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

Percentage Accurate: 73.3% → 82.5%

Time: 31.5s

Alternatives: 18

Speedup: 0.5×

• 59.1% 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: 73.3% accurate, 1.0× speedup

Math

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

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: 82.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z))))
          (* 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 = ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))) + (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 = ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))) + (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 = ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))) + (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(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + 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 = ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))) + (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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(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 92.3%

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

   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. Taylor expanded in z around inf 58.3%

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

      1. *-commutative 58.3%

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

   4. Simplified 58.3%

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

4. Final simplification 87.3%

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

Alternative 2: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -11.5:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t_2\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (* z c))))
   (if (<= a -2.6e+110)
     t_1
     (if (<= a -11.5)
       (- (* j (- (* a c) (* y i))) t_2)
       (if (<= a -8.8e-17)
         (* t (- (* b i) (* x a)))
         (if (<= a -2e-286)
           (* z (- (* x y) (* b c)))
           (if (<= a 1.7e-217)
             (* y (- (* x z) (* i j)))
             (if (<= a 1.05e+164)
               (- (+ (* a (* c j)) (* x (* y z))) t_2)
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * (z * c);
	double tmp;
	if (a <= -2.6e+110) {
		tmp = t_1;
	} else if (a <= -11.5) {
		tmp = (j * ((a * c) - (y * i))) - t_2;
	} else if (a <= -8.8e-17) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= -2e-286) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 1.7e-217) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.05e+164) {
		tmp = ((a * (c * j)) + (x * (y * z))) - t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * (z * c)
    if (a <= (-2.6d+110)) then
        tmp = t_1
    else if (a <= (-11.5d0)) then
        tmp = (j * ((a * c) - (y * i))) - t_2
    else if (a <= (-8.8d-17)) then
        tmp = t * ((b * i) - (x * a))
    else if (a <= (-2d-286)) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 1.7d-217) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 1.05d+164) then
        tmp = ((a * (c * j)) + (x * (y * z))) - t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * (z * c);
	double tmp;
	if (a <= -2.6e+110) {
		tmp = t_1;
	} else if (a <= -11.5) {
		tmp = (j * ((a * c) - (y * i))) - t_2;
	} else if (a <= -8.8e-17) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= -2e-286) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 1.7e-217) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.05e+164) {
		tmp = ((a * (c * j)) + (x * (y * z))) - t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * (z * c)
	tmp = 0
	if a <= -2.6e+110:
		tmp = t_1
	elif a <= -11.5:
		tmp = (j * ((a * c) - (y * i))) - t_2
	elif a <= -8.8e-17:
		tmp = t * ((b * i) - (x * a))
	elif a <= -2e-286:
		tmp = z * ((x * y) - (b * c))
	elif a <= 1.7e-217:
		tmp = y * ((x * z) - (i * j))
	elif a <= 1.05e+164:
		tmp = ((a * (c * j)) + (x * (y * z))) - t_2
	else:
		tmp = t_1
	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(z * c))
	tmp = 0.0
	if (a <= -2.6e+110)
		tmp = t_1;
	elseif (a <= -11.5)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - t_2);
	elseif (a <= -8.8e-17)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (a <= -2e-286)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 1.7e-217)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 1.05e+164)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) + Float64(x * Float64(y * z))) - t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * (z * c);
	tmp = 0.0;
	if (a <= -2.6e+110)
		tmp = t_1;
	elseif (a <= -11.5)
		tmp = (j * ((a * c) - (y * i))) - t_2;
	elseif (a <= -8.8e-17)
		tmp = t * ((b * i) - (x * a));
	elseif (a <= -2e-286)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 1.7e-217)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 1.05e+164)
		tmp = ((a * (c * j)) + (x * (y * z))) - t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+110], t$95$1, If[LessEqual[a, -11.5], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[a, -8.8e-17], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-286], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-217], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+164], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.6e110 or 1.04999999999999995e164 < a

   1. Initial program 73.4%

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

   2. Taylor expanded in a around inf 81.3%

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

      1. +-commutative 81.3%

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

      2. mul-1-neg 81.3%

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

      3. unsub-neg 81.3%

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

      4. *-commutative 81.3%

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

      5. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -2.6e110 < a < -11.5

   1. Initial program 82.8%

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

   2. Taylor expanded in x around 0 69.9%

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

      1. cancel-sign-sub-inv 69.9%

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

      2. *-commutative 69.9%

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

      3. *-commutative 69.9%

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

      4. cancel-sign-sub-inv 69.9%

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

      5. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in z around inf 60.8%

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

   if -11.5 < a < -8.8e-17

   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. Taylor expanded in t around inf 67.7%

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

      1. distribute-lft-out-- 67.7%

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

      2. *-commutative 67.7%

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

      3. *-commutative 67.7%

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

   4. Simplified 67.7%

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

   if -8.8e-17 < a < -2.0000000000000001e-286

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   if -2.0000000000000001e-286 < a < 1.70000000000000008e-217

   1. Initial program 81.0%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. *-commutative 74.8%

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

   4. Simplified 74.8%

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

   if 1.70000000000000008e-217 < a < 1.04999999999999995e164

   1. Initial program 82.6%

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

   2. Taylor expanded in i around 0 71.0%

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

   3. Taylor expanded in y around inf 62.7%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -11.5:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 3: 69.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - t_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_3 - t_1\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z))))
        (t_2 (- (* b (- (* t i) (* z c))) t_1))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (- t_3 t_1)))
   (if (<= j -2.5e+39)
     t_4
     (if (<= j 1.45e-46)
       t_2
       (if (<= j 2.45e+34)
         t_4
         (if (<= j 2.15e+77) t_2 (- t_3 (* b (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_3 - t_1;
	double tmp;
	if (j <= -2.5e+39) {
		tmp = t_4;
	} else if (j <= 1.45e-46) {
		tmp = t_2;
	} else if (j <= 2.45e+34) {
		tmp = t_4;
	} else if (j <= 2.15e+77) {
		tmp = t_2;
	} else {
		tmp = t_3 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((t * a) - (y * z))
    t_2 = (b * ((t * i) - (z * c))) - t_1
    t_3 = j * ((a * c) - (y * i))
    t_4 = t_3 - t_1
    if (j <= (-2.5d+39)) then
        tmp = t_4
    else if (j <= 1.45d-46) then
        tmp = t_2
    else if (j <= 2.45d+34) then
        tmp = t_4
    else if (j <= 2.15d+77) then
        tmp = t_2
    else
        tmp = t_3 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_3 - t_1;
	double tmp;
	if (j <= -2.5e+39) {
		tmp = t_4;
	} else if (j <= 1.45e-46) {
		tmp = t_2;
	} else if (j <= 2.45e+34) {
		tmp = t_4;
	} else if (j <= 2.15e+77) {
		tmp = t_2;
	} else {
		tmp = t_3 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = (b * ((t * i) - (z * c))) - t_1
	t_3 = j * ((a * c) - (y * i))
	t_4 = t_3 - t_1
	tmp = 0
	if j <= -2.5e+39:
		tmp = t_4
	elif j <= 1.45e-46:
		tmp = t_2
	elif j <= 2.45e+34:
		tmp = t_4
	elif j <= 2.15e+77:
		tmp = t_2
	else:
		tmp = t_3 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(t_3 - t_1)
	tmp = 0.0
	if (j <= -2.5e+39)
		tmp = t_4;
	elseif (j <= 1.45e-46)
		tmp = t_2;
	elseif (j <= 2.45e+34)
		tmp = t_4;
	elseif (j <= 2.15e+77)
		tmp = t_2;
	else
		tmp = Float64(t_3 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = (b * ((t * i) - (z * c))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	t_4 = t_3 - t_1;
	tmp = 0.0;
	if (j <= -2.5e+39)
		tmp = t_4;
	elseif (j <= 1.45e-46)
		tmp = t_2;
	elseif (j <= 2.45e+34)
		tmp = t_4;
	elseif (j <= 2.15e+77)
		tmp = t_2;
	else
		tmp = t_3 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - t$95$1), $MachinePrecision]}, If[LessEqual[j, -2.5e+39], t$95$4, If[LessEqual[j, 1.45e-46], t$95$2, If[LessEqual[j, 2.45e+34], t$95$4, If[LessEqual[j, 2.15e+77], t$95$2, N[(t$95$3 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.50000000000000008e39 or 1.45000000000000002e-46 < j < 2.4500000000000001e34

   1. Initial program 80.1%

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

   2. Taylor expanded in b around 0 85.4%

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

   if -2.50000000000000008e39 < j < 1.45000000000000002e-46 or 2.4500000000000001e34 < j < 2.14999999999999996e77

   1. Initial program 80.6%

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

      1. add-sqr-sqrt 40.0%

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

      2. pow2 40.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 40.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 40.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 80.9%

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

      1. *-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. *-commutative 80.9%

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

      4. *-commutative 80.9%

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

   6. Simplified 80.9%

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

   if 2.14999999999999996e77 < j

   1. Initial program 71.1%

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

   2. Taylor expanded in x around 0 69.5%

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

      1. cancel-sign-sub-inv 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. cancel-sign-sub-inv 69.5%

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

      5. *-commutative 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in z around inf 71.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 4: 49.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -760000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+154} \lor \neg \left(b \leq 2.5 \cdot 10^{+218}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

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 -2.5e+192)
     t_2
     (if (<= b -3.5e+120)
       t_1
       (if (<= b -760000000.0)
         t_2
         (if (<= b -4.2e-292)
           t_1
           (if (<= b 1.6e-261)
             (* z (* x y))
             (if (<= b 5.5e+39)
               t_1
               (if (or (<= b 4.7e+154) (not (<= b 2.5e+218)))
                 t_2
                 (* c (- (* a j) (* z b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.5e+192) {
		tmp = t_2;
	} else if (b <= -3.5e+120) {
		tmp = t_1;
	} else if (b <= -760000000.0) {
		tmp = t_2;
	} else if (b <= -4.2e-292) {
		tmp = t_1;
	} else if (b <= 1.6e-261) {
		tmp = z * (x * y);
	} else if (b <= 5.5e+39) {
		tmp = t_1;
	} else if ((b <= 4.7e+154) || !(b <= 2.5e+218)) {
		tmp = t_2;
	} else {
		tmp = c * ((a * j) - (z * 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) :: 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 <= (-2.5d+192)) then
        tmp = t_2
    else if (b <= (-3.5d+120)) then
        tmp = t_1
    else if (b <= (-760000000.0d0)) then
        tmp = t_2
    else if (b <= (-4.2d-292)) then
        tmp = t_1
    else if (b <= 1.6d-261) then
        tmp = z * (x * y)
    else if (b <= 5.5d+39) then
        tmp = t_1
    else if ((b <= 4.7d+154) .or. (.not. (b <= 2.5d+218))) then
        tmp = t_2
    else
        tmp = c * ((a * j) - (z * 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 t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.5e+192) {
		tmp = t_2;
	} else if (b <= -3.5e+120) {
		tmp = t_1;
	} else if (b <= -760000000.0) {
		tmp = t_2;
	} else if (b <= -4.2e-292) {
		tmp = t_1;
	} else if (b <= 1.6e-261) {
		tmp = z * (x * y);
	} else if (b <= 5.5e+39) {
		tmp = t_1;
	} else if ((b <= 4.7e+154) || !(b <= 2.5e+218)) {
		tmp = t_2;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	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 <= -2.5e+192:
		tmp = t_2
	elif b <= -3.5e+120:
		tmp = t_1
	elif b <= -760000000.0:
		tmp = t_2
	elif b <= -4.2e-292:
		tmp = t_1
	elif b <= 1.6e-261:
		tmp = z * (x * y)
	elif b <= 5.5e+39:
		tmp = t_1
	elif (b <= 4.7e+154) or not (b <= 2.5e+218):
		tmp = t_2
	else:
		tmp = c * ((a * j) - (z * b))
	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 <= -2.5e+192)
		tmp = t_2;
	elseif (b <= -3.5e+120)
		tmp = t_1;
	elseif (b <= -760000000.0)
		tmp = t_2;
	elseif (b <= -4.2e-292)
		tmp = t_1;
	elseif (b <= 1.6e-261)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 5.5e+39)
		tmp = t_1;
	elseif ((b <= 4.7e+154) || !(b <= 2.5e+218))
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 <= -2.5e+192)
		tmp = t_2;
	elseif (b <= -3.5e+120)
		tmp = t_1;
	elseif (b <= -760000000.0)
		tmp = t_2;
	elseif (b <= -4.2e-292)
		tmp = t_1;
	elseif (b <= 1.6e-261)
		tmp = z * (x * y);
	elseif (b <= 5.5e+39)
		tmp = t_1;
	elseif ((b <= 4.7e+154) || ~((b <= 2.5e+218)))
		tmp = t_2;
	else
		tmp = c * ((a * j) - (z * b));
	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, -2.5e+192], t$95$2, If[LessEqual[b, -3.5e+120], t$95$1, If[LessEqual[b, -760000000.0], t$95$2, If[LessEqual[b, -4.2e-292], t$95$1, If[LessEqual[b, 1.6e-261], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+39], t$95$1, If[Or[LessEqual[b, 4.7e+154], N[Not[LessEqual[b, 2.5e+218]], $MachinePrecision]], t$95$2, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.50000000000000017e192 or -3.50000000000000007e120 < b < -7.6e8 or 5.4999999999999997e39 < b < 4.69999999999999983e154 or 2.49999999999999991e218 < b

   1. Initial program 82.3%

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

   2. Taylor expanded in b around inf 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -2.50000000000000017e192 < b < -3.50000000000000007e120 or -7.6e8 < b < -4.19999999999999977e-292 or 1.60000000000000002e-261 < b < 5.4999999999999997e39

   1. Initial program 77.0%

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

   2. Taylor expanded in a around inf 53.9%

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

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

      4. *-commutative 53.9%

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

      5. *-commutative 53.9%

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

   4. Simplified 53.9%

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

   if -4.19999999999999977e-292 < b < 1.60000000000000002e-261

   1. Initial program 73.4%

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

      1. add-sqr-sqrt 47.5%

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

      2. pow2 47.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 47.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 47.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. *-commutative 55.1%

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

      3. *-commutative 55.1%

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

      4. *-commutative 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in y around inf 55.2%

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

      1. associate-*r* 63.4%

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

      2. *-commutative 63.4%

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

   9. Simplified 63.4%

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

   if 4.69999999999999983e154 < b < 2.49999999999999991e218

   1. Initial program 73.1%

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

   2. Taylor expanded in c around inf 82.6%

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

      1. *-commutative 82.6%

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

   4. Simplified 82.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -760000000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+154} \lor \neg \left(b \leq 2.5 \cdot 10^{+218}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5: 52.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 160000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+210}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* b (* z c))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -2.7e+56)
     t_3
     (if (<= t -1.95e-17)
       t_2
       (if (<= t 5.5e-300)
         t_1
         (if (<= t 2.2e-127)
           t_2
           (if (<= t 160000000000.0)
             t_1
             (if (<= t 1.95e+210) t_3 (* c (- (* a j) (* z b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - (b * (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.7e+56) {
		tmp = t_3;
	} else if (t <= -1.95e-17) {
		tmp = t_2;
	} else if (t <= 5.5e-300) {
		tmp = t_1;
	} else if (t <= 2.2e-127) {
		tmp = t_2;
	} else if (t <= 160000000000.0) {
		tmp = t_1;
	} else if (t <= 1.95e+210) {
		tmp = t_3;
	} else {
		tmp = c * ((a * j) - (z * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) - (b * (z * c))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-2.7d+56)) then
        tmp = t_3
    else if (t <= (-1.95d-17)) then
        tmp = t_2
    else if (t <= 5.5d-300) then
        tmp = t_1
    else if (t <= 2.2d-127) then
        tmp = t_2
    else if (t <= 160000000000.0d0) then
        tmp = t_1
    else if (t <= 1.95d+210) then
        tmp = t_3
    else
        tmp = c * ((a * j) - (z * 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 t_1 = (j * ((a * c) - (y * i))) - (b * (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.7e+56) {
		tmp = t_3;
	} else if (t <= -1.95e-17) {
		tmp = t_2;
	} else if (t <= 5.5e-300) {
		tmp = t_1;
	} else if (t <= 2.2e-127) {
		tmp = t_2;
	} else if (t <= 160000000000.0) {
		tmp = t_1;
	} else if (t <= 1.95e+210) {
		tmp = t_3;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (b * (z * c))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.7e+56:
		tmp = t_3
	elif t <= -1.95e-17:
		tmp = t_2
	elif t <= 5.5e-300:
		tmp = t_1
	elif t <= 2.2e-127:
		tmp = t_2
	elif t <= 160000000000.0:
		tmp = t_1
	elif t <= 1.95e+210:
		tmp = t_3
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.7e+56)
		tmp = t_3;
	elseif (t <= -1.95e-17)
		tmp = t_2;
	elseif (t <= 5.5e-300)
		tmp = t_1;
	elseif (t <= 2.2e-127)
		tmp = t_2;
	elseif (t <= 160000000000.0)
		tmp = t_1;
	elseif (t <= 1.95e+210)
		tmp = t_3;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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))) - (b * (z * c));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.7e+56)
		tmp = t_3;
	elseif (t <= -1.95e-17)
		tmp = t_2;
	elseif (t <= 5.5e-300)
		tmp = t_1;
	elseif (t <= 2.2e-127)
		tmp = t_2;
	elseif (t <= 160000000000.0)
		tmp = t_1;
	elseif (t <= 1.95e+210)
		tmp = t_3;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+56], t$95$3, If[LessEqual[t, -1.95e-17], t$95$2, If[LessEqual[t, 5.5e-300], t$95$1, If[LessEqual[t, 2.2e-127], t$95$2, If[LessEqual[t, 160000000000.0], t$95$1, If[LessEqual[t, 1.95e+210], t$95$3, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7000000000000001e56 or 1.6e11 < t < 1.95e210

   1. Initial program 72.1%

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

   2. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

      3. *-commutative 64.8%

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

   4. Simplified 64.8%

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

   if -2.7000000000000001e56 < t < -1.94999999999999995e-17 or 5.4999999999999999e-300 < t < 2.2000000000000001e-127

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

   4. Simplified 65.1%

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

   if -1.94999999999999995e-17 < t < 5.4999999999999999e-300 or 2.2000000000000001e-127 < t < 1.6e11

   1. Initial program 85.6%

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

   2. Taylor expanded in x around 0 75.2%

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

      1. cancel-sign-sub-inv 75.2%

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

      2. *-commutative 75.2%

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

      3. *-commutative 75.2%

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

      4. cancel-sign-sub-inv 75.2%

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

      5. *-commutative 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in z around inf 70.6%

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

   if 1.95e210 < t

   1. Initial program 77.7%

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

   2. Taylor expanded in c around inf 72.8%

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

      1. *-commutative 72.8%

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

   4. Simplified 72.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-300}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 160000000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+210}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;t_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;t_2 - t_3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* b (* z c))))
   (if (<= z -5e+142)
     t_1
     (if (<= z 1.2e-125)
       (- t_2 (* x (- (* t a) (* y z))))
       (if (<= z 1.5e+49)
         (- t_2 t_3)
         (if (<= z 2.4e+125) (- (+ (* a (* c j)) (* x (* y z))) 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 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = b * (z * c);
	double tmp;
	if (z <= -5e+142) {
		tmp = t_1;
	} else if (z <= 1.2e-125) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else if (z <= 1.5e+49) {
		tmp = t_2 - t_3;
	} else if (z <= 2.4e+125) {
		tmp = ((a * (c * j)) + (x * (y * z))) - 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 = z * ((x * y) - (b * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = b * (z * c)
    if (z <= (-5d+142)) then
        tmp = t_1
    else if (z <= 1.2d-125) then
        tmp = t_2 - (x * ((t * a) - (y * z)))
    else if (z <= 1.5d+49) then
        tmp = t_2 - t_3
    else if (z <= 2.4d+125) then
        tmp = ((a * (c * j)) + (x * (y * z))) - 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 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = b * (z * c);
	double tmp;
	if (z <= -5e+142) {
		tmp = t_1;
	} else if (z <= 1.2e-125) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else if (z <= 1.5e+49) {
		tmp = t_2 - t_3;
	} else if (z <= 2.4e+125) {
		tmp = ((a * (c * j)) + (x * (y * z))) - t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = b * (z * c)
	tmp = 0
	if z <= -5e+142:
		tmp = t_1
	elif z <= 1.2e-125:
		tmp = t_2 - (x * ((t * a) - (y * z)))
	elif z <= 1.5e+49:
		tmp = t_2 - t_3
	elif z <= 2.4e+125:
		tmp = ((a * (c * j)) + (x * (y * z))) - t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(b * Float64(z * c))
	tmp = 0.0
	if (z <= -5e+142)
		tmp = t_1;
	elseif (z <= 1.2e-125)
		tmp = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (z <= 1.5e+49)
		tmp = Float64(t_2 - t_3);
	elseif (z <= 2.4e+125)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) + Float64(x * Float64(y * z))) - 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 = z * ((x * y) - (b * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = b * (z * c);
	tmp = 0.0;
	if (z <= -5e+142)
		tmp = t_1;
	elseif (z <= 1.2e-125)
		tmp = t_2 - (x * ((t * a) - (y * z)));
	elseif (z <= 1.5e+49)
		tmp = t_2 - t_3;
	elseif (z <= 2.4e+125)
		tmp = ((a * (c * j)) + (x * (y * z))) - 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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+142], t$95$1, If[LessEqual[z, 1.2e-125], N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+49], N[(t$95$2 - t$95$3), $MachinePrecision], If[LessEqual[z, 2.4e+125], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.0000000000000001e142 or 2.4e125 < z

   1. Initial program 68.7%

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

   2. Taylor expanded in z around inf 77.3%

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

      1. *-commutative 77.3%

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

   4. Simplified 77.3%

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

   if -5.0000000000000001e142 < z < 1.2000000000000001e-125

   1. Initial program 84.8%

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

   2. Taylor expanded in b around 0 70.8%

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

   if 1.2000000000000001e-125 < z < 1.5000000000000001e49

   1. Initial program 86.8%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. cancel-sign-sub-inv 77.8%

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

      2. *-commutative 77.8%

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

      3. *-commutative 77.8%

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

      4. cancel-sign-sub-inv 77.8%

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

      5. *-commutative 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in z around inf 74.9%

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

   if 1.5000000000000001e49 < z < 2.4e125

   1. Initial program 64.2%

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

   2. Taylor expanded in i around 0 76.6%

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

   3. Taylor expanded in y around inf 65.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+142}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 7: 68.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+39} \lor \neg \left(b \leq 1.3 \cdot 10^{-32}\right):\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= b -4e+39) (not (<= b 1.3e-32)))
     (+ t_1 (* b (- (* t i) (* z c))))
     (- t_1 (* x (- (* t a) (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((b <= -4e+39) || !(b <= 1.3e-32)) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if ((b <= (-4d+39)) .or. (.not. (b <= 1.3d-32))) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else
        tmp = t_1 - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((b <= -4e+39) || !(b <= 1.3e-32)) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	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 <= -4e+39) or not (b <= 1.3e-32):
		tmp = t_1 + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	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 <= -4e+39) || !(b <= 1.3e-32))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	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 <= -4e+39) || ~((b <= 1.3e-32)))
		tmp = t_1 + (b * ((t * i) - (z * c)));
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	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[Or[LessEqual[b, -4e+39], N[Not[LessEqual[b, 1.3e-32]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.99999999999999976e39 or 1.2999999999999999e-32 < b

   1. Initial program 80.9%

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

   2. Taylor expanded in x around 0 75.1%

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

      1. cancel-sign-sub-inv 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

      4. cancel-sign-sub-inv 75.1%

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

      5. *-commutative 75.1%

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

   4. Simplified 75.1%

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

   if -3.99999999999999976e39 < b < 1.2999999999999999e-32

   1. Initial program 76.2%

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

   2. Taylor expanded in b around 0 75.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+39} \lor \neg \left(b \leq 1.3 \cdot 10^{-32}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]

Alternative 8: 30.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ t_2 := \left(x \cdot t\right) \cdot \left(-a\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -380000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-233}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.96 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+143}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))) (t_2 (* (* x t) (- a))) (t_3 (* a (* c j))))
   (if (<= j -380000000.0)
     t_3
     (if (<= j -4.6e-160)
       t_1
       (if (<= j 7.5e-306)
         t_2
         (if (<= j 1.15e-233)
           (* i (* t b))
           (if (<= j 5.8e-180)
             t_2
             (if (<= j 1.96e-88)
               t_1
               (if (<= j 5.7e-11)
                 (* y (* x z))
                 (if (<= j 1.7e+143) (* i (* y (- j))) 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 = t * (b * i);
	double t_2 = (x * t) * -a;
	double t_3 = a * (c * j);
	double tmp;
	if (j <= -380000000.0) {
		tmp = t_3;
	} else if (j <= -4.6e-160) {
		tmp = t_1;
	} else if (j <= 7.5e-306) {
		tmp = t_2;
	} else if (j <= 1.15e-233) {
		tmp = i * (t * b);
	} else if (j <= 5.8e-180) {
		tmp = t_2;
	} else if (j <= 1.96e-88) {
		tmp = t_1;
	} else if (j <= 5.7e-11) {
		tmp = y * (x * z);
	} else if (j <= 1.7e+143) {
		tmp = i * (y * -j);
	} 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 = t * (b * i)
    t_2 = (x * t) * -a
    t_3 = a * (c * j)
    if (j <= (-380000000.0d0)) then
        tmp = t_3
    else if (j <= (-4.6d-160)) then
        tmp = t_1
    else if (j <= 7.5d-306) then
        tmp = t_2
    else if (j <= 1.15d-233) then
        tmp = i * (t * b)
    else if (j <= 5.8d-180) then
        tmp = t_2
    else if (j <= 1.96d-88) then
        tmp = t_1
    else if (j <= 5.7d-11) then
        tmp = y * (x * z)
    else if (j <= 1.7d+143) then
        tmp = i * (y * -j)
    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 = t * (b * i);
	double t_2 = (x * t) * -a;
	double t_3 = a * (c * j);
	double tmp;
	if (j <= -380000000.0) {
		tmp = t_3;
	} else if (j <= -4.6e-160) {
		tmp = t_1;
	} else if (j <= 7.5e-306) {
		tmp = t_2;
	} else if (j <= 1.15e-233) {
		tmp = i * (t * b);
	} else if (j <= 5.8e-180) {
		tmp = t_2;
	} else if (j <= 1.96e-88) {
		tmp = t_1;
	} else if (j <= 5.7e-11) {
		tmp = y * (x * z);
	} else if (j <= 1.7e+143) {
		tmp = i * (y * -j);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	t_2 = (x * t) * -a
	t_3 = a * (c * j)
	tmp = 0
	if j <= -380000000.0:
		tmp = t_3
	elif j <= -4.6e-160:
		tmp = t_1
	elif j <= 7.5e-306:
		tmp = t_2
	elif j <= 1.15e-233:
		tmp = i * (t * b)
	elif j <= 5.8e-180:
		tmp = t_2
	elif j <= 1.96e-88:
		tmp = t_1
	elif j <= 5.7e-11:
		tmp = y * (x * z)
	elif j <= 1.7e+143:
		tmp = i * (y * -j)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	t_2 = Float64(Float64(x * t) * Float64(-a))
	t_3 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -380000000.0)
		tmp = t_3;
	elseif (j <= -4.6e-160)
		tmp = t_1;
	elseif (j <= 7.5e-306)
		tmp = t_2;
	elseif (j <= 1.15e-233)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 5.8e-180)
		tmp = t_2;
	elseif (j <= 1.96e-88)
		tmp = t_1;
	elseif (j <= 5.7e-11)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.7e+143)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	t_2 = (x * t) * -a;
	t_3 = a * (c * j);
	tmp = 0.0;
	if (j <= -380000000.0)
		tmp = t_3;
	elseif (j <= -4.6e-160)
		tmp = t_1;
	elseif (j <= 7.5e-306)
		tmp = t_2;
	elseif (j <= 1.15e-233)
		tmp = i * (t * b);
	elseif (j <= 5.8e-180)
		tmp = t_2;
	elseif (j <= 1.96e-88)
		tmp = t_1;
	elseif (j <= 5.7e-11)
		tmp = y * (x * z);
	elseif (j <= 1.7e+143)
		tmp = i * (y * -j);
	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[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -380000000.0], t$95$3, If[LessEqual[j, -4.6e-160], t$95$1, If[LessEqual[j, 7.5e-306], t$95$2, If[LessEqual[j, 1.15e-233], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-180], t$95$2, If[LessEqual[j, 1.96e-88], t$95$1, If[LessEqual[j, 5.7e-11], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e+143], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.8e8 or 1.69999999999999991e143 < j

   1. Initial program 80.7%

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

   2. Taylor expanded in a around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

      5. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in j around inf 55.2%

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

   if -3.8e8 < j < -4.5999999999999997e-160 or 5.79999999999999961e-180 < j < 1.96e-88

   1. Initial program 87.4%

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

   2. Taylor expanded in t around inf 49.3%

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

      1. distribute-lft-out-- 49.3%

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

      2. *-commutative 49.3%

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

      3. *-commutative 49.3%

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

   4. Simplified 49.3%

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

   5. Taylor expanded in x around 0 31.3%

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

      1. *-commutative 31.3%

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

      2. *-commutative 31.3%

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

      3. associate-*l* 34.8%

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

   7. Simplified 34.8%

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

   if -4.5999999999999997e-160 < j < 7.5000000000000003e-306 or 1.1500000000000001e-233 < j < 5.79999999999999961e-180

   1. Initial program 78.9%

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

   2. Taylor expanded in a around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

      4. *-commutative 52.6%

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

      5. *-commutative 52.6%

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

   4. Simplified 52.6%

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

   5. Taylor expanded in j around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. *-commutative 48.5%

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

      3. distribute-rgt-neg-in 48.5%

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

   7. Simplified 48.5%

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

   if 7.5000000000000003e-306 < j < 1.1500000000000001e-233

   1. Initial program 73.8%

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

   2. Taylor expanded in x around 0 53.7%

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

      1. cancel-sign-sub-inv 53.7%

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

      2. *-commutative 53.7%

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

      3. *-commutative 53.7%

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

      4. cancel-sign-sub-inv 53.7%

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

      5. *-commutative 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in t around inf 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-*r* 54.0%

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

      3. *-commutative 54.0%

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

   7. Simplified 54.0%

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

   if 1.96e-88 < j < 5.6999999999999997e-11

   1. Initial program 64.8%

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

   2. Taylor expanded in y around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

      4. *-commutative 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in x around inf 56.3%

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

   if 5.6999999999999997e-11 < j < 1.69999999999999991e143

   1. Initial program 71.3%

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

   2. Taylor expanded in y around inf 41.1%

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

      1. +-commutative 41.1%

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

      2. mul-1-neg 41.1%

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

      3. unsub-neg 41.1%

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

      4. *-commutative 41.1%

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

   4. Simplified 41.1%

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

   5. Taylor expanded in x around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. distribute-rgt-neg-in 35.7%

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

      3. *-commutative 35.7%

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

      4. distribute-rgt-neg-in 35.7%

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

   7. Simplified 35.7%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -380000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-160}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-306}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-233}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-180}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.96 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+143}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 9: 48.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 455000000000 \lor \neg \left(t \leq 1.95 \cdot 10^{+210}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.8e+56)
     t_2
     (if (<= t -4.6e-20)
       t_1
       (if (<= t -2.7e-155)
         (* j (- (* a c) (* y i)))
         (if (<= t 5.6e-183)
           t_1
           (if (or (<= t 455000000000.0) (not (<= t 1.95e+210)))
             (* c (- (* a j) (* z b)))
             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) - (b * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.8e+56) {
		tmp = t_2;
	} else if (t <= -4.6e-20) {
		tmp = t_1;
	} else if (t <= -2.7e-155) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 5.6e-183) {
		tmp = t_1;
	} else if ((t <= 455000000000.0) || !(t <= 1.95e+210)) {
		tmp = c * ((a * j) - (z * b));
	} 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) - (b * c))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.8d+56)) then
        tmp = t_2
    else if (t <= (-4.6d-20)) then
        tmp = t_1
    else if (t <= (-2.7d-155)) then
        tmp = j * ((a * c) - (y * i))
    else if (t <= 5.6d-183) then
        tmp = t_1
    else if ((t <= 455000000000.0d0) .or. (.not. (t <= 1.95d+210))) then
        tmp = c * ((a * j) - (z * b))
    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) - (b * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.8e+56) {
		tmp = t_2;
	} else if (t <= -4.6e-20) {
		tmp = t_1;
	} else if (t <= -2.7e-155) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 5.6e-183) {
		tmp = t_1;
	} else if ((t <= 455000000000.0) || !(t <= 1.95e+210)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.8e+56:
		tmp = t_2
	elif t <= -4.6e-20:
		tmp = t_1
	elif t <= -2.7e-155:
		tmp = j * ((a * c) - (y * i))
	elif t <= 5.6e-183:
		tmp = t_1
	elif (t <= 455000000000.0) or not (t <= 1.95e+210):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.8e+56)
		tmp = t_2;
	elseif (t <= -4.6e-20)
		tmp = t_1;
	elseif (t <= -2.7e-155)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (t <= 5.6e-183)
		tmp = t_1;
	elseif ((t <= 455000000000.0) || !(t <= 1.95e+210))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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) - (b * c));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.8e+56)
		tmp = t_2;
	elseif (t <= -4.6e-20)
		tmp = t_1;
	elseif (t <= -2.7e-155)
		tmp = j * ((a * c) - (y * i));
	elseif (t <= 5.6e-183)
		tmp = t_1;
	elseif ((t <= 455000000000.0) || ~((t <= 1.95e+210)))
		tmp = c * ((a * j) - (z * b));
	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[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+56], t$95$2, If[LessEqual[t, -4.6e-20], t$95$1, If[LessEqual[t, -2.7e-155], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-183], t$95$1, If[Or[LessEqual[t, 455000000000.0], N[Not[LessEqual[t, 1.95e+210]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000008e56 or 4.55e11 < t < 1.95e210

   1. Initial program 72.1%

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

   2. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

      3. *-commutative 64.8%

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

   4. Simplified 64.8%

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

   if -2.80000000000000008e56 < t < -4.5999999999999998e-20 or -2.69999999999999981e-155 < t < 5.5999999999999997e-183

   1. Initial program 80.5%

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

   2. Taylor expanded in z around inf 64.3%

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

      1. *-commutative 64.3%

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

   4. Simplified 64.3%

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

   if -4.5999999999999998e-20 < t < -2.69999999999999981e-155

   1. Initial program 91.5%

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

      1. add-sqr-sqrt 37.4%

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

      2. pow2 37.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 37.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 37.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around inf 61.8%

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

      1. sub-neg 61.8%

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

      2. *-commutative 61.8%

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

      3. sub-neg 61.8%

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

   6. Simplified 61.8%

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

   if 5.5999999999999997e-183 < t < 4.55e11 or 1.95e210 < t

   1. Initial program 81.8%

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

   2. Taylor expanded in c around inf 66.5%

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

      1. *-commutative 66.5%

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

   4. Simplified 66.5%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-155}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-183}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 455000000000 \lor \neg \left(t \leq 1.95 \cdot 10^{+210}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 10: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5800000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-259}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -2.6e+192)
     t_2
     (if (<= b -7.5e+117)
       t_1
       (if (<= b -5800000.0)
         t_2
         (if (<= b -8e-292)
           t_1
           (if (<= b 9.4e-259) (* z (* x y)) (if (<= b 2.6e+39) 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 <= -2.6e+192) {
		tmp = t_2;
	} else if (b <= -7.5e+117) {
		tmp = t_1;
	} else if (b <= -5800000.0) {
		tmp = t_2;
	} else if (b <= -8e-292) {
		tmp = t_1;
	} else if (b <= 9.4e-259) {
		tmp = z * (x * y);
	} else if (b <= 2.6e+39) {
		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 <= (-2.6d+192)) then
        tmp = t_2
    else if (b <= (-7.5d+117)) then
        tmp = t_1
    else if (b <= (-5800000.0d0)) then
        tmp = t_2
    else if (b <= (-8d-292)) then
        tmp = t_1
    else if (b <= 9.4d-259) then
        tmp = z * (x * y)
    else if (b <= 2.6d+39) 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 <= -2.6e+192) {
		tmp = t_2;
	} else if (b <= -7.5e+117) {
		tmp = t_1;
	} else if (b <= -5800000.0) {
		tmp = t_2;
	} else if (b <= -8e-292) {
		tmp = t_1;
	} else if (b <= 9.4e-259) {
		tmp = z * (x * y);
	} else if (b <= 2.6e+39) {
		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 <= -2.6e+192:
		tmp = t_2
	elif b <= -7.5e+117:
		tmp = t_1
	elif b <= -5800000.0:
		tmp = t_2
	elif b <= -8e-292:
		tmp = t_1
	elif b <= 9.4e-259:
		tmp = z * (x * y)
	elif b <= 2.6e+39:
		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 <= -2.6e+192)
		tmp = t_2;
	elseif (b <= -7.5e+117)
		tmp = t_1;
	elseif (b <= -5800000.0)
		tmp = t_2;
	elseif (b <= -8e-292)
		tmp = t_1;
	elseif (b <= 9.4e-259)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 2.6e+39)
		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 <= -2.6e+192)
		tmp = t_2;
	elseif (b <= -7.5e+117)
		tmp = t_1;
	elseif (b <= -5800000.0)
		tmp = t_2;
	elseif (b <= -8e-292)
		tmp = t_1;
	elseif (b <= 9.4e-259)
		tmp = z * (x * y);
	elseif (b <= 2.6e+39)
		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, -2.6e+192], t$95$2, If[LessEqual[b, -7.5e+117], t$95$1, If[LessEqual[b, -5800000.0], t$95$2, If[LessEqual[b, -8e-292], t$95$1, If[LessEqual[b, 9.4e-259], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+39], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.60000000000000003e192 or -7.5e117 < b < -5.8e6 or 2.6e39 < b

   1. Initial program 81.4%

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

   2. Taylor expanded in b around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

   4. Simplified 70.9%

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

   if -2.60000000000000003e192 < b < -7.5e117 or -5.8e6 < b < -8.0000000000000004e-292 or 9.39999999999999996e-259 < b < 2.6e39

   1. Initial program 77.0%

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

   2. Taylor expanded in a around inf 53.9%

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

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

      4. *-commutative 53.9%

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

      5. *-commutative 53.9%

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

   4. Simplified 53.9%

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

   if -8.0000000000000004e-292 < b < 9.39999999999999996e-259

   1. Initial program 73.4%

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

      1. add-sqr-sqrt 47.5%

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

      2. pow2 47.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 47.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 47.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. *-commutative 55.1%

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

      3. *-commutative 55.1%

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

      4. *-commutative 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in y around inf 55.2%

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

      1. associate-*r* 63.4%

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

      2. *-commutative 63.4%

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

   9. Simplified 63.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -5800000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-259}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 11: 51.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -7e+65)
     t_2
     (if (<= a -1.85e-287)
       t_1
       (if (<= a 6e-221)
         (* y (- (* x z) (* i j)))
         (if (<= a 1.25e+41) 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) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7e+65) {
		tmp = t_2;
	} else if (a <= -1.85e-287) {
		tmp = t_1;
	} else if (a <= 6e-221) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.25e+41) {
		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) - (b * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-7d+65)) then
        tmp = t_2
    else if (a <= (-1.85d-287)) then
        tmp = t_1
    else if (a <= 6d-221) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 1.25d+41) 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) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7e+65) {
		tmp = t_2;
	} else if (a <= -1.85e-287) {
		tmp = t_1;
	} else if (a <= 6e-221) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.25e+41) {
		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) - (b * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -7e+65:
		tmp = t_2
	elif a <= -1.85e-287:
		tmp = t_1
	elif a <= 6e-221:
		tmp = y * ((x * z) - (i * j))
	elif a <= 1.25e+41:
		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(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7e+65)
		tmp = t_2;
	elseif (a <= -1.85e-287)
		tmp = t_1;
	elseif (a <= 6e-221)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 1.25e+41)
		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) - (b * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -7e+65)
		tmp = t_2;
	elseif (a <= -1.85e-287)
		tmp = t_1;
	elseif (a <= 6e-221)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 1.25e+41)
		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[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+65], t$95$2, If[LessEqual[a, -1.85e-287], t$95$1, If[LessEqual[a, 6e-221], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000002e65 or 1.25000000000000006e41 < a

   1. Initial program 72.4%

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

   2. Taylor expanded in a around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. *-commutative 69.0%

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

      5. *-commutative 69.0%

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

   4. Simplified 69.0%

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

   if -7.0000000000000002e65 < a < -1.85000000000000013e-287 or 6.0000000000000003e-221 < a < 1.25000000000000006e41

   1. Initial program 83.4%

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

   2. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

   4. Simplified 56.1%

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

   if -1.85000000000000013e-287 < a < 6.0000000000000003e-221

   1. Initial program 79.7%

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

   2. Taylor expanded in y around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

   4. Simplified 73.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-287}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 12: 29.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+231} \lor \neg \left(b \leq 8.2 \cdot 10^{+296}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))))
   (if (<= b -2.3e+42)
     t_1
     (if (<= b 5.6e-49)
       (* z (* x y))
       (if (<= b 8.6e+79)
         (* b (* t i))
         (if (or (<= b 2.65e+231) (not (<= b 8.2e+296)))
           t_1
           (* 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 t_1 = z * (c * -b);
	double tmp;
	if (b <= -2.3e+42) {
		tmp = t_1;
	} else if (b <= 5.6e-49) {
		tmp = z * (x * y);
	} else if (b <= 8.6e+79) {
		tmp = b * (t * i);
	} else if ((b <= 2.65e+231) || !(b <= 8.2e+296)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * (c * -b)
    if (b <= (-2.3d+42)) then
        tmp = t_1
    else if (b <= 5.6d-49) then
        tmp = z * (x * y)
    else if (b <= 8.6d+79) then
        tmp = b * (t * i)
    else if ((b <= 2.65d+231) .or. (.not. (b <= 8.2d+296))) then
        tmp = t_1
    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 t_1 = z * (c * -b);
	double tmp;
	if (b <= -2.3e+42) {
		tmp = t_1;
	} else if (b <= 5.6e-49) {
		tmp = z * (x * y);
	} else if (b <= 8.6e+79) {
		tmp = b * (t * i);
	} else if ((b <= 2.65e+231) || !(b <= 8.2e+296)) {
		tmp = t_1;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	tmp = 0
	if b <= -2.3e+42:
		tmp = t_1
	elif b <= 5.6e-49:
		tmp = z * (x * y)
	elif b <= 8.6e+79:
		tmp = b * (t * i)
	elif (b <= 2.65e+231) or not (b <= 8.2e+296):
		tmp = t_1
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	tmp = 0.0
	if (b <= -2.3e+42)
		tmp = t_1;
	elseif (b <= 5.6e-49)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 8.6e+79)
		tmp = Float64(b * Float64(t * i));
	elseif ((b <= 2.65e+231) || !(b <= 8.2e+296))
		tmp = t_1;
	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)
	t_1 = z * (c * -b);
	tmp = 0.0;
	if (b <= -2.3e+42)
		tmp = t_1;
	elseif (b <= 5.6e-49)
		tmp = z * (x * y);
	elseif (b <= 8.6e+79)
		tmp = b * (t * i);
	elseif ((b <= 2.65e+231) || ~((b <= 8.2e+296)))
		tmp = t_1;
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+42], t$95$1, If[LessEqual[b, 5.6e-49], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+79], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.65e+231], N[Not[LessEqual[b, 8.2e+296]], $MachinePrecision]], t$95$1, N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.3e42 or 8.6000000000000006e79 < b < 2.6499999999999999e231 or 8.20000000000000003e296 < b

   1. Initial program 81.9%

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

   2. Taylor expanded in z around inf 55.0%

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

      1. *-commutative 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in x around 0 50.6%

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

      1. neg-mul-1 50.6%

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

      2. distribute-rgt-neg-in 50.6%

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

   7. Simplified 50.6%

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

   if -2.3e42 < b < 5.59999999999999995e-49

   1. Initial program 76.1%

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

      1. add-sqr-sqrt 44.2%

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

      2. pow2 44.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 44.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 44.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 62.7%

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

      1. *-commutative 62.7%

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

      2. *-commutative 62.7%

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

      3. *-commutative 62.7%

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

      4. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   7. Taylor expanded in y around inf 37.2%

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

      1. associate-*r* 37.2%

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

      2. *-commutative 37.2%

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

   9. Simplified 37.2%

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

   if 5.59999999999999995e-49 < b < 8.6000000000000006e79

   1. Initial program 83.9%

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

   2. Taylor expanded in t around inf 45.7%

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

      1. distribute-lft-out-- 45.7%

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

      2. *-commutative 45.7%

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

      3. *-commutative 45.7%

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

   4. Simplified 45.7%

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

   5. Taylor expanded in x around 0 36.9%

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

      1. *-commutative 36.9%

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

   7. Simplified 36.9%

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

   if 2.6499999999999999e231 < b < 8.20000000000000003e296

   1. Initial program 68.7%

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

   2. Taylor expanded in x around 0 68.7%

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

      1. cancel-sign-sub-inv 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

      4. cancel-sign-sub-inv 68.7%

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

      5. *-commutative 68.7%

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

   4. Simplified 68.7%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-*r* 62.6%

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

      3. *-commutative 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+231} \lor \neg \left(b \leq 8.2 \cdot 10^{+296}\right):\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 13: 52.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.2)
     t_1
     (if (<= y 5.2e-199)
       (* a (- (* c j) (* x t)))
       (if (<= y 2.9e+30) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.2) {
		tmp = t_1;
	} else if (y <= 5.2e-199) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 2.9e+30) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.2d0)) then
        tmp = t_1
    else if (y <= 5.2d-199) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 2.9d+30) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.2) {
		tmp = t_1;
	} else if (y <= 5.2e-199) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 2.9e+30) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.2:
		tmp = t_1
	elif y <= 5.2e-199:
		tmp = a * ((c * j) - (x * t))
	elif y <= 2.9e+30:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.2)
		tmp = t_1;
	elseif (y <= 5.2e-199)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 2.9e+30)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.2)
		tmp = t_1;
	elseif (y <= 5.2e-199)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 2.9e+30)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2], t$95$1, If[LessEqual[y, 5.2e-199], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+30], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999996 or 2.8999999999999998e30 < y

   1. Initial program 73.1%

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

   2. Taylor expanded in y around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. *-commutative 62.8%

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

   4. Simplified 62.8%

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

   if -1.19999999999999996 < y < 5.2000000000000001e-199

   1. Initial program 81.8%

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

   2. Taylor expanded in a around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

      5. *-commutative 57.4%

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

   4. Simplified 57.4%

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

   if 5.2000000000000001e-199 < y < 2.8999999999999998e30

   1. Initial program 83.7%

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

   2. Taylor expanded in b around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. *-commutative 55.9%

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

   4. Simplified 55.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 14: 29.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (* c j))))
   (if (<= c -3e+16)
     t_2
     (if (<= c -5.1e-138)
       t_1
       (if (<= c 2.9e-294) (* b (* t i)) (if (<= c 7.8e+51) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * (c * j);
	double tmp;
	if (c <= -3e+16) {
		tmp = t_2;
	} else if (c <= -5.1e-138) {
		tmp = t_1;
	} else if (c <= 2.9e-294) {
		tmp = b * (t * i);
	} else if (c <= 7.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * (c * j)
    if (c <= (-3d+16)) then
        tmp = t_2
    else if (c <= (-5.1d-138)) then
        tmp = t_1
    else if (c <= 2.9d-294) then
        tmp = b * (t * i)
    else if (c <= 7.8d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * (c * j);
	double tmp;
	if (c <= -3e+16) {
		tmp = t_2;
	} else if (c <= -5.1e-138) {
		tmp = t_1;
	} else if (c <= 2.9e-294) {
		tmp = b * (t * i);
	} else if (c <= 7.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * (c * j)
	tmp = 0
	if c <= -3e+16:
		tmp = t_2
	elif c <= -5.1e-138:
		tmp = t_1
	elif c <= 2.9e-294:
		tmp = b * (t * i)
	elif c <= 7.8e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -3e+16)
		tmp = t_2;
	elseif (c <= -5.1e-138)
		tmp = t_1;
	elseif (c <= 2.9e-294)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 7.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (c <= -3e+16)
		tmp = t_2;
	elseif (c <= -5.1e-138)
		tmp = t_1;
	elseif (c <= 2.9e-294)
		tmp = b * (t * i);
	elseif (c <= 7.8e+51)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+16], t$95$2, If[LessEqual[c, -5.1e-138], t$95$1, If[LessEqual[c, 2.9e-294], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.8e+51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3e16 or 7.79999999999999968e51 < c

   1. Initial program 70.1%

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

   2. Taylor expanded in a around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

      5. *-commutative 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in j around inf 42.9%

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

   if -3e16 < c < -5.1000000000000002e-138 or 2.9000000000000001e-294 < c < 7.79999999999999968e51

   1. Initial program 84.2%

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

      1. add-sqr-sqrt 40.2%

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

      2. pow2 40.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 40.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 40.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. *-commutative 67.9%

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

      3. *-commutative 67.9%

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

      4. *-commutative 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in y around inf 35.6%

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

      1. *-commutative 35.6%

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

   9. Simplified 35.6%

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

   if -5.1000000000000002e-138 < c < 2.9000000000000001e-294

   1. Initial program 88.5%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in x around 0 42.6%

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

      1. *-commutative 42.6%

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

   7. Simplified 42.6%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-294}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 15: 29.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -23000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -23000000.0)
     t_1
     (if (<= c -8e-139)
       (* (* x t) (- a))
       (if (<= c 2.35e-296)
         (* b (* t i))
         (if (<= c 7.2e+51) (* 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 = a * (c * j);
	double tmp;
	if (c <= -23000000.0) {
		tmp = t_1;
	} else if (c <= -8e-139) {
		tmp = (x * t) * -a;
	} else if (c <= 2.35e-296) {
		tmp = b * (t * i);
	} else if (c <= 7.2e+51) {
		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 = a * (c * j)
    if (c <= (-23000000.0d0)) then
        tmp = t_1
    else if (c <= (-8d-139)) then
        tmp = (x * t) * -a
    else if (c <= 2.35d-296) then
        tmp = b * (t * i)
    else if (c <= 7.2d+51) 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 = a * (c * j);
	double tmp;
	if (c <= -23000000.0) {
		tmp = t_1;
	} else if (c <= -8e-139) {
		tmp = (x * t) * -a;
	} else if (c <= 2.35e-296) {
		tmp = b * (t * i);
	} else if (c <= 7.2e+51) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -23000000.0:
		tmp = t_1
	elif c <= -8e-139:
		tmp = (x * t) * -a
	elif c <= 2.35e-296:
		tmp = b * (t * i)
	elif c <= 7.2e+51:
		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(a * Float64(c * j))
	tmp = 0.0
	if (c <= -23000000.0)
		tmp = t_1;
	elseif (c <= -8e-139)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (c <= 2.35e-296)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 7.2e+51)
		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 = a * (c * j);
	tmp = 0.0;
	if (c <= -23000000.0)
		tmp = t_1;
	elseif (c <= -8e-139)
		tmp = (x * t) * -a;
	elseif (c <= 2.35e-296)
		tmp = b * (t * i);
	elseif (c <= 7.2e+51)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -23000000.0], t$95$1, If[LessEqual[c, -8e-139], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[c, 2.35e-296], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.2e+51], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.3e7 or 7.20000000000000022e51 < c

   1. Initial program 70.3%

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

   2. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

      4. *-commutative 54.0%

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

      5. *-commutative 54.0%

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

   4. Simplified 54.0%

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

   5. Taylor expanded in j around inf 43.1%

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

   if -2.3e7 < c < -8.00000000000000024e-139

   1. Initial program 84.5%

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

   2. Taylor expanded in a around inf 41.4%

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

      1. +-commutative 41.4%

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

      2. mul-1-neg 41.4%

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

      3. unsub-neg 41.4%

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

      4. *-commutative 41.4%

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

      5. *-commutative 41.4%

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

   4. Simplified 41.4%

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

   5. Taylor expanded in j around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. *-commutative 37.3%

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

      3. distribute-rgt-neg-in 37.3%

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

   7. Simplified 37.3%

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

   if -8.00000000000000024e-139 < c < 2.35e-296

   1. Initial program 88.3%

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

   2. Taylor expanded in t around inf 60.1%

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

      1. distribute-lft-out-- 60.1%

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

      2. *-commutative 60.1%

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

      3. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in x around 0 43.6%

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

      1. *-commutative 43.6%

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

   7. Simplified 43.6%

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

   if 2.35e-296 < c < 7.20000000000000022e51

   1. Initial program 84.7%

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

      1. add-sqr-sqrt 37.9%

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

      2. pow2 37.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 37.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 37.9%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 66.3%

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

      1. *-commutative 66.3%

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

      2. *-commutative 66.3%

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

      3. *-commutative 66.3%

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

      4. *-commutative 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in y around inf 35.1%

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

      1. *-commutative 35.1%

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

   9. Simplified 35.1%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -23000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 16: 42.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+232}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))))
   (if (<= z -1.15e+135)
     t_1
     (if (<= z 3.8e+174)
       (* a (- (* c j) (* x t)))
       (if (<= z 1.4e+232) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double tmp;
	if (z <= -1.15e+135) {
		tmp = t_1;
	} else if (z <= 3.8e+174) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 1.4e+232) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (c * -b)
    if (z <= (-1.15d+135)) then
        tmp = t_1
    else if (z <= 3.8d+174) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 1.4d+232) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double tmp;
	if (z <= -1.15e+135) {
		tmp = t_1;
	} else if (z <= 3.8e+174) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 1.4e+232) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	tmp = 0
	if z <= -1.15e+135:
		tmp = t_1
	elif z <= 3.8e+174:
		tmp = a * ((c * j) - (x * t))
	elif z <= 1.4e+232:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	tmp = 0.0
	if (z <= -1.15e+135)
		tmp = t_1;
	elseif (z <= 3.8e+174)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 1.4e+232)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	tmp = 0.0;
	if (z <= -1.15e+135)
		tmp = t_1;
	elseif (z <= 3.8e+174)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 1.4e+232)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+135], t$95$1, If[LessEqual[z, 3.8e+174], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+232], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e135 or 1.3999999999999999e232 < z

   1. Initial program 72.8%

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

   2. Taylor expanded in z around inf 76.3%

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

      1. *-commutative 76.3%

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

   4. Simplified 76.3%

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

   5. Taylor expanded in x around 0 53.0%

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

      1. neg-mul-1 53.0%

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

      2. distribute-rgt-neg-in 53.0%

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

   7. Simplified 53.0%

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

   if -1.1500000000000001e135 < z < 3.8000000000000002e174

   1. Initial program 78.6%

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

   2. Taylor expanded in a around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

      4. *-commutative 48.5%

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

      5. *-commutative 48.5%

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

   4. Simplified 48.5%

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

   if 3.8000000000000002e174 < z < 1.3999999999999999e232

   1. Initial program 95.2%

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

      1. add-sqr-sqrt 42.0%

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

      2. pow2 42.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 42.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{2}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 42.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{2}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in j around 0 84.9%

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

      1. *-commutative 84.9%

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

      2. *-commutative 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in y around inf 59.3%

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

      1. associate-*r* 64.2%

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

      2. *-commutative 64.2%

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

   9. Simplified 64.2%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+232}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 17: 30.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -900000000 \lor \neg \left(j \leq 1.75 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -900000000.0) (not (<= j 1.75e+45)))
   (* a (* c j))
   (* 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 ((j <= -900000000.0) || !(j <= 1.75e+45)) {
		tmp = a * (c * j);
	} 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 ((j <= (-900000000.0d0)) .or. (.not. (j <= 1.75d+45))) then
        tmp = a * (c * j)
    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 ((j <= -900000000.0) || !(j <= 1.75e+45)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -900000000.0) or not (j <= 1.75e+45):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -900000000.0) || !(j <= 1.75e+45))
		tmp = Float64(a * Float64(c * j));
	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 ((j <= -900000000.0) || ~((j <= 1.75e+45)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -900000000.0], N[Not[LessEqual[j, 1.75e+45]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9e8 or 1.75000000000000011e45 < j

   1. Initial program 78.4%

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

   2. Taylor expanded in a around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in j around inf 48.9%

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

   if -9e8 < j < 1.75000000000000011e45

   1. Initial program 78.7%

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

   2. Taylor expanded in t around inf 47.4%

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

      1. distribute-lft-out-- 47.4%

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

      2. *-commutative 47.4%

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

      3. *-commutative 47.4%

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

   4. Simplified 47.4%

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

   5. Taylor expanded in x around 0 26.0%

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

      1. *-commutative 26.0%

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

   7. Simplified 26.0%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -900000000 \lor \neg \left(j \leq 1.75 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 18: 22.0% 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 78.6%

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

2. Taylor expanded in a around inf 41.9%

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

   1. +-commutative 41.9%

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

   2. mul-1-neg 41.9%

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

   3. unsub-neg 41.9%

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

   4. *-commutative 41.9%

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

   5. *-commutative 41.9%

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

4. Simplified 41.9%

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

5. Taylor expanded in j around inf 25.0%

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

6. Final simplification 25.0%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.3% 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 2023320 
(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)))))