Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 74.0% → 65.5%

Time: 31.1s

Alternatives: 26

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

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

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

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

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ t_4 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+143}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.22 \cdot 10^{+49}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-299}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+81}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_3 (+ (* z (- (* x y) (* b c))) t_1))
        (t_4 (* t (- (* b i) (* x a)))))
   (if (<= t -1.3e+143)
     t_4
     (if (<= t -2.05e+96)
       t_2
       (if (<= t -2.22e+49)
         t_4
         (if (<= t -5.2e-192)
           t_3
           (if (<= t -5.2e-214)
             t_2
             (if (<= t 3.9e-299)
               (+ t_1 (* x (- (* y z) (* t a))))
               (if (<= t 6.5e+81) t_3 t_4)))))))))

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 * ((a * c) - (y * i));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (z * ((x * y) - (b * c))) + t_1;
	double t_4 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.3e+143) {
		tmp = t_4;
	} else if (t <= -2.05e+96) {
		tmp = t_2;
	} else if (t <= -2.22e+49) {
		tmp = t_4;
	} else if (t <= -5.2e-192) {
		tmp = t_3;
	} else if (t <= -5.2e-214) {
		tmp = t_2;
	} else if (t <= 3.9e-299) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (t <= 6.5e+81) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    t_3 = (z * ((x * y) - (b * c))) + t_1
    t_4 = t * ((b * i) - (x * a))
    if (t <= (-1.3d+143)) then
        tmp = t_4
    else if (t <= (-2.05d+96)) then
        tmp = t_2
    else if (t <= (-2.22d+49)) then
        tmp = t_4
    else if (t <= (-5.2d-192)) then
        tmp = t_3
    else if (t <= (-5.2d-214)) then
        tmp = t_2
    else if (t <= 3.9d-299) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (t <= 6.5d+81) then
        tmp = t_3
    else
        tmp = t_4
    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 * ((a * c) - (y * i));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (z * ((x * y) - (b * c))) + t_1;
	double t_4 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.3e+143) {
		tmp = t_4;
	} else if (t <= -2.05e+96) {
		tmp = t_2;
	} else if (t <= -2.22e+49) {
		tmp = t_4;
	} else if (t <= -5.2e-192) {
		tmp = t_3;
	} else if (t <= -5.2e-214) {
		tmp = t_2;
	} else if (t <= 3.9e-299) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (t <= 6.5e+81) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	t_3 = (z * ((x * y) - (b * c))) + t_1
	t_4 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.3e+143:
		tmp = t_4
	elif t <= -2.05e+96:
		tmp = t_2
	elif t <= -2.22e+49:
		tmp = t_4
	elif t <= -5.2e-192:
		tmp = t_3
	elif t <= -5.2e-214:
		tmp = t_2
	elif t <= 3.9e-299:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif t <= 6.5e+81:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1)
	t_4 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.3e+143)
		tmp = t_4;
	elseif (t <= -2.05e+96)
		tmp = t_2;
	elseif (t <= -2.22e+49)
		tmp = t_4;
	elseif (t <= -5.2e-192)
		tmp = t_3;
	elseif (t <= -5.2e-214)
		tmp = t_2;
	elseif (t <= 3.9e-299)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (t <= 6.5e+81)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	t_3 = (z * ((x * y) - (b * c))) + t_1;
	t_4 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.3e+143)
		tmp = t_4;
	elseif (t <= -2.05e+96)
		tmp = t_2;
	elseif (t <= -2.22e+49)
		tmp = t_4;
	elseif (t <= -5.2e-192)
		tmp = t_3;
	elseif (t <= -5.2e-214)
		tmp = t_2;
	elseif (t <= 3.9e-299)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (t <= 6.5e+81)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+143], t$95$4, If[LessEqual[t, -2.05e+96], t$95$2, If[LessEqual[t, -2.22e+49], t$95$4, If[LessEqual[t, -5.2e-192], t$95$3, If[LessEqual[t, -5.2e-214], t$95$2, If[LessEqual[t, 3.9e-299], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+81], t$95$3, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2999999999999999e143 or -2.04999999999999999e96 < t < -2.21999999999999995e49 or 6.4999999999999996e81 < t

   1. Initial program 58.7%

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

   3. Taylor expanded in t around inf 76.4%

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

      1. distribute-lft-out-- 76.4%

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

      2. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if -1.2999999999999999e143 < t < -2.04999999999999999e96 or -5.2000000000000003e-192 < t < -5.2e-214

   1. Initial program 74.3%

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

   3. Taylor expanded in x around 0 83.0%

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

      1. *-commutative 83.0%

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

   5. Simplified 83.0%

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

   if -2.21999999999999995e49 < t < -5.2000000000000003e-192 or 3.8999999999999998e-299 < t < 6.4999999999999996e81

   1. Initial program 75.0%

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

   3. Taylor expanded in z around 0 84.2%

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

   4. Taylor expanded in t around 0 83.0%

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

   if -5.2e-214 < t < 3.8999999999999998e-299

   1. Initial program 89.9%

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

   3. Taylor expanded in b around 0 85.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.22 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 89.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 47.9%

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

4. Final simplification 80.9%

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

Alternative 3: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-107}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* c (- (* a j) (* z b))))
        (t_3 (* x (- (* y z) (* t a))))
        (t_4 (* j (- (* a c) (* y i)))))
   (if (<= j -2.7e+71)
     t_4
     (if (<= j -8.6e-61)
       t_2
       (if (<= j -6.5e-107)
         t_4
         (if (<= j -2e-160)
           t_1
           (if (<= j -6.5e-281)
             t_3
             (if (<= j 1.1e-244)
               t_1
               (if (<= j 5e-36) t_3 (if (<= j 7.2e+55) t_2 t_4))))))))))

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 * ((t * i) - (z * c));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.7e+71) {
		tmp = t_4;
	} else if (j <= -8.6e-61) {
		tmp = t_2;
	} else if (j <= -6.5e-107) {
		tmp = t_4;
	} else if (j <= -2e-160) {
		tmp = t_1;
	} else if (j <= -6.5e-281) {
		tmp = t_3;
	} else if (j <= 1.1e-244) {
		tmp = t_1;
	} else if (j <= 5e-36) {
		tmp = t_3;
	} else if (j <= 7.2e+55) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = c * ((a * j) - (z * b))
    t_3 = x * ((y * z) - (t * a))
    t_4 = j * ((a * c) - (y * i))
    if (j <= (-2.7d+71)) then
        tmp = t_4
    else if (j <= (-8.6d-61)) then
        tmp = t_2
    else if (j <= (-6.5d-107)) then
        tmp = t_4
    else if (j <= (-2d-160)) then
        tmp = t_1
    else if (j <= (-6.5d-281)) then
        tmp = t_3
    else if (j <= 1.1d-244) then
        tmp = t_1
    else if (j <= 5d-36) then
        tmp = t_3
    else if (j <= 7.2d+55) then
        tmp = t_2
    else
        tmp = t_4
    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 * ((t * i) - (z * c));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.7e+71) {
		tmp = t_4;
	} else if (j <= -8.6e-61) {
		tmp = t_2;
	} else if (j <= -6.5e-107) {
		tmp = t_4;
	} else if (j <= -2e-160) {
		tmp = t_1;
	} else if (j <= -6.5e-281) {
		tmp = t_3;
	} else if (j <= 1.1e-244) {
		tmp = t_1;
	} else if (j <= 5e-36) {
		tmp = t_3;
	} else if (j <= 7.2e+55) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = c * ((a * j) - (z * b))
	t_3 = x * ((y * z) - (t * a))
	t_4 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.7e+71:
		tmp = t_4
	elif j <= -8.6e-61:
		tmp = t_2
	elif j <= -6.5e-107:
		tmp = t_4
	elif j <= -2e-160:
		tmp = t_1
	elif j <= -6.5e-281:
		tmp = t_3
	elif j <= 1.1e-244:
		tmp = t_1
	elif j <= 5e-36:
		tmp = t_3
	elif j <= 7.2e+55:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_4 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.7e+71)
		tmp = t_4;
	elseif (j <= -8.6e-61)
		tmp = t_2;
	elseif (j <= -6.5e-107)
		tmp = t_4;
	elseif (j <= -2e-160)
		tmp = t_1;
	elseif (j <= -6.5e-281)
		tmp = t_3;
	elseif (j <= 1.1e-244)
		tmp = t_1;
	elseif (j <= 5e-36)
		tmp = t_3;
	elseif (j <= 7.2e+55)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = c * ((a * j) - (z * b));
	t_3 = x * ((y * z) - (t * a));
	t_4 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.7e+71)
		tmp = t_4;
	elseif (j <= -8.6e-61)
		tmp = t_2;
	elseif (j <= -6.5e-107)
		tmp = t_4;
	elseif (j <= -2e-160)
		tmp = t_1;
	elseif (j <= -6.5e-281)
		tmp = t_3;
	elseif (j <= 1.1e-244)
		tmp = t_1;
	elseif (j <= 5e-36)
		tmp = t_3;
	elseif (j <= 7.2e+55)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+71], t$95$4, If[LessEqual[j, -8.6e-61], t$95$2, If[LessEqual[j, -6.5e-107], t$95$4, If[LessEqual[j, -2e-160], t$95$1, If[LessEqual[j, -6.5e-281], t$95$3, If[LessEqual[j, 1.1e-244], t$95$1, If[LessEqual[j, 5e-36], t$95$3, If[LessEqual[j, 7.2e+55], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.69999999999999997e71 or -8.6000000000000007e-61 < j < -6.5000000000000002e-107 or 7.19999999999999975e55 < j

   1. Initial program 68.0%

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

   3. Taylor expanded in z around 0 68.9%

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

   4. Taylor expanded in j around inf 67.0%

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

   if -2.69999999999999997e71 < j < -8.6000000000000007e-61 or 5.00000000000000004e-36 < j < 7.19999999999999975e55

   1. Initial program 73.2%

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

   3. Taylor expanded in c around inf 66.3%

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

   if -6.5000000000000002e-107 < j < -2e-160 or -6.5e-281 < j < 1.09999999999999992e-244

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 66.4%

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

   if -2e-160 < j < -6.5e-281 or 1.09999999999999992e-244 < j < 5.00000000000000004e-36

   1. Initial program 74.8%

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

   3. Taylor expanded in z around 0 73.8%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

   6. Simplified 59.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+71}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-61}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-160}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot t\right) \cdot \left(-a\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+258}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x t) (- a))) (t_2 (* z (* x y))) (t_3 (* c (* a j))))
   (if (<= a -4.8e+159)
     t_3
     (if (<= a -2.8e-82)
       t_1
       (if (<= a -2.6e-126)
         (* x (* y z))
         (if (<= a -6.5e-229)
           (* c (* z (- b)))
           (if (<= a 1.25e-227)
             t_2
             (if (<= a 2.85e-124)
               (* t (* b i))
               (if (<= a 8.5e+29) t_2 (if (<= a 3e+258) 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 * t) * -a;
	double t_2 = z * (x * y);
	double t_3 = c * (a * j);
	double tmp;
	if (a <= -4.8e+159) {
		tmp = t_3;
	} else if (a <= -2.8e-82) {
		tmp = t_1;
	} else if (a <= -2.6e-126) {
		tmp = x * (y * z);
	} else if (a <= -6.5e-229) {
		tmp = c * (z * -b);
	} else if (a <= 1.25e-227) {
		tmp = t_2;
	} else if (a <= 2.85e-124) {
		tmp = t * (b * i);
	} else if (a <= 8.5e+29) {
		tmp = t_2;
	} else if (a <= 3e+258) {
		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 * t) * -a
    t_2 = z * (x * y)
    t_3 = c * (a * j)
    if (a <= (-4.8d+159)) then
        tmp = t_3
    else if (a <= (-2.8d-82)) then
        tmp = t_1
    else if (a <= (-2.6d-126)) then
        tmp = x * (y * z)
    else if (a <= (-6.5d-229)) then
        tmp = c * (z * -b)
    else if (a <= 1.25d-227) then
        tmp = t_2
    else if (a <= 2.85d-124) then
        tmp = t * (b * i)
    else if (a <= 8.5d+29) then
        tmp = t_2
    else if (a <= 3d+258) 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 * t) * -a;
	double t_2 = z * (x * y);
	double t_3 = c * (a * j);
	double tmp;
	if (a <= -4.8e+159) {
		tmp = t_3;
	} else if (a <= -2.8e-82) {
		tmp = t_1;
	} else if (a <= -2.6e-126) {
		tmp = x * (y * z);
	} else if (a <= -6.5e-229) {
		tmp = c * (z * -b);
	} else if (a <= 1.25e-227) {
		tmp = t_2;
	} else if (a <= 2.85e-124) {
		tmp = t * (b * i);
	} else if (a <= 8.5e+29) {
		tmp = t_2;
	} else if (a <= 3e+258) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * t) * -a
	t_2 = z * (x * y)
	t_3 = c * (a * j)
	tmp = 0
	if a <= -4.8e+159:
		tmp = t_3
	elif a <= -2.8e-82:
		tmp = t_1
	elif a <= -2.6e-126:
		tmp = x * (y * z)
	elif a <= -6.5e-229:
		tmp = c * (z * -b)
	elif a <= 1.25e-227:
		tmp = t_2
	elif a <= 2.85e-124:
		tmp = t * (b * i)
	elif a <= 8.5e+29:
		tmp = t_2
	elif a <= 3e+258:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * t) * Float64(-a))
	t_2 = Float64(z * Float64(x * y))
	t_3 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -4.8e+159)
		tmp = t_3;
	elseif (a <= -2.8e-82)
		tmp = t_1;
	elseif (a <= -2.6e-126)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -6.5e-229)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (a <= 1.25e-227)
		tmp = t_2;
	elseif (a <= 2.85e-124)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 8.5e+29)
		tmp = t_2;
	elseif (a <= 3e+258)
		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 * t) * -a;
	t_2 = z * (x * y);
	t_3 = c * (a * j);
	tmp = 0.0;
	if (a <= -4.8e+159)
		tmp = t_3;
	elseif (a <= -2.8e-82)
		tmp = t_1;
	elseif (a <= -2.6e-126)
		tmp = x * (y * z);
	elseif (a <= -6.5e-229)
		tmp = c * (z * -b);
	elseif (a <= 1.25e-227)
		tmp = t_2;
	elseif (a <= 2.85e-124)
		tmp = t * (b * i);
	elseif (a <= 8.5e+29)
		tmp = t_2;
	elseif (a <= 3e+258)
		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[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+159], t$95$3, If[LessEqual[a, -2.8e-82], t$95$1, If[LessEqual[a, -2.6e-126], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.5e-229], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-227], t$95$2, If[LessEqual[a, 2.85e-124], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+29], t$95$2, If[LessEqual[a, 3e+258], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.8e159 or 8.5000000000000006e29 < a < 3e258

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 52.5%

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

   4. Taylor expanded in a around inf 44.1%

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

      1. *-commutative 44.1%

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

   6. Simplified 44.1%

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

   if -4.8e159 < a < -2.80000000000000024e-82 or 3e258 < a

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in c around 0 43.7%

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

      1. neg-mul-1 43.7%

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

      2. distribute-rgt-neg-in 43.7%

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

      3. distribute-lft-neg-in 43.7%

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

      4. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if -2.80000000000000024e-82 < a < -2.59999999999999999e-126

   1. Initial program 82.1%

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

   3. Taylor expanded in z around inf 46.8%

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

   4. Taylor expanded in x around inf 55.9%

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

   if -2.59999999999999999e-126 < a < -6.5e-229

   1. Initial program 69.2%

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

   3. Taylor expanded in c around inf 42.5%

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

   4. Taylor expanded in a around 0 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-lft-neg-out 38.8%

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

      3. *-commutative 38.8%

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

   6. Simplified 38.8%

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

   if -6.5e-229 < a < 1.2499999999999999e-227 or 2.84999999999999988e-124 < a < 8.5000000000000006e29

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf 60.9%

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

   4. Taylor expanded in x around inf 47.5%

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

      1. *-commutative 47.5%

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

   6. Simplified 47.5%

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

   if 1.2499999999999999e-227 < a < 2.84999999999999988e-124

   1. Initial program 88.7%

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

   3. Taylor expanded in i around inf 62.2%

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

      1. distribute-lft-out-- 62.2%

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

      2. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around 0 45.7%

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

      1. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+256}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* a j))))
   (if (<= a -5.8e+159)
     t_2
     (if (<= a -2.8e-82)
       (* x (* t (- a)))
       (if (<= a -5.5e-124)
         (* x (* y z))
         (if (<= a -6.6e-229)
           (* c (* z (- b)))
           (if (<= a 1.55e-227)
             t_1
             (if (<= a 7.8e-122)
               (* t (* b i))
               (if (<= a 5.7e+29)
                 t_1
                 (if (<= a 7e+256) t_2 (* (* x t) (- a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -5.8e+159) {
		tmp = t_2;
	} else if (a <= -2.8e-82) {
		tmp = x * (t * -a);
	} else if (a <= -5.5e-124) {
		tmp = x * (y * z);
	} else if (a <= -6.6e-229) {
		tmp = c * (z * -b);
	} else if (a <= 1.55e-227) {
		tmp = t_1;
	} else if (a <= 7.8e-122) {
		tmp = t * (b * i);
	} else if (a <= 5.7e+29) {
		tmp = t_1;
	} else if (a <= 7e+256) {
		tmp = t_2;
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = c * (a * j)
    if (a <= (-5.8d+159)) then
        tmp = t_2
    else if (a <= (-2.8d-82)) then
        tmp = x * (t * -a)
    else if (a <= (-5.5d-124)) then
        tmp = x * (y * z)
    else if (a <= (-6.6d-229)) then
        tmp = c * (z * -b)
    else if (a <= 1.55d-227) then
        tmp = t_1
    else if (a <= 7.8d-122) then
        tmp = t * (b * i)
    else if (a <= 5.7d+29) then
        tmp = t_1
    else if (a <= 7d+256) then
        tmp = t_2
    else
        tmp = (x * t) * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -5.8e+159) {
		tmp = t_2;
	} else if (a <= -2.8e-82) {
		tmp = x * (t * -a);
	} else if (a <= -5.5e-124) {
		tmp = x * (y * z);
	} else if (a <= -6.6e-229) {
		tmp = c * (z * -b);
	} else if (a <= 1.55e-227) {
		tmp = t_1;
	} else if (a <= 7.8e-122) {
		tmp = t * (b * i);
	} else if (a <= 5.7e+29) {
		tmp = t_1;
	} else if (a <= 7e+256) {
		tmp = t_2;
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (a * j)
	tmp = 0
	if a <= -5.8e+159:
		tmp = t_2
	elif a <= -2.8e-82:
		tmp = x * (t * -a)
	elif a <= -5.5e-124:
		tmp = x * (y * z)
	elif a <= -6.6e-229:
		tmp = c * (z * -b)
	elif a <= 1.55e-227:
		tmp = t_1
	elif a <= 7.8e-122:
		tmp = t * (b * i)
	elif a <= 5.7e+29:
		tmp = t_1
	elif a <= 7e+256:
		tmp = t_2
	else:
		tmp = (x * t) * -a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -5.8e+159)
		tmp = t_2;
	elseif (a <= -2.8e-82)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (a <= -5.5e-124)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -6.6e-229)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (a <= 1.55e-227)
		tmp = t_1;
	elseif (a <= 7.8e-122)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 5.7e+29)
		tmp = t_1;
	elseif (a <= 7e+256)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * t) * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (a <= -5.8e+159)
		tmp = t_2;
	elseif (a <= -2.8e-82)
		tmp = x * (t * -a);
	elseif (a <= -5.5e-124)
		tmp = x * (y * z);
	elseif (a <= -6.6e-229)
		tmp = c * (z * -b);
	elseif (a <= 1.55e-227)
		tmp = t_1;
	elseif (a <= 7.8e-122)
		tmp = t * (b * i);
	elseif (a <= 5.7e+29)
		tmp = t_1;
	elseif (a <= 7e+256)
		tmp = t_2;
	else
		tmp = (x * t) * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+159], t$95$2, If[LessEqual[a, -2.8e-82], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-124], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-229], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-227], t$95$1, If[LessEqual[a, 7.8e-122], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e+29], t$95$1, If[LessEqual[a, 7e+256], t$95$2, N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.80000000000000029e159 or 5.6999999999999999e29 < a < 6.9999999999999995e256

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 52.5%

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

   4. Taylor expanded in a around inf 44.1%

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

      1. *-commutative 44.1%

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

   6. Simplified 44.1%

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

   if -5.80000000000000029e159 < a < -2.80000000000000024e-82

   1. Initial program 71.4%

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

   3. Taylor expanded in a around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in c around 0 40.1%

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

      1. neg-mul-1 40.1%

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

      2. *-commutative 40.1%

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

      3. *-commutative 40.1%

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

      4. associate-*r* 40.1%

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

      5. *-commutative 40.1%

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

      6. distribute-rgt-neg-out 40.1%

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

      7. distribute-rgt-neg-in 40.1%

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

   8. Simplified 40.1%

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

   if -2.80000000000000024e-82 < a < -5.50000000000000016e-124

   1. Initial program 82.1%

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

   3. Taylor expanded in z around inf 46.8%

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

   4. Taylor expanded in x around inf 55.9%

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

   if -5.50000000000000016e-124 < a < -6.60000000000000042e-229

   1. Initial program 69.2%

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

   3. Taylor expanded in c around inf 42.5%

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

   4. Taylor expanded in a around 0 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-lft-neg-out 38.8%

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

      3. *-commutative 38.8%

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

   6. Simplified 38.8%

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

   if -6.60000000000000042e-229 < a < 1.5499999999999999e-227 or 7.79999999999999979e-122 < a < 5.6999999999999999e29

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf 60.9%

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

   4. Taylor expanded in x around inf 47.5%

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

      1. *-commutative 47.5%

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

   6. Simplified 47.5%

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

   if 1.5499999999999999e-227 < a < 7.79999999999999979e-122

   1. Initial program 88.7%

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

   3. Taylor expanded in i around inf 62.2%

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

      1. distribute-lft-out-- 62.2%

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

      2. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around 0 45.7%

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

      1. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

   if 6.9999999999999995e256 < a

   1. Initial program 50.9%

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

   3. Taylor expanded in a around inf 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in c around 0 59.9%

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

      1. neg-mul-1 59.9%

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

      2. distribute-rgt-neg-in 59.9%

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

      3. distribute-lft-neg-in 59.9%

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

      4. *-commutative 59.9%

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

   8. Simplified 59.9%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(-t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+256}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -1.45e-82)
     t_3
     (if (<= a -1.12e-130)
       t_2
       (if (<= a -1.08e-228)
         t_1
         (if (<= a 2.8e-227)
           t_2
           (if (<= a 3.6e-117)
             t_1
             (if (<= a 1.1e-8)
               (* x (- (* y z) (* t a)))
               (if (<= a 6.8e+43) 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 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.45e-82) {
		tmp = t_3;
	} else if (a <= -1.12e-130) {
		tmp = t_2;
	} else if (a <= -1.08e-228) {
		tmp = t_1;
	} else if (a <= 2.8e-227) {
		tmp = t_2;
	} else if (a <= 3.6e-117) {
		tmp = t_1;
	} else if (a <= 1.1e-8) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 6.8e+43) {
		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 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-1.45d-82)) then
        tmp = t_3
    else if (a <= (-1.12d-130)) then
        tmp = t_2
    else if (a <= (-1.08d-228)) then
        tmp = t_1
    else if (a <= 2.8d-227) then
        tmp = t_2
    else if (a <= 3.6d-117) then
        tmp = t_1
    else if (a <= 1.1d-8) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= 6.8d+43) 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 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.45e-82) {
		tmp = t_3;
	} else if (a <= -1.12e-130) {
		tmp = t_2;
	} else if (a <= -1.08e-228) {
		tmp = t_1;
	} else if (a <= 2.8e-227) {
		tmp = t_2;
	} else if (a <= 3.6e-117) {
		tmp = t_1;
	} else if (a <= 1.1e-8) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 6.8e+43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.45e-82:
		tmp = t_3
	elif a <= -1.12e-130:
		tmp = t_2
	elif a <= -1.08e-228:
		tmp = t_1
	elif a <= 2.8e-227:
		tmp = t_2
	elif a <= 3.6e-117:
		tmp = t_1
	elif a <= 1.1e-8:
		tmp = x * ((y * z) - (t * a))
	elif a <= 6.8e+43:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.45e-82)
		tmp = t_3;
	elseif (a <= -1.12e-130)
		tmp = t_2;
	elseif (a <= -1.08e-228)
		tmp = t_1;
	elseif (a <= 2.8e-227)
		tmp = t_2;
	elseif (a <= 3.6e-117)
		tmp = t_1;
	elseif (a <= 1.1e-8)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= 6.8e+43)
		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 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.45e-82)
		tmp = t_3;
	elseif (a <= -1.12e-130)
		tmp = t_2;
	elseif (a <= -1.08e-228)
		tmp = t_1;
	elseif (a <= 2.8e-227)
		tmp = t_2;
	elseif (a <= 3.6e-117)
		tmp = t_1;
	elseif (a <= 1.1e-8)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= 6.8e+43)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e-82], t$95$3, If[LessEqual[a, -1.12e-130], t$95$2, If[LessEqual[a, -1.08e-228], t$95$1, If[LessEqual[a, 2.8e-227], t$95$2, If[LessEqual[a, 3.6e-117], t$95$1, If[LessEqual[a, 1.1e-8], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+43], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.44999999999999989e-82 or 6.80000000000000024e43 < a

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   if -1.44999999999999989e-82 < a < -1.12e-130 or -1.0799999999999999e-228 < a < 2.7999999999999998e-227

   1. Initial program 65.6%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -1.12e-130 < a < -1.0799999999999999e-228 or 2.7999999999999998e-227 < a < 3.6e-117 or 1.0999999999999999e-8 < a < 6.80000000000000024e43

   1. Initial program 82.5%

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

   3. Taylor expanded in b around inf 67.8%

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

   if 3.6e-117 < a < 1.0999999999999999e-8

   1. Initial program 79.2%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in x around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

   6. Simplified 65.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -2.8e-82)
     t_3
     (if (<= a -2.8e-132)
       t_2
       (if (<= a -2.8e-229)
         t_1
         (if (<= a 2.9e-227)
           t_2
           (if (<= a 2.45e-191)
             t_1
             (if (<= a 8.5e-185)
               t_2
               (if (<= a 6.4e+42) (* z (- (* x y) (* b c))) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.8e-82) {
		tmp = t_3;
	} else if (a <= -2.8e-132) {
		tmp = t_2;
	} else if (a <= -2.8e-229) {
		tmp = t_1;
	} else if (a <= 2.9e-227) {
		tmp = t_2;
	} else if (a <= 2.45e-191) {
		tmp = t_1;
	} else if (a <= 8.5e-185) {
		tmp = t_2;
	} else if (a <= 6.4e+42) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-2.8d-82)) then
        tmp = t_3
    else if (a <= (-2.8d-132)) then
        tmp = t_2
    else if (a <= (-2.8d-229)) then
        tmp = t_1
    else if (a <= 2.9d-227) then
        tmp = t_2
    else if (a <= 2.45d-191) then
        tmp = t_1
    else if (a <= 8.5d-185) then
        tmp = t_2
    else if (a <= 6.4d+42) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.8e-82) {
		tmp = t_3;
	} else if (a <= -2.8e-132) {
		tmp = t_2;
	} else if (a <= -2.8e-229) {
		tmp = t_1;
	} else if (a <= 2.9e-227) {
		tmp = t_2;
	} else if (a <= 2.45e-191) {
		tmp = t_1;
	} else if (a <= 8.5e-185) {
		tmp = t_2;
	} else if (a <= 6.4e+42) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.8e-82:
		tmp = t_3
	elif a <= -2.8e-132:
		tmp = t_2
	elif a <= -2.8e-229:
		tmp = t_1
	elif a <= 2.9e-227:
		tmp = t_2
	elif a <= 2.45e-191:
		tmp = t_1
	elif a <= 8.5e-185:
		tmp = t_2
	elif a <= 6.4e+42:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.8e-82)
		tmp = t_3;
	elseif (a <= -2.8e-132)
		tmp = t_2;
	elseif (a <= -2.8e-229)
		tmp = t_1;
	elseif (a <= 2.9e-227)
		tmp = t_2;
	elseif (a <= 2.45e-191)
		tmp = t_1;
	elseif (a <= 8.5e-185)
		tmp = t_2;
	elseif (a <= 6.4e+42)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.8e-82)
		tmp = t_3;
	elseif (a <= -2.8e-132)
		tmp = t_2;
	elseif (a <= -2.8e-229)
		tmp = t_1;
	elseif (a <= 2.9e-227)
		tmp = t_2;
	elseif (a <= 2.45e-191)
		tmp = t_1;
	elseif (a <= 8.5e-185)
		tmp = t_2;
	elseif (a <= 6.4e+42)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-82], t$95$3, If[LessEqual[a, -2.8e-132], t$95$2, If[LessEqual[a, -2.8e-229], t$95$1, If[LessEqual[a, 2.9e-227], t$95$2, If[LessEqual[a, 2.45e-191], t$95$1, If[LessEqual[a, 8.5e-185], t$95$2, If[LessEqual[a, 6.4e+42], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.80000000000000024e-82 or 6.40000000000000004e42 < a

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   if -2.80000000000000024e-82 < a < -2.80000000000000002e-132 or -2.7999999999999999e-229 < a < 2.90000000000000011e-227 or 2.45e-191 < a < 8.5000000000000001e-185

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -2.80000000000000002e-132 < a < -2.7999999999999999e-229 or 2.90000000000000011e-227 < a < 2.45e-191

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 72.1%

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

   if 8.5000000000000001e-185 < a < 6.40000000000000004e42

   1. Initial program 85.9%

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

   3. Taylor expanded in z around inf 61.2%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+50}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-168}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+235}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.15e+50)
   (* (* x t) (- a))
   (if (<= t -1.02e-168)
     (* c (* a j))
     (if (<= t 3e-215)
       (* i (* y (- j)))
       (if (<= t 1.8e-133)
         (* z (* x y))
         (if (<= t 5e-7)
           (* c (* z (- b)))
           (if (<= t 7.2e+37)
             (* y (* x z))
             (if (<= t 2e+235) (* x (* t (- a))) (* b (* t 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 (t <= -1.15e+50) {
		tmp = (x * t) * -a;
	} else if (t <= -1.02e-168) {
		tmp = c * (a * j);
	} else if (t <= 3e-215) {
		tmp = i * (y * -j);
	} else if (t <= 1.8e-133) {
		tmp = z * (x * y);
	} else if (t <= 5e-7) {
		tmp = c * (z * -b);
	} else if (t <= 7.2e+37) {
		tmp = y * (x * z);
	} else if (t <= 2e+235) {
		tmp = x * (t * -a);
	} else {
		tmp = b * (t * 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 (t <= (-1.15d+50)) then
        tmp = (x * t) * -a
    else if (t <= (-1.02d-168)) then
        tmp = c * (a * j)
    else if (t <= 3d-215) then
        tmp = i * (y * -j)
    else if (t <= 1.8d-133) then
        tmp = z * (x * y)
    else if (t <= 5d-7) then
        tmp = c * (z * -b)
    else if (t <= 7.2d+37) then
        tmp = y * (x * z)
    else if (t <= 2d+235) then
        tmp = x * (t * -a)
    else
        tmp = b * (t * 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 (t <= -1.15e+50) {
		tmp = (x * t) * -a;
	} else if (t <= -1.02e-168) {
		tmp = c * (a * j);
	} else if (t <= 3e-215) {
		tmp = i * (y * -j);
	} else if (t <= 1.8e-133) {
		tmp = z * (x * y);
	} else if (t <= 5e-7) {
		tmp = c * (z * -b);
	} else if (t <= 7.2e+37) {
		tmp = y * (x * z);
	} else if (t <= 2e+235) {
		tmp = x * (t * -a);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.15e+50:
		tmp = (x * t) * -a
	elif t <= -1.02e-168:
		tmp = c * (a * j)
	elif t <= 3e-215:
		tmp = i * (y * -j)
	elif t <= 1.8e-133:
		tmp = z * (x * y)
	elif t <= 5e-7:
		tmp = c * (z * -b)
	elif t <= 7.2e+37:
		tmp = y * (x * z)
	elif t <= 2e+235:
		tmp = x * (t * -a)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.15e+50)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (t <= -1.02e-168)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= 3e-215)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= 1.8e-133)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 5e-7)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 7.2e+37)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2e+235)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.15e+50)
		tmp = (x * t) * -a;
	elseif (t <= -1.02e-168)
		tmp = c * (a * j);
	elseif (t <= 3e-215)
		tmp = i * (y * -j);
	elseif (t <= 1.8e-133)
		tmp = z * (x * y);
	elseif (t <= 5e-7)
		tmp = c * (z * -b);
	elseif (t <= 7.2e+37)
		tmp = y * (x * z);
	elseif (t <= 2e+235)
		tmp = x * (t * -a);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.15e+50], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[t, -1.02e-168], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-215], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-133], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-7], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+37], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+235], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.14999999999999998e50

   1. Initial program 61.2%

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

   3. Taylor expanded in a around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in c around 0 46.2%

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

      1. neg-mul-1 46.2%

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

      2. distribute-rgt-neg-in 46.2%

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

      3. distribute-lft-neg-in 46.2%

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

      4. *-commutative 46.2%

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

   8. Simplified 46.2%

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

   if -1.14999999999999998e50 < t < -1.01999999999999999e-168

   1. Initial program 75.5%

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

   3. Taylor expanded in c around inf 58.3%

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

   4. Taylor expanded in a around inf 34.2%

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

      1. *-commutative 34.2%

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

   6. Simplified 34.2%

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

   if -1.01999999999999999e-168 < t < 3.00000000000000025e-215

   1. Initial program 85.1%

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

   3. Taylor expanded in i around inf 44.1%

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

      1. distribute-lft-out-- 44.1%

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

      2. *-commutative 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in y around inf 35.9%

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

      1. associate-*r* 35.9%

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

      2. *-commutative 35.9%

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

      3. mul-1-neg 35.9%

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

   8. Simplified 35.9%

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

   if 3.00000000000000025e-215 < t < 1.8000000000000002e-133

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 57.5%

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

   4. Taylor expanded in x around inf 45.0%

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

      1. *-commutative 45.0%

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

   6. Simplified 45.0%

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

   if 1.8000000000000002e-133 < t < 4.99999999999999977e-7

   1. Initial program 69.3%

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

   3. Taylor expanded in c around inf 69.6%

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

   4. Taylor expanded in a around 0 43.5%

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

      1. mul-1-neg 43.5%

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

      2. distribute-lft-neg-out 43.5%

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

      3. *-commutative 43.5%

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

   6. Simplified 43.5%

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

   if 4.99999999999999977e-7 < t < 7.19999999999999995e37

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 64.6%

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

   4. Taylor expanded in x around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*r* 55.2%

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

   6. Simplified 55.2%

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

   if 7.19999999999999995e37 < t < 2.0000000000000001e235

   1. Initial program 64.5%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in c around 0 49.5%

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

      1. neg-mul-1 49.5%

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

      2. *-commutative 49.5%

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

      3. *-commutative 49.5%

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

      4. associate-*r* 52.6%

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

      5. *-commutative 52.6%

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

      6. distribute-rgt-neg-out 52.6%

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

      7. distribute-rgt-neg-in 52.6%

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

   8. Simplified 52.6%

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

   if 2.0000000000000001e235 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 93.8%

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

      1. distribute-lft-out-- 93.8%

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

      2. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in x around 0 69.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+50}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-168}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+235}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+56}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+234}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6.3e+56)
   (* (* x t) (- a))
   (if (<= t -5e-170)
     (* c (* a j))
     (if (<= t 8e-215)
       (* i (* y (- j)))
       (if (<= t 9.6e-133)
         (* z (* x y))
         (if (<= t 9.5e-8)
           (* c (* z (- b)))
           (if (<= t 5.5e+36)
             (* y (* x z))
             (if (<= t 1.4e+234) (* t (* a (- x))) (* b (* t 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 (t <= -6.3e+56) {
		tmp = (x * t) * -a;
	} else if (t <= -5e-170) {
		tmp = c * (a * j);
	} else if (t <= 8e-215) {
		tmp = i * (y * -j);
	} else if (t <= 9.6e-133) {
		tmp = z * (x * y);
	} else if (t <= 9.5e-8) {
		tmp = c * (z * -b);
	} else if (t <= 5.5e+36) {
		tmp = y * (x * z);
	} else if (t <= 1.4e+234) {
		tmp = t * (a * -x);
	} else {
		tmp = b * (t * 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 (t <= (-6.3d+56)) then
        tmp = (x * t) * -a
    else if (t <= (-5d-170)) then
        tmp = c * (a * j)
    else if (t <= 8d-215) then
        tmp = i * (y * -j)
    else if (t <= 9.6d-133) then
        tmp = z * (x * y)
    else if (t <= 9.5d-8) then
        tmp = c * (z * -b)
    else if (t <= 5.5d+36) then
        tmp = y * (x * z)
    else if (t <= 1.4d+234) then
        tmp = t * (a * -x)
    else
        tmp = b * (t * 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 (t <= -6.3e+56) {
		tmp = (x * t) * -a;
	} else if (t <= -5e-170) {
		tmp = c * (a * j);
	} else if (t <= 8e-215) {
		tmp = i * (y * -j);
	} else if (t <= 9.6e-133) {
		tmp = z * (x * y);
	} else if (t <= 9.5e-8) {
		tmp = c * (z * -b);
	} else if (t <= 5.5e+36) {
		tmp = y * (x * z);
	} else if (t <= 1.4e+234) {
		tmp = t * (a * -x);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6.3e+56:
		tmp = (x * t) * -a
	elif t <= -5e-170:
		tmp = c * (a * j)
	elif t <= 8e-215:
		tmp = i * (y * -j)
	elif t <= 9.6e-133:
		tmp = z * (x * y)
	elif t <= 9.5e-8:
		tmp = c * (z * -b)
	elif t <= 5.5e+36:
		tmp = y * (x * z)
	elif t <= 1.4e+234:
		tmp = t * (a * -x)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6.3e+56)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (t <= -5e-170)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= 8e-215)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= 9.6e-133)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 9.5e-8)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 5.5e+36)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.4e+234)
		tmp = Float64(t * Float64(a * Float64(-x)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -6.3e+56)
		tmp = (x * t) * -a;
	elseif (t <= -5e-170)
		tmp = c * (a * j);
	elseif (t <= 8e-215)
		tmp = i * (y * -j);
	elseif (t <= 9.6e-133)
		tmp = z * (x * y);
	elseif (t <= 9.5e-8)
		tmp = c * (z * -b);
	elseif (t <= 5.5e+36)
		tmp = y * (x * z);
	elseif (t <= 1.4e+234)
		tmp = t * (a * -x);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6.3e+56], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[t, -5e-170], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-215], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e-133], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-8], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+36], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+234], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -6.3000000000000001e56

   1. Initial program 61.2%

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

   3. Taylor expanded in a around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in c around 0 46.2%

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

      1. neg-mul-1 46.2%

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

      2. distribute-rgt-neg-in 46.2%

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

      3. distribute-lft-neg-in 46.2%

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

      4. *-commutative 46.2%

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

   8. Simplified 46.2%

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

   if -6.3000000000000001e56 < t < -5.0000000000000001e-170

   1. Initial program 75.5%

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

   3. Taylor expanded in c around inf 58.3%

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

   4. Taylor expanded in a around inf 34.2%

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

      1. *-commutative 34.2%

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

   6. Simplified 34.2%

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

   if -5.0000000000000001e-170 < t < 8.00000000000000033e-215

   1. Initial program 85.1%

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

   3. Taylor expanded in i around inf 44.1%

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

      1. distribute-lft-out-- 44.1%

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

      2. *-commutative 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in y around inf 35.9%

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

      1. associate-*r* 35.9%

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

      2. *-commutative 35.9%

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

      3. mul-1-neg 35.9%

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

   8. Simplified 35.9%

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

   if 8.00000000000000033e-215 < t < 9.6e-133

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 57.5%

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

   4. Taylor expanded in x around inf 45.0%

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

      1. *-commutative 45.0%

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

   6. Simplified 45.0%

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

   if 9.6e-133 < t < 9.50000000000000036e-8

   1. Initial program 69.3%

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

   3. Taylor expanded in c around inf 69.6%

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

   4. Taylor expanded in a around 0 43.5%

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

      1. mul-1-neg 43.5%

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

      2. distribute-lft-neg-out 43.5%

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

      3. *-commutative 43.5%

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

   6. Simplified 43.5%

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

   if 9.50000000000000036e-8 < t < 5.5000000000000002e36

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 64.6%

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

   4. Taylor expanded in x around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*r* 55.2%

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

   6. Simplified 55.2%

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

   if 5.5000000000000002e36 < t < 1.3999999999999999e234

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 70.0%

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

      1. distribute-lft-out-- 70.0%

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

      2. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around inf 55.2%

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

   if 1.3999999999999999e234 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 93.8%

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

      1. distribute-lft-out-- 93.8%

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

      2. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in x around 0 69.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+56}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+234}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+262}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-84}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (* x y))))
   (if (<= y -8.2e+262)
     (* y (* x z))
     (if (<= y -3e+226)
       (* y (* i (- j)))
       (if (<= y -6.5e+114)
         t_2
         (if (<= y 3.3e-112)
           t_1
           (if (<= y 1e-84)
             (* i (* y (- j)))
             (if (<= y 2.3e+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 = a * ((c * j) - (x * t));
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -8.2e+262) {
		tmp = y * (x * z);
	} else if (y <= -3e+226) {
		tmp = y * (i * -j);
	} else if (y <= -6.5e+114) {
		tmp = t_2;
	} else if (y <= 3.3e-112) {
		tmp = t_1;
	} else if (y <= 1e-84) {
		tmp = i * (y * -j);
	} else if (y <= 2.3e+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 = a * ((c * j) - (x * t))
    t_2 = z * (x * y)
    if (y <= (-8.2d+262)) then
        tmp = y * (x * z)
    else if (y <= (-3d+226)) then
        tmp = y * (i * -j)
    else if (y <= (-6.5d+114)) then
        tmp = t_2
    else if (y <= 3.3d-112) then
        tmp = t_1
    else if (y <= 1d-84) then
        tmp = i * (y * -j)
    else if (y <= 2.3d+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 = a * ((c * j) - (x * t));
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -8.2e+262) {
		tmp = y * (x * z);
	} else if (y <= -3e+226) {
		tmp = y * (i * -j);
	} else if (y <= -6.5e+114) {
		tmp = t_2;
	} else if (y <= 3.3e-112) {
		tmp = t_1;
	} else if (y <= 1e-84) {
		tmp = i * (y * -j);
	} else if (y <= 2.3e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * (x * y)
	tmp = 0
	if y <= -8.2e+262:
		tmp = y * (x * z)
	elif y <= -3e+226:
		tmp = y * (i * -j)
	elif y <= -6.5e+114:
		tmp = t_2
	elif y <= 3.3e-112:
		tmp = t_1
	elif y <= 1e-84:
		tmp = i * (y * -j)
	elif y <= 2.3e+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(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -8.2e+262)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -3e+226)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (y <= -6.5e+114)
		tmp = t_2;
	elseif (y <= 3.3e-112)
		tmp = t_1;
	elseif (y <= 1e-84)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 2.3e+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 = a * ((c * j) - (x * t));
	t_2 = z * (x * y);
	tmp = 0.0;
	if (y <= -8.2e+262)
		tmp = y * (x * z);
	elseif (y <= -3e+226)
		tmp = y * (i * -j);
	elseif (y <= -6.5e+114)
		tmp = t_2;
	elseif (y <= 3.3e-112)
		tmp = t_1;
	elseif (y <= 1e-84)
		tmp = i * (y * -j);
	elseif (y <= 2.3e+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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+262], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+226], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e+114], t$95$2, If[LessEqual[y, 3.3e-112], t$95$1, If[LessEqual[y, 1e-84], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+122], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.20000000000000055e262

   1. Initial program 61.3%

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

   3. Taylor expanded in z around inf 71.3%

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

   4. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r* 81.3%

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

   6. Simplified 81.3%

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

   if -8.20000000000000055e262 < y < -2.99999999999999975e226

   1. Initial program 62.9%

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

   3. Taylor expanded in i around inf 75.9%

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

      1. distribute-lft-out-- 75.9%

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

      2. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around inf 75.9%

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

      1. associate-*r* 75.9%

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

      2. *-commutative 75.9%

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

      3. *-commutative 75.9%

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

      4. associate-*l* 75.9%

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

      5. mul-1-neg 75.9%

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

   8. Simplified 75.9%

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

   if -2.99999999999999975e226 < y < -6.5000000000000001e114 or 2.3000000000000001e122 < y

   1. Initial program 51.1%

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

   3. Taylor expanded in z around inf 63.5%

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

   4. Taylor expanded in x around inf 55.6%

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

      1. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   if -6.5000000000000001e114 < y < 3.3000000000000001e-112 or 1e-84 < y < 2.3000000000000001e122

   1. Initial program 78.2%

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

   3. Taylor expanded in a around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

   5. Simplified 48.6%

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

   if 3.3000000000000001e-112 < y < 1e-84

   1. Initial program 71.2%

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

   3. Taylor expanded in i around inf 72.5%

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

      1. distribute-lft-out-- 72.5%

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

      2. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in y around inf 71.9%

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

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. mul-1-neg 71.9%

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

   8. Simplified 71.9%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+262}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-84}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot t\right) \cdot \left(-a\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+257}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x t) (- a))) (t_2 (* z (* x y))) (t_3 (* c (* a j))))
   (if (<= a -5.5e+159)
     t_3
     (if (<= a -2.8e-82)
       t_1
       (if (<= a 1.2e-227)
         t_2
         (if (<= a 3.35e-124)
           (* t (* b i))
           (if (<= a 6.1e+29) t_2 (if (<= a 6.8e+257) 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 * t) * -a;
	double t_2 = z * (x * y);
	double t_3 = c * (a * j);
	double tmp;
	if (a <= -5.5e+159) {
		tmp = t_3;
	} else if (a <= -2.8e-82) {
		tmp = t_1;
	} else if (a <= 1.2e-227) {
		tmp = t_2;
	} else if (a <= 3.35e-124) {
		tmp = t * (b * i);
	} else if (a <= 6.1e+29) {
		tmp = t_2;
	} else if (a <= 6.8e+257) {
		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 * t) * -a
    t_2 = z * (x * y)
    t_3 = c * (a * j)
    if (a <= (-5.5d+159)) then
        tmp = t_3
    else if (a <= (-2.8d-82)) then
        tmp = t_1
    else if (a <= 1.2d-227) then
        tmp = t_2
    else if (a <= 3.35d-124) then
        tmp = t * (b * i)
    else if (a <= 6.1d+29) then
        tmp = t_2
    else if (a <= 6.8d+257) 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 * t) * -a;
	double t_2 = z * (x * y);
	double t_3 = c * (a * j);
	double tmp;
	if (a <= -5.5e+159) {
		tmp = t_3;
	} else if (a <= -2.8e-82) {
		tmp = t_1;
	} else if (a <= 1.2e-227) {
		tmp = t_2;
	} else if (a <= 3.35e-124) {
		tmp = t * (b * i);
	} else if (a <= 6.1e+29) {
		tmp = t_2;
	} else if (a <= 6.8e+257) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * t) * -a
	t_2 = z * (x * y)
	t_3 = c * (a * j)
	tmp = 0
	if a <= -5.5e+159:
		tmp = t_3
	elif a <= -2.8e-82:
		tmp = t_1
	elif a <= 1.2e-227:
		tmp = t_2
	elif a <= 3.35e-124:
		tmp = t * (b * i)
	elif a <= 6.1e+29:
		tmp = t_2
	elif a <= 6.8e+257:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * t) * Float64(-a))
	t_2 = Float64(z * Float64(x * y))
	t_3 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -5.5e+159)
		tmp = t_3;
	elseif (a <= -2.8e-82)
		tmp = t_1;
	elseif (a <= 1.2e-227)
		tmp = t_2;
	elseif (a <= 3.35e-124)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 6.1e+29)
		tmp = t_2;
	elseif (a <= 6.8e+257)
		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 * t) * -a;
	t_2 = z * (x * y);
	t_3 = c * (a * j);
	tmp = 0.0;
	if (a <= -5.5e+159)
		tmp = t_3;
	elseif (a <= -2.8e-82)
		tmp = t_1;
	elseif (a <= 1.2e-227)
		tmp = t_2;
	elseif (a <= 3.35e-124)
		tmp = t * (b * i);
	elseif (a <= 6.1e+29)
		tmp = t_2;
	elseif (a <= 6.8e+257)
		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[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+159], t$95$3, If[LessEqual[a, -2.8e-82], t$95$1, If[LessEqual[a, 1.2e-227], t$95$2, If[LessEqual[a, 3.35e-124], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.1e+29], t$95$2, If[LessEqual[a, 6.8e+257], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.4999999999999998e159 or 6.0999999999999998e29 < a < 6.8000000000000005e257

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 52.5%

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

   4. Taylor expanded in a around inf 44.1%

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

      1. *-commutative 44.1%

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

   6. Simplified 44.1%

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

   if -5.4999999999999998e159 < a < -2.80000000000000024e-82 or 6.8000000000000005e257 < a

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in c around 0 43.7%

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

      1. neg-mul-1 43.7%

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

      2. distribute-rgt-neg-in 43.7%

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

      3. distribute-lft-neg-in 43.7%

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

      4. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if -2.80000000000000024e-82 < a < 1.2e-227 or 3.35e-124 < a < 6.0999999999999998e29

   1. Initial program 72.0%

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

   3. Taylor expanded in z around inf 55.6%

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

   4. Taylor expanded in x around inf 40.8%

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

      1. *-commutative 40.8%

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

   6. Simplified 40.8%

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

   if 1.2e-227 < a < 3.35e-124

   1. Initial program 88.7%

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

   3. Taylor expanded in i around inf 62.2%

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

      1. distribute-lft-out-- 62.2%

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

      2. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around 0 45.7%

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

      1. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+257}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-227}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -5e+48)
     t_1
     (if (<= t -3.1e-227)
       (* c (- (* a j) (* z b)))
       (if (<= t -2.2e-279)
         (* x (- (* y z) (* t a)))
         (if (<= t 4.3e-101)
           (* j (- (* a c) (* y i)))
           (if (<= t 5.6e+76) (* z (- (* x y) (* b c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -5e+48) {
		tmp = t_1;
	} else if (t <= -3.1e-227) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -2.2e-279) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 4.3e-101) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 5.6e+76) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-5d+48)) then
        tmp = t_1
    else if (t <= (-3.1d-227)) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= (-2.2d-279)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 4.3d-101) then
        tmp = j * ((a * c) - (y * i))
    else if (t <= 5.6d+76) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -5e+48) {
		tmp = t_1;
	} else if (t <= -3.1e-227) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -2.2e-279) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 4.3e-101) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 5.6e+76) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -5e+48:
		tmp = t_1
	elif t <= -3.1e-227:
		tmp = c * ((a * j) - (z * b))
	elif t <= -2.2e-279:
		tmp = x * ((y * z) - (t * a))
	elif t <= 4.3e-101:
		tmp = j * ((a * c) - (y * i))
	elif t <= 5.6e+76:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5e+48)
		tmp = t_1;
	elseif (t <= -3.1e-227)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= -2.2e-279)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 4.3e-101)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (t <= 5.6e+76)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -5e+48)
		tmp = t_1;
	elseif (t <= -3.1e-227)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= -2.2e-279)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 4.3e-101)
		tmp = j * ((a * c) - (y * i));
	elseif (t <= 5.6e+76)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+48], t$95$1, If[LessEqual[t, -3.1e-227], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-279], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-101], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+76], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.99999999999999973e48 or 5.5999999999999997e76 < t

   1. Initial program 61.1%

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

   3. Taylor expanded in t around inf 70.6%

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

      1. distribute-lft-out-- 70.6%

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

      2. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   if -4.99999999999999973e48 < t < -3.09999999999999979e-227

   1. Initial program 75.6%

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

   3. Taylor expanded in c around inf 55.6%

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

   if -3.09999999999999979e-227 < t < -2.2e-279

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 87.7%

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

   4. Taylor expanded in x around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   6. Simplified 75.3%

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

   if -2.2e-279 < t < 4.2999999999999997e-101

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0 85.8%

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

   4. Taylor expanded in j around inf 62.0%

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

   if 4.2999999999999997e-101 < t < 5.5999999999999997e76

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 65.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-227}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -2.6e+110)
     t_1
     (if (<= b -8.5e+42)
       (* z (- (* x y) (* b c)))
       (if (<= b 8.2e+107)
         (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.6e+110) {
		tmp = t_1;
	} else if (b <= -8.5e+42) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 8.2e+107) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (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 * ((t * i) - (z * c))
    if (b <= (-2.6d+110)) then
        tmp = t_1
    else if (b <= (-8.5d+42)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 8.2d+107) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (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 * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.6e+110) {
		tmp = t_1;
	} else if (b <= -8.5e+42) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 8.2e+107) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.6e+110:
		tmp = t_1
	elif b <= -8.5e+42:
		tmp = z * ((x * y) - (b * c))
	elif b <= 8.2e+107:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (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(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.6e+110)
		tmp = t_1;
	elseif (b <= -8.5e+42)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 8.2e+107)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * 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 * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.6e+110)
		tmp = t_1;
	elseif (b <= -8.5e+42)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 8.2e+107)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+110], t$95$1, If[LessEqual[b, -8.5e+42], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+107], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6e110 or 8.1999999999999998e107 < b

   1. Initial program 67.7%

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

   3. Taylor expanded in b around inf 65.3%

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

   if -2.6e110 < b < -8.5000000000000003e42

   1. Initial program 80.0%

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

   3. Taylor expanded in z around inf 72.8%

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

   if -8.5000000000000003e42 < b < 8.1999999999999998e107

   1. Initial program 71.0%

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

   3. Taylor expanded in b around 0 72.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.4:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* z (* x y))))
   (if (<= x -1.75e+189)
     t_2
     (if (<= x -4.2e-65)
       t_1
       (if (<= x 5.4)
         (* c (* a j))
         (if (<= x 1.7e+34) t_1 (if (<= x 8.6e+89) (* y (* i (- j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.75e+189) {
		tmp = t_2;
	} else if (x <= -4.2e-65) {
		tmp = t_1;
	} else if (x <= 5.4) {
		tmp = c * (a * j);
	} else if (x <= 1.7e+34) {
		tmp = t_1;
	} else if (x <= 8.6e+89) {
		tmp = y * (i * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t * -a)
    t_2 = z * (x * y)
    if (x <= (-1.75d+189)) then
        tmp = t_2
    else if (x <= (-4.2d-65)) then
        tmp = t_1
    else if (x <= 5.4d0) then
        tmp = c * (a * j)
    else if (x <= 1.7d+34) then
        tmp = t_1
    else if (x <= 8.6d+89) then
        tmp = y * (i * -j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.75e+189) {
		tmp = t_2;
	} else if (x <= -4.2e-65) {
		tmp = t_1;
	} else if (x <= 5.4) {
		tmp = c * (a * j);
	} else if (x <= 1.7e+34) {
		tmp = t_1;
	} else if (x <= 8.6e+89) {
		tmp = y * (i * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -1.75e+189:
		tmp = t_2
	elif x <= -4.2e-65:
		tmp = t_1
	elif x <= 5.4:
		tmp = c * (a * j)
	elif x <= 1.7e+34:
		tmp = t_1
	elif x <= 8.6e+89:
		tmp = y * (i * -j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.75e+189)
		tmp = t_2;
	elseif (x <= -4.2e-65)
		tmp = t_1;
	elseif (x <= 5.4)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 1.7e+34)
		tmp = t_1;
	elseif (x <= 8.6e+89)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.75e+189)
		tmp = t_2;
	elseif (x <= -4.2e-65)
		tmp = t_1;
	elseif (x <= 5.4)
		tmp = c * (a * j);
	elseif (x <= 1.7e+34)
		tmp = t_1;
	elseif (x <= 8.6e+89)
		tmp = y * (i * -j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+189], t$95$2, If[LessEqual[x, -4.2e-65], t$95$1, If[LessEqual[x, 5.4], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+34], t$95$1, If[LessEqual[x, 8.6e+89], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.74999999999999998e189 or 8.6000000000000003e89 < x

   1. Initial program 74.2%

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

   3. Taylor expanded in z around inf 56.4%

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

   4. Taylor expanded in x around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   if -1.74999999999999998e189 < x < -4.20000000000000006e-65 or 5.4000000000000004 < x < 1.7e34

   1. Initial program 73.2%

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

   3. Taylor expanded in a around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in c around 0 44.5%

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

      1. neg-mul-1 44.5%

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

      2. *-commutative 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-*r* 44.5%

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

      5. *-commutative 44.5%

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

      6. distribute-rgt-neg-out 44.5%

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

      7. distribute-rgt-neg-in 44.5%

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

   8. Simplified 44.5%

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

   if -4.20000000000000006e-65 < x < 5.4000000000000004

   1. Initial program 66.8%

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

   3. Taylor expanded in c around inf 52.0%

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

   4. Taylor expanded in a around inf 30.9%

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

      1. *-commutative 30.9%

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

   6. Simplified 30.9%

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

   if 1.7e34 < x < 8.6000000000000003e89

   1. Initial program 73.3%

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

   3. Taylor expanded in i around inf 48.4%

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

      1. distribute-lft-out-- 48.4%

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

      2. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in y around inf 48.2%

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

      1. associate-*r* 48.2%

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

      2. *-commutative 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*l* 54.4%

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

      5. mul-1-neg 54.4%

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

   8. Simplified 54.4%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+189}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 5.4:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-109}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.8e-30)
     t_2
     (if (<= b 1.3e-278)
       t_1
       (if (<= b 3.8e-109) (* z (* x y)) (if (<= b 2.6e+64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.8e-30) {
		tmp = t_2;
	} else if (b <= 1.3e-278) {
		tmp = t_1;
	} else if (b <= 3.8e-109) {
		tmp = z * (x * y);
	} else if (b <= 2.6e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.8d-30)) then
        tmp = t_2
    else if (b <= 1.3d-278) then
        tmp = t_1
    else if (b <= 3.8d-109) then
        tmp = z * (x * y)
    else if (b <= 2.6d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.8e-30) {
		tmp = t_2;
	} else if (b <= 1.3e-278) {
		tmp = t_1;
	} else if (b <= 3.8e-109) {
		tmp = z * (x * y);
	} else if (b <= 2.6e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.8e-30:
		tmp = t_2
	elif b <= 1.3e-278:
		tmp = t_1
	elif b <= 3.8e-109:
		tmp = z * (x * y)
	elif b <= 2.6e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.8e-30)
		tmp = t_2;
	elseif (b <= 1.3e-278)
		tmp = t_1;
	elseif (b <= 3.8e-109)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 2.6e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.8e-30)
		tmp = t_2;
	elseif (b <= 1.3e-278)
		tmp = t_1;
	elseif (b <= 3.8e-109)
		tmp = z * (x * y);
	elseif (b <= 2.6e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e-30], t$95$2, If[LessEqual[b, 1.3e-278], t$95$1, If[LessEqual[b, 3.8e-109], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000002e-30 or 2.59999999999999997e64 < b

   1. Initial program 70.4%

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

   3. Taylor expanded in b around inf 57.3%

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

   if -1.8000000000000002e-30 < b < 1.2999999999999999e-278 or 3.80000000000000002e-109 < b < 2.59999999999999997e64

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   if 1.2999999999999999e-278 < b < 3.80000000000000002e-109

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 45.9%

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

   4. Taylor expanded in x around inf 40.8%

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

      1. *-commutative 40.8%

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

   6. Simplified 40.8%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-109}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.8e-31)
     t_2
     (if (<= b -1.26e-147)
       t_1
       (if (<= b 3.9e-104)
         (* j (- (* a c) (* y i)))
         (if (<= b 6.5e+64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.8e-31) {
		tmp = t_2;
	} else if (b <= -1.26e-147) {
		tmp = t_1;
	} else if (b <= 3.9e-104) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 6.5e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.8d-31)) then
        tmp = t_2
    else if (b <= (-1.26d-147)) then
        tmp = t_1
    else if (b <= 3.9d-104) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 6.5d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.8e-31) {
		tmp = t_2;
	} else if (b <= -1.26e-147) {
		tmp = t_1;
	} else if (b <= 3.9e-104) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 6.5e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.8e-31:
		tmp = t_2
	elif b <= -1.26e-147:
		tmp = t_1
	elif b <= 3.9e-104:
		tmp = j * ((a * c) - (y * i))
	elif b <= 6.5e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.8e-31)
		tmp = t_2;
	elseif (b <= -1.26e-147)
		tmp = t_1;
	elseif (b <= 3.9e-104)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 6.5e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.8e-31)
		tmp = t_2;
	elseif (b <= -1.26e-147)
		tmp = t_1;
	elseif (b <= 3.9e-104)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 6.5e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e-31], t$95$2, If[LessEqual[b, -1.26e-147], t$95$1, If[LessEqual[b, 3.9e-104], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.8e-31 or 6.50000000000000007e64 < b

   1. Initial program 70.4%

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

   3. Taylor expanded in b around inf 57.3%

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

   if -3.8e-31 < b < -1.26e-147 or 3.9000000000000002e-104 < b < 6.50000000000000007e64

   1. Initial program 74.1%

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

   3. Taylor expanded in a around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

   5. Simplified 62.8%

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

   if -1.26e-147 < b < 3.9000000000000002e-104

   1. Initial program 68.1%

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

   3. Taylor expanded in z around 0 77.8%

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

   4. Taylor expanded in j around inf 59.4%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+108}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= b -6.2e+37)
     (+ (* z (- (* x y) (* b c))) t_1)
     (if (<= b 9.8e+108)
       (+ t_1 (* x (- (* y z) (* t a))))
       (* b (- (* t i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -6.2e+37) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else if (b <= 9.8e+108) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (b <= (-6.2d+37)) then
        tmp = (z * ((x * y) - (b * c))) + t_1
    else if (b <= 9.8d+108) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -6.2e+37) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else if (b <= 9.8e+108) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if b <= -6.2e+37:
		tmp = (z * ((x * y) - (b * c))) + t_1
	elif b <= 9.8e+108:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -6.2e+37)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1);
	elseif (b <= 9.8e+108)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (b <= -6.2e+37)
		tmp = (z * ((x * y) - (b * c))) + t_1;
	elseif (b <= 9.8e+108)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+37], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 9.8e+108], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.2000000000000004e37

   1. Initial program 79.1%

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

   3. Taylor expanded in z around 0 70.8%

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

   4. Taylor expanded in t around 0 65.2%

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

   if -6.2000000000000004e37 < b < 9.80000000000000028e108

   1. Initial program 71.2%

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

   3. Taylor expanded in b around 0 73.1%

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

   if 9.80000000000000028e108 < b

   1. Initial program 56.9%

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

   3. Taylor expanded in b around inf 70.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= a -8.5e+94)
     t_1
     (if (<= a 8e-228)
       (* y (* x z))
       (if (<= a 1.7e-167)
         (* i (* t b))
         (if (<= a 4.6e+29) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (a <= -8.5e+94) {
		tmp = t_1;
	} else if (a <= 8e-228) {
		tmp = y * (x * z);
	} else if (a <= 1.7e-167) {
		tmp = i * (t * b);
	} else if (a <= 4.6e+29) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (a * j)
    if (a <= (-8.5d+94)) then
        tmp = t_1
    else if (a <= 8d-228) then
        tmp = y * (x * z)
    else if (a <= 1.7d-167) then
        tmp = i * (t * b)
    else if (a <= 4.6d+29) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (a <= -8.5e+94) {
		tmp = t_1;
	} else if (a <= 8e-228) {
		tmp = y * (x * z);
	} else if (a <= 1.7e-167) {
		tmp = i * (t * b);
	} else if (a <= 4.6e+29) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if a <= -8.5e+94:
		tmp = t_1
	elif a <= 8e-228:
		tmp = y * (x * z)
	elif a <= 1.7e-167:
		tmp = i * (t * b)
	elif a <= 4.6e+29:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -8.5e+94)
		tmp = t_1;
	elseif (a <= 8e-228)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.7e-167)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 4.6e+29)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	tmp = 0.0;
	if (a <= -8.5e+94)
		tmp = t_1;
	elseif (a <= 8e-228)
		tmp = y * (x * z);
	elseif (a <= 1.7e-167)
		tmp = i * (t * b);
	elseif (a <= 4.6e+29)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+94], t$95$1, If[LessEqual[a, 8e-228], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-167], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+29], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.50000000000000054e94 or 4.6000000000000002e29 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in c around inf 48.6%

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

   4. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   6. Simplified 38.6%

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

   if -8.50000000000000054e94 < a < 8.00000000000000026e-228

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf 47.7%

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

   4. Taylor expanded in x around inf 27.8%

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

      1. *-commutative 27.8%

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

      2. associate-*r* 32.2%

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

   6. Simplified 32.2%

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

   if 8.00000000000000026e-228 < a < 1.6999999999999999e-167

   1. Initial program 83.1%

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

   3. Taylor expanded in t around inf 59.6%

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

      1. distribute-lft-out-- 59.6%

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

      2. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in x around 0 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*l* 67.5%

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

      3. *-commutative 67.5%

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

   8. Simplified 67.5%

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

   if 1.6999999999999999e-167 < a < 4.6000000000000002e29

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 61.0%

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

   4. Taylor expanded in x around inf 41.5%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* a j))))
   (if (<= a -9.5e+107)
     t_2
     (if (<= a 1.8e-231)
       t_1
       (if (<= a 4.5e-167) (* i (* t b)) (if (<= a 7e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -9.5e+107) {
		tmp = t_2;
	} else if (a <= 1.8e-231) {
		tmp = t_1;
	} else if (a <= 4.5e-167) {
		tmp = i * (t * b);
	} else if (a <= 7e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = c * (a * j)
    if (a <= (-9.5d+107)) then
        tmp = t_2
    else if (a <= 1.8d-231) then
        tmp = t_1
    else if (a <= 4.5d-167) then
        tmp = i * (t * b)
    else if (a <= 7d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -9.5e+107) {
		tmp = t_2;
	} else if (a <= 1.8e-231) {
		tmp = t_1;
	} else if (a <= 4.5e-167) {
		tmp = i * (t * b);
	} else if (a <= 7e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (a * j)
	tmp = 0
	if a <= -9.5e+107:
		tmp = t_2
	elif a <= 1.8e-231:
		tmp = t_1
	elif a <= 4.5e-167:
		tmp = i * (t * b)
	elif a <= 7e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -9.5e+107)
		tmp = t_2;
	elseif (a <= 1.8e-231)
		tmp = t_1;
	elseif (a <= 4.5e-167)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 7e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (a <= -9.5e+107)
		tmp = t_2;
	elseif (a <= 1.8e-231)
		tmp = t_1;
	elseif (a <= 4.5e-167)
		tmp = i * (t * b);
	elseif (a <= 7e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+107], t$95$2, If[LessEqual[a, 1.8e-231], t$95$1, If[LessEqual[a, 4.5e-167], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000019e107 or 6.99999999999999958e29 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in c around inf 48.6%

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

   4. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   6. Simplified 38.6%

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

   if -9.50000000000000019e107 < a < 1.79999999999999987e-231 or 4.5000000000000001e-167 < a < 6.99999999999999958e29

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf 50.7%

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

   4. Taylor expanded in x around inf 35.0%

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

      1. *-commutative 35.0%

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

   6. Simplified 35.0%

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

   if 1.79999999999999987e-231 < a < 4.5000000000000001e-167

   1. Initial program 83.1%

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

   3. Taylor expanded in t around inf 59.6%

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

      1. distribute-lft-out-- 59.6%

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

      2. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in x around 0 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*l* 67.5%

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

      3. *-commutative 67.5%

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

   8. Simplified 67.5%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -3.45 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* a j))))
   (if (<= a -3.45e+102)
     t_2
     (if (<= a 3.3e-227)
       t_1
       (if (<= a 1.7e-124) (* t (* b i)) (if (<= a 4.6e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -3.45e+102) {
		tmp = t_2;
	} else if (a <= 3.3e-227) {
		tmp = t_1;
	} else if (a <= 1.7e-124) {
		tmp = t * (b * i);
	} else if (a <= 4.6e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = c * (a * j)
    if (a <= (-3.45d+102)) then
        tmp = t_2
    else if (a <= 3.3d-227) then
        tmp = t_1
    else if (a <= 1.7d-124) then
        tmp = t * (b * i)
    else if (a <= 4.6d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -3.45e+102) {
		tmp = t_2;
	} else if (a <= 3.3e-227) {
		tmp = t_1;
	} else if (a <= 1.7e-124) {
		tmp = t * (b * i);
	} else if (a <= 4.6e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (a * j)
	tmp = 0
	if a <= -3.45e+102:
		tmp = t_2
	elif a <= 3.3e-227:
		tmp = t_1
	elif a <= 1.7e-124:
		tmp = t * (b * i)
	elif a <= 4.6e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -3.45e+102)
		tmp = t_2;
	elseif (a <= 3.3e-227)
		tmp = t_1;
	elseif (a <= 1.7e-124)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 4.6e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (a <= -3.45e+102)
		tmp = t_2;
	elseif (a <= 3.3e-227)
		tmp = t_1;
	elseif (a <= 1.7e-124)
		tmp = t * (b * i);
	elseif (a <= 4.6e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.45e+102], t$95$2, If[LessEqual[a, 3.3e-227], t$95$1, If[LessEqual[a, 1.7e-124], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.44999999999999983e102 or 4.6000000000000002e29 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in c around inf 48.6%

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

   4. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   6. Simplified 38.6%

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

   if -3.44999999999999983e102 < a < 3.2999999999999999e-227 or 1.7e-124 < a < 4.6000000000000002e29

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 50.6%

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

   4. Taylor expanded in x around inf 36.5%

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

      1. *-commutative 36.5%

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

   6. Simplified 36.5%

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

   if 3.2999999999999999e-227 < a < 1.7e-124

   1. Initial program 88.7%

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

   3. Taylor expanded in i around inf 62.2%

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

      1. distribute-lft-out-- 62.2%

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

      2. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in y around 0 45.7%

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

      1. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{+102}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+48} \lor \neg \left(t \leq 2 \cdot 10^{+106}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -6.4e+48) (not (<= t 2e+106))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -6.4e+48) || !(t <= 2e+106)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-6.4d+48)) .or. (.not. (t <= 2d+106))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -6.4e+48) || !(t <= 2e+106)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -6.4e+48) or not (t <= 2e+106):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -6.4e+48) || !(t <= 2e+106))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -6.4e+48) || ~((t <= 2e+106)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -6.4e+48], N[Not[LessEqual[t, 2e+106]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4000000000000003e48 or 2.00000000000000018e106 < t

   1. Initial program 59.6%

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

   3. Taylor expanded in t around inf 70.8%

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

      1. distribute-lft-out-- 70.8%

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

      2. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x around 0 38.9%

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

   if -6.4000000000000003e48 < t < 2.00000000000000018e106

   1. Initial program 76.9%

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

   3. Taylor expanded in a around inf 35.7%

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

      1. +-commutative 35.7%

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

      2. mul-1-neg 35.7%

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

      3. unsub-neg 35.7%

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

   5. Simplified 35.7%

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

   6. Taylor expanded in c around inf 27.0%

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

      1. *-commutative 27.0%

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

   8. Simplified 27.0%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+48} \lor \neg \left(t \leq 2 \cdot 10^{+106}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+96} \lor \neg \left(t \leq 1.02 \cdot 10^{+110}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.45e+96) (not (<= t 1.02e+110))) (* b (* t i)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.45e+96) || !(t <= 1.02e+110)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.45d+96)) .or. (.not. (t <= 1.02d+110))) then
        tmp = b * (t * i)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.45e+96) || !(t <= 1.02e+110)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.45e+96) or not (t <= 1.02e+110):
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.45e+96) || !(t <= 1.02e+110))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.45e+96) || ~((t <= 1.02e+110)))
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.45e+96], N[Not[LessEqual[t, 1.02e+110]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999989e96 or 1.02e110 < t

   1. Initial program 58.2%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. distribute-lft-out-- 69.9%

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

      2. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in x around 0 40.1%

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

   if -1.44999999999999989e96 < t < 1.02e110

   1. Initial program 76.8%

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

   3. Taylor expanded in c around inf 46.9%

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

   4. Taylor expanded in a around inf 29.1%

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

      1. *-commutative 29.1%

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

   6. Simplified 29.1%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+96} \lor \neg \left(t \leq 1.02 \cdot 10^{+110}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-11} \lor \neg \left(a \leq 2.95 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -4.6e-11) (not (<= a 2.95e+29))) (* c (* a j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.6e-11) || !(a <= 2.95e+29)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-4.6d-11)) .or. (.not. (a <= 2.95d+29))) then
        tmp = c * (a * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.6e-11) || !(a <= 2.95e+29)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -4.6e-11) or not (a <= 2.95e+29):
		tmp = c * (a * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -4.6e-11) || !(a <= 2.95e+29))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -4.6e-11) || ~((a <= 2.95e+29)))
		tmp = c * (a * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -4.6e-11], N[Not[LessEqual[a, 2.95e+29]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.60000000000000027e-11 or 2.9499999999999999e29 < a

   1. Initial program 65.9%

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

   3. Taylor expanded in c around inf 45.8%

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

   4. Taylor expanded in a around inf 35.5%

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

      1. *-commutative 35.5%

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

   6. Simplified 35.5%

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

   if -4.60000000000000027e-11 < a < 2.9499999999999999e29

   1. Initial program 75.1%

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

   3. Taylor expanded in t around inf 32.2%

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

      1. distribute-lft-out-- 32.2%

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

      2. *-commutative 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in x around 0 26.2%

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

      1. *-commutative 26.2%

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

      2. associate-*l* 27.7%

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

      3. *-commutative 27.7%

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

   8. Simplified 27.7%

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

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-11} \lor \neg \left(a \leq 2.95 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+39} \lor \neg \left(y \leq 1.7 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -5.2e+39) (not (<= y 1.7e+84))) (* x (* y z)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -5.2e+39) || !(y <= 1.7e+84)) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-5.2d+39)) .or. (.not. (y <= 1.7d+84))) then
        tmp = x * (y * z)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -5.2e+39) || !(y <= 1.7e+84)) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -5.2e+39) or not (y <= 1.7e+84):
		tmp = x * (y * z)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -5.2e+39) || !(y <= 1.7e+84))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -5.2e+39) || ~((y <= 1.7e+84)))
		tmp = x * (y * z);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -5.2e+39], N[Not[LessEqual[y, 1.7e+84]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e39 or 1.6999999999999999e84 < y

   1. Initial program 57.2%

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

   3. Taylor expanded in z around inf 55.1%

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

   4. Taylor expanded in x around inf 42.3%

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

   if -5.2e39 < y < 1.6999999999999999e84

   1. Initial program 78.5%

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

   3. Taylor expanded in c around inf 48.3%

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

   4. Taylor expanded in a around inf 30.6%

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

      1. *-commutative 30.6%

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

   6. Simplified 30.6%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+39} \lor \neg \left(y \leq 1.7 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t 2.5e+117) (* a (* c j)) (* a (* x t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= 2.5e+117) {
		tmp = a * (c * j);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= 2.5d+117) then
        tmp = a * (c * j)
    else
        tmp = a * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= 2.5e+117) {
		tmp = a * (c * j);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= 2.5e+117:
		tmp = a * (c * j)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= 2.5e+117)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= 2.5e+117)
		tmp = a * (c * j);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, 2.5e+117], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.49999999999999992e117

   1. Initial program 73.2%

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

   3. Taylor expanded in a around inf 38.9%

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

      1. +-commutative 38.9%

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

      2. mul-1-neg 38.9%

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

      3. unsub-neg 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in c around inf 23.8%

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

      1. *-commutative 23.8%

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

   8. Simplified 23.8%

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

   if 2.49999999999999992e117 < t

   1. Initial program 55.2%

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

   3. Taylor expanded in t around inf 84.0%

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

      1. distribute-lft-out-- 84.0%

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

      2. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around inf 44.0%

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

      1. expm1-log1p-u 24.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(-1 \cdot \left(a \cdot x\right)\right)\right)\right)} \]

      2. expm1-udef 21.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(-1 \cdot \left(a \cdot x\right)\right)\right)} - 1} \]

      3. add-sqr-sqrt 21.5%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(\sqrt{-1 \cdot \left(a \cdot x\right)} \cdot \sqrt{-1 \cdot \left(a \cdot x\right)}\right)}\right)} - 1 \]

      4. sqrt-unprod 27.3%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \color{blue}{\sqrt{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot \left(-1 \cdot \left(a \cdot x\right)\right)}}\right)} - 1 \]

      5. mul-1-neg 27.3%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \sqrt{\color{blue}{\left(-a \cdot x\right)} \cdot \left(-1 \cdot \left(a \cdot x\right)\right)}\right)} - 1 \]

      6. mul-1-neg 27.3%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \sqrt{\left(-a \cdot x\right) \cdot \color{blue}{\left(-a \cdot x\right)}}\right)} - 1 \]

      7. sqr-neg 27.3%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \sqrt{\color{blue}{\left(a \cdot x\right) \cdot \left(a \cdot x\right)}}\right)} - 1 \]

      8. sqrt-unprod 5.9%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(\sqrt{a \cdot x} \cdot \sqrt{a \cdot x}\right)}\right)} - 1 \]

      9. add-sqr-sqrt 6.1%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \color{blue}{\left(a \cdot x\right)}\right)} - 1 \]

   8. Applied egg-rr 6.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \left(a \cdot x\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 6.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(a \cdot x\right)\right)\right)} \]

      2. expm1-log1p 12.4%

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

      3. *-commutative 12.4%

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

      4. associate-*r* 22.4%

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

   10. Simplified 22.4%

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

4. Final simplification 23.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.6% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

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 * (c * j)
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 * (c * j);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.6%

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

3. Taylor expanded in a around inf 39.6%

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

   1. +-commutative 39.6%

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

   2. mul-1-neg 39.6%

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

   3. unsub-neg 39.6%

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

5. Simplified 39.6%

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

6. Taylor expanded in c around inf 21.3%

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

   1. *-commutative 21.3%

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

8. Simplified 21.3%

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

9. Final simplification 21.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - 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 * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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