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (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 ((b <= (-1.05d+56)) .or. (.not. (b <= 3.7d+120))) then
        tmp = b * (c * ((a * (i / c)) - z))
    else
        tmp = (j * ((t * c) - (y * i))) + (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 ((b <= -1.05e+56) || !(b <= 3.7e+120)) {
		tmp = b * (c * ((a * (i / c)) - z));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.05e+56) or not (b <= 3.7e+120):
		tmp = b * (c * ((a * (i / c)) - z))
	else:
		tmp = (j * ((t * c) - (y * i))) + (y * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.05e+56) || !(b <= 3.7e+120))
		tmp = Float64(b * Float64(c * Float64(Float64(a * Float64(i / c)) - z)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + 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 ((b <= -1.05e+56) || ~((b <= 3.7e+120)))
		tmp = b * (c * ((a * (i / c)) - z));
	else
		tmp = (j * ((t * c) - (y * i))) + (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.05e+56], N[Not[LessEqual[b, 3.7e+120]], $MachinePrecision]], N[(b * N[(c * N[(N[(a * N[(i / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.05000000000000009e56 or 3.70000000000000024e120 < b

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around inf 65.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

   if -1.05000000000000009e56 < b < 3.70000000000000024e120

   1. Initial program 79.8%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-*r* 67.5%

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

   5. Simplified 67.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+56} \lor \neg \left(b \leq 3.7 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -8.2e-9)
     t_1
     (if (<= b 1.35e-264)
       (* y (* x z))
       (if (<= b 8.2e-45) (* x (* 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 (b <= -8.2e-9) {
		tmp = t_1;
	} else if (b <= 1.35e-264) {
		tmp = y * (x * z);
	} else if (b <= 8.2e-45) {
		tmp = x * (t * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-8.2d-9)) then
        tmp = t_1
    else if (b <= 1.35d-264) then
        tmp = y * (x * z)
    else if (b <= 8.2d-45) then
        tmp = x * (t * -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8.2e-9) {
		tmp = t_1;
	} else if (b <= 1.35e-264) {
		tmp = y * (x * z);
	} else if (b <= 8.2e-45) {
		tmp = x * (t * -a);
	} else {
		tmp = 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 b <= -8.2e-9:
		tmp = t_1
	elif b <= 1.35e-264:
		tmp = y * (x * z)
	elif b <= 8.2e-45:
		tmp = x * (t * -a)
	else:
		tmp = 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 (b <= -8.2e-9)
		tmp = t_1;
	elseif (b <= 1.35e-264)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 8.2e-45)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -8.2e-9)
		tmp = t_1;
	elseif (b <= 1.35e-264)
		tmp = y * (x * z);
	elseif (b <= 8.2e-45)
		tmp = x * (t * -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e-9], t$95$1, If[LessEqual[b, 1.35e-264], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-45], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.2000000000000006e-9 or 8.1999999999999998e-45 < b

   1. Initial program 70.0%

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

   3. Taylor expanded in b around inf 57.3%

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

      1. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   if -8.2000000000000006e-9 < b < 1.34999999999999997e-264

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

      4. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf 39.9%

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

   if 1.34999999999999997e-264 < b < 8.1999999999999998e-45

   1. Initial program 72.1%

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

   3. Taylor expanded in x around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in y around 0 42.0%

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

      1. neg-mul-1 42.0%

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

      2. distribute-rgt-neg-in 42.0%

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

   8. Simplified 42.0%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -5.8e-9)
     t_1
     (if (<= b 1.05e-307)
       (* y (* x z))
       (if (<= b 8e+33) (* c (- (* t j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.8e-9) {
		tmp = t_1;
	} else if (b <= 1.05e-307) {
		tmp = y * (x * z);
	} else if (b <= 8e+33) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-5.8d-9)) then
        tmp = t_1
    else if (b <= 1.05d-307) then
        tmp = y * (x * z)
    else if (b <= 8d+33) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.8e-9) {
		tmp = t_1;
	} else if (b <= 1.05e-307) {
		tmp = y * (x * z);
	} else if (b <= 8e+33) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.8e-9:
		tmp = t_1
	elif b <= 1.05e-307:
		tmp = y * (x * z)
	elif b <= 8e+33:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.8e-9)
		tmp = t_1;
	elseif (b <= 1.05e-307)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 8e+33)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.8e-9)
		tmp = t_1;
	elseif (b <= 1.05e-307)
		tmp = y * (x * z);
	elseif (b <= 8e+33)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e-9], t$95$1, If[LessEqual[b, 1.05e-307], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+33], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.79999999999999982e-9 or 7.9999999999999996e33 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in b around inf 60.2%

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

      1. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if -5.79999999999999982e-9 < b < 1.0500000000000001e-307

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in z around inf 40.3%

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

   if 1.0500000000000001e-307 < b < 7.9999999999999996e33

   1. Initial program 71.0%

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

   3. Taylor expanded in c around inf 42.9%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+15} \lor \neg \left(j \leq 3.8 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.8e+15) (not (<= j 3.8e+33))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.8e+15) || !(j <= 3.8e+33)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-6.8d+15)) .or. (.not. (j <= 3.8d+33))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.8e+15) || !(j <= 3.8e+33)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.8e+15) or not (j <= 3.8e+33):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.8e+15) || !(j <= 3.8e+33))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6.8e+15) || ~((j <= 3.8e+33)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.8e+15], N[Not[LessEqual[j, 3.8e+33]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.8e15 or 3.80000000000000002e33 < j

   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. Add Preprocessing

   3. Taylor expanded in t around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. distribute-rgt-neg-in 69.8%

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

      3. distribute-rgt-neg-in 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in c around inf 41.5%

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

      1. *-commutative 41.5%

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

   8. Simplified 41.5%

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

   if -6.8e15 < j < 3.80000000000000002e33

   1. Initial program 72.2%

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

   3. Taylor expanded in b around inf 48.3%

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

      1. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in i around inf 35.0%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+15} \lor \neg \left(j \leq 3.8 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 22.5% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.1%

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

3. Taylor expanded in b around inf 38.0%

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

   1. *-commutative 38.0%

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

5. Simplified 38.0%

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

6. Taylor expanded in i around inf 23.1%

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

7. Final simplification 23.1%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 69.6% 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 2024089 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

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

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