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

Percentage Accurate: 73.8% → 82.3%

Time: 43.5s

Alternatives: 25

Speedup: 0.5×

• 58.4% 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: 73.8% 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: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 93.2%

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

   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 y around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

   4. Simplified 59.3%

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

4. Final simplification 85.8%

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

Alternative 2: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_2 + t_3\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+223}:\\ \;\;\;\;t_2 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -52:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-214}:\\ \;\;\;\;t_3 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-275}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-19} \lor \neg \left(x \leq 2.6 \cdot 10^{+50}\right) \land x \leq 1.02 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* i (- (* t b) (* y j))) (* c (- (* a j) (* z b)))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ t_2 t_3)))
   (if (<= x -9.2e+223)
     (- t_2 (* z (* b c)))
     (if (<= x -52.0)
       t_4
       (if (<= x -1.3e-172)
         t_1
         (if (<= x -2.9e-214)
           (+ t_3 (* x (* y z)))
           (if (<= x 9.5e-275)
             (- (* b (- (* t i) (* z c))) (* a (* x t)))
             (if (or (<= x 1.12e-19)
                     (and (not (<= x 2.6e+50)) (<= x 1.02e+92)))
               t_1
               t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((t * b) - (y * j))) + (c * ((a * j) - (z * b)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_2 + t_3;
	double tmp;
	if (x <= -9.2e+223) {
		tmp = t_2 - (z * (b * c));
	} else if (x <= -52.0) {
		tmp = t_4;
	} else if (x <= -1.3e-172) {
		tmp = t_1;
	} else if (x <= -2.9e-214) {
		tmp = t_3 + (x * (y * z));
	} else if (x <= 9.5e-275) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else if ((x <= 1.12e-19) || (!(x <= 2.6e+50) && (x <= 1.02e+92))) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (i * ((t * b) - (y * j))) + (c * ((a * j) - (z * b)))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    t_4 = t_2 + t_3
    if (x <= (-9.2d+223)) then
        tmp = t_2 - (z * (b * c))
    else if (x <= (-52.0d0)) then
        tmp = t_4
    else if (x <= (-1.3d-172)) then
        tmp = t_1
    else if (x <= (-2.9d-214)) then
        tmp = t_3 + (x * (y * z))
    else if (x <= 9.5d-275) then
        tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
    else if ((x <= 1.12d-19) .or. (.not. (x <= 2.6d+50)) .and. (x <= 1.02d+92)) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((t * b) - (y * j))) + (c * ((a * j) - (z * b)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_2 + t_3;
	double tmp;
	if (x <= -9.2e+223) {
		tmp = t_2 - (z * (b * c));
	} else if (x <= -52.0) {
		tmp = t_4;
	} else if (x <= -1.3e-172) {
		tmp = t_1;
	} else if (x <= -2.9e-214) {
		tmp = t_3 + (x * (y * z));
	} else if (x <= 9.5e-275) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else if ((x <= 1.12e-19) || (!(x <= 2.6e+50) && (x <= 1.02e+92))) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * ((t * b) - (y * j))) + (c * ((a * j) - (z * b)))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	t_4 = t_2 + t_3
	tmp = 0
	if x <= -9.2e+223:
		tmp = t_2 - (z * (b * c))
	elif x <= -52.0:
		tmp = t_4
	elif x <= -1.3e-172:
		tmp = t_1
	elif x <= -2.9e-214:
		tmp = t_3 + (x * (y * z))
	elif x <= 9.5e-275:
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
	elif (x <= 1.12e-19) or (not (x <= 2.6e+50) and (x <= 1.02e+92)):
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) + Float64(c * Float64(Float64(a * j) - Float64(z * b))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(t_2 + t_3)
	tmp = 0.0
	if (x <= -9.2e+223)
		tmp = Float64(t_2 - Float64(z * Float64(b * c)));
	elseif (x <= -52.0)
		tmp = t_4;
	elseif (x <= -1.3e-172)
		tmp = t_1;
	elseif (x <= -2.9e-214)
		tmp = Float64(t_3 + Float64(x * Float64(y * z)));
	elseif (x <= 9.5e-275)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	elseif ((x <= 1.12e-19) || (!(x <= 2.6e+50) && (x <= 1.02e+92)))
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * ((t * b) - (y * j))) + (c * ((a * j) - (z * b)));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	t_4 = t_2 + t_3;
	tmp = 0.0;
	if (x <= -9.2e+223)
		tmp = t_2 - (z * (b * c));
	elseif (x <= -52.0)
		tmp = t_4;
	elseif (x <= -1.3e-172)
		tmp = t_1;
	elseif (x <= -2.9e-214)
		tmp = t_3 + (x * (y * z));
	elseif (x <= 9.5e-275)
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	elseif ((x <= 1.12e-19) || (~((x <= 2.6e+50)) && (x <= 1.02e+92)))
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $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$2 + t$95$3), $MachinePrecision]}, If[LessEqual[x, -9.2e+223], N[(t$95$2 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -52.0], t$95$4, If[LessEqual[x, -1.3e-172], t$95$1, If[LessEqual[x, -2.9e-214], N[(t$95$3 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-275], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.12e-19], And[N[Not[LessEqual[x, 2.6e+50]], $MachinePrecision], LessEqual[x, 1.02e+92]]], t$95$1, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.20000000000000017e223

   1. Initial program 64.7%

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

   2. Taylor expanded in j around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. *-commutative 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in c around inf 94.1%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

   7. Simplified 94.1%

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

   if -9.20000000000000017e223 < x < -52 or 1.1200000000000001e-19 < x < 2.6000000000000002e50 or 1.02000000000000003e92 < x

   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 b around 0 78.5%

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

   if -52 < x < -1.2999999999999999e-172 or 9.49999999999999961e-275 < x < 1.1200000000000001e-19 or 2.6000000000000002e50 < x < 1.02000000000000003e92

   1. Initial program 71.6%

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

   2. Taylor expanded in c around -inf 72.3%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in x around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. +-commutative 74.8%

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

      5. mul-1-neg 74.8%

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

      6. unsub-neg 74.8%

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

      7. +-commutative 74.8%

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

      8. mul-1-neg 74.8%

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

      9. unsub-neg 74.8%

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

      10. *-commutative 74.8%

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

   7. Simplified 74.8%

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

   if -1.2999999999999999e-172 < x < -2.89999999999999985e-214

   1. Initial program 50.0%

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

   2. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-*l* 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in b around 0 83.3%

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

   if -2.89999999999999985e-214 < x < 9.49999999999999961e-275

   1. Initial program 61.4%

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

   2. Taylor expanded in j around 0 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -52:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-172}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-214}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-275}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-19} \lor \neg \left(x \leq 2.6 \cdot 10^{+50}\right) \land x \leq 1.02 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 3: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_3 + t_2\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-91}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_1\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-197}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) + t_1\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;j \leq 7.9 \cdot 10^{+151} \lor \neg \left(j \leq 8 \cdot 10^{+245}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* x (- (* y z) (* t a))))
        (t_4 (+ t_3 t_2)))
   (if (<= j -1.55e+34)
     t_4
     (if (<= j -4.5e-52)
       (+ (* y (- (* x z) (* i j))) (* c (- (* a j) (* z b))))
       (if (<= j -1.65e-91)
         (+ (- (* a (* c j)) (* a (* x t))) t_1)
         (if (<= j -6.8e-197)
           (- (+ (* z (* x y)) t_1) (* i (* y j)))
           (if (<= j 3.8e-42)
             (+ t_3 t_1)
             (if (or (<= j 7.9e+151) (not (<= j 8e+245))) t_4 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = t_3 + t_2;
	double tmp;
	if (j <= -1.55e+34) {
		tmp = t_4;
	} else if (j <= -4.5e-52) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	} else if (j <= -1.65e-91) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	} else if (j <= -6.8e-197) {
		tmp = ((z * (x * y)) + t_1) - (i * (y * j));
	} else if (j <= 3.8e-42) {
		tmp = t_3 + t_1;
	} else if ((j <= 7.9e+151) || !(j <= 8e+245)) {
		tmp = t_4;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    t_4 = t_3 + t_2
    if (j <= (-1.55d+34)) then
        tmp = t_4
    else if (j <= (-4.5d-52)) then
        tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)))
    else if (j <= (-1.65d-91)) then
        tmp = ((a * (c * j)) - (a * (x * t))) + t_1
    else if (j <= (-6.8d-197)) then
        tmp = ((z * (x * y)) + t_1) - (i * (y * j))
    else if (j <= 3.8d-42) then
        tmp = t_3 + t_1
    else if ((j <= 7.9d+151) .or. (.not. (j <= 8d+245))) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = t_3 + t_2;
	double tmp;
	if (j <= -1.55e+34) {
		tmp = t_4;
	} else if (j <= -4.5e-52) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	} else if (j <= -1.65e-91) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	} else if (j <= -6.8e-197) {
		tmp = ((z * (x * y)) + t_1) - (i * (y * j));
	} else if (j <= 3.8e-42) {
		tmp = t_3 + t_1;
	} else if ((j <= 7.9e+151) || !(j <= 8e+245)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	t_4 = t_3 + t_2
	tmp = 0
	if j <= -1.55e+34:
		tmp = t_4
	elif j <= -4.5e-52:
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)))
	elif j <= -1.65e-91:
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1
	elif j <= -6.8e-197:
		tmp = ((z * (x * y)) + t_1) - (i * (y * j))
	elif j <= 3.8e-42:
		tmp = t_3 + t_1
	elif (j <= 7.9e+151) or not (j <= 8e+245):
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_4 = Float64(t_3 + t_2)
	tmp = 0.0
	if (j <= -1.55e+34)
		tmp = t_4;
	elseif (j <= -4.5e-52)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(a * j) - Float64(z * b))));
	elseif (j <= -1.65e-91)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))) + t_1);
	elseif (j <= -6.8e-197)
		tmp = Float64(Float64(Float64(z * Float64(x * y)) + t_1) - Float64(i * Float64(y * j)));
	elseif (j <= 3.8e-42)
		tmp = Float64(t_3 + t_1);
	elseif ((j <= 7.9e+151) || !(j <= 8e+245))
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	t_4 = t_3 + t_2;
	tmp = 0.0;
	if (j <= -1.55e+34)
		tmp = t_4;
	elseif (j <= -4.5e-52)
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	elseif (j <= -1.65e-91)
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	elseif (j <= -6.8e-197)
		tmp = ((z * (x * y)) + t_1) - (i * (y * j));
	elseif (j <= 3.8e-42)
		tmp = t_3 + t_1;
	elseif ((j <= 7.9e+151) || ~((j <= 8e+245)))
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$2), $MachinePrecision]}, If[LessEqual[j, -1.55e+34], t$95$4, If[LessEqual[j, -4.5e-52], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.65e-91], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, -6.8e-197], N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-42], N[(t$95$3 + t$95$1), $MachinePrecision], If[Or[LessEqual[j, 7.9e+151], N[Not[LessEqual[j, 8e+245]], $MachinePrecision]], t$95$4, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.54999999999999989e34 or 3.80000000000000017e-42 < j < 7.9e151 or 8.00000000000000035e245 < j

   1. Initial program 73.0%

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

   2. Taylor expanded in b around 0 77.7%

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

   if -1.54999999999999989e34 < j < -4.5e-52

   1. Initial program 77.4%

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

   2. Taylor expanded in c around -inf 86.2%

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

   4. Simplified 95.3%

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

   5. Taylor expanded in t around 0 90.8%

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

      1. +-commutative 90.8%

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

      2. mul-1-neg 90.8%

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

      3. unsub-neg 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-*r* 86.6%

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

      6. associate-*r* 86.6%

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

      7. associate-*r* 86.6%

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

      8. distribute-rgt-in 91.1%

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

      9. +-commutative 91.1%

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

      10. mul-1-neg 91.1%

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

      11. unsub-neg 91.1%

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

      12. +-commutative 91.1%

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

      13. mul-1-neg 91.1%

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

      14. unsub-neg 91.1%

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

   7. Simplified 91.1%

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

   if -4.5e-52 < j < -1.65000000000000006e-91

   1. Initial program 77.1%

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

   2. Taylor expanded in y around 0 91.9%

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

   if -1.65000000000000006e-91 < j < -6.7999999999999996e-197

   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 y around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*l* 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in c around 0 78.7%

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

      1. associate-*r* 78.7%

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

      2. neg-mul-1 78.7%

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

   7. Simplified 78.7%

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

   if -6.7999999999999996e-197 < j < 3.80000000000000017e-42

   1. Initial program 72.9%

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

   2. Taylor expanded in j around 0 76.1%

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

      1. *-commutative 76.1%

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

      2. *-commutative 76.1%

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

   4. Simplified 76.1%

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

   if 7.9e151 < j < 8.00000000000000035e245

   1. Initial program 50.3%

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

   2. Taylor expanded in j around inf 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-91}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-197}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.9 \cdot 10^{+151} \lor \neg \left(j \leq 8 \cdot 10^{+245}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+221}:\\ \;\;\;\;t_2 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -450 \lor \neg \left(x \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -7e+221)
     (- t_2 (* z (* b c)))
     (if (or (<= x -450.0) (not (<= x 1.1e-5)))
       (+ t_2 t_1)
       (+ (+ (* z (* x y)) (* 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e+221) {
		tmp = t_2 - (z * (b * c));
	} else if ((x <= -450.0) || !(x <= 1.1e-5)) {
		tmp = t_2 + t_1;
	} else {
		tmp = ((z * (x * y)) + (b * ((t * i) - (z * c)))) + 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 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-7d+221)) then
        tmp = t_2 - (z * (b * c))
    else if ((x <= (-450.0d0)) .or. (.not. (x <= 1.1d-5))) then
        tmp = t_2 + t_1
    else
        tmp = ((z * (x * y)) + (b * ((t * i) - (z * c)))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e+221) {
		tmp = t_2 - (z * (b * c));
	} else if ((x <= -450.0) || !(x <= 1.1e-5)) {
		tmp = t_2 + t_1;
	} else {
		tmp = ((z * (x * y)) + (b * ((t * i) - (z * c)))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -7e+221:
		tmp = t_2 - (z * (b * c))
	elif (x <= -450.0) or not (x <= 1.1e-5):
		tmp = t_2 + t_1
	else:
		tmp = ((z * (x * y)) + (b * ((t * i) - (z * c)))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -7e+221)
		tmp = Float64(t_2 - Float64(z * Float64(b * c)));
	elseif ((x <= -450.0) || !(x <= 1.1e-5))
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -7e+221)
		tmp = t_2 - (z * (b * c));
	elseif ((x <= -450.0) || ~((x <= 1.1e-5)))
		tmp = t_2 + t_1;
	else
		tmp = ((z * (x * y)) + (b * ((t * i) - (z * c)))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+221], N[(t$95$2 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -450.0], N[Not[LessEqual[x, 1.1e-5]], $MachinePrecision]], N[(t$95$2 + t$95$1), $MachinePrecision], N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000003e221

   1. Initial program 64.7%

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

   2. Taylor expanded in j around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. *-commutative 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in c around inf 94.1%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

   7. Simplified 94.1%

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

   if -7.0000000000000003e221 < x < -450 or 1.1e-5 < x

   1. Initial program 76.5%

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

   2. Taylor expanded in b around 0 75.9%

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

   if -450 < x < 1.1e-5

   1. Initial program 70.5%

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

   2. Taylor expanded in y around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*l* 73.0%

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

   4. Simplified 73.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+221}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -450 \lor \neg \left(x \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ \mathbf{if}\;j \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-42}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+154} \lor \neg \left(j \leq 1.15 \cdot 10^{+246}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 t_1)))
   (if (<= j -5.8e+33)
     t_3
     (if (<= j -1.05e-52)
       (+ (* y (- (* x z) (* i j))) (* c (- (* a j) (* z b))))
       (if (<= j 1.32e-42)
         (+ t_2 (* b (- (* t i) (* z c))))
         (if (or (<= j 8e+154) (not (<= j 1.15e+246))) 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double tmp;
	if (j <= -5.8e+33) {
		tmp = t_3;
	} else if (j <= -1.05e-52) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	} else if (j <= 1.32e-42) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if ((j <= 8e+154) || !(j <= 1.15e+246)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + t_1
    if (j <= (-5.8d+33)) then
        tmp = t_3
    else if (j <= (-1.05d-52)) then
        tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)))
    else if (j <= 1.32d-42) then
        tmp = t_2 + (b * ((t * i) - (z * c)))
    else if ((j <= 8d+154) .or. (.not. (j <= 1.15d+246))) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double tmp;
	if (j <= -5.8e+33) {
		tmp = t_3;
	} else if (j <= -1.05e-52) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	} else if (j <= 1.32e-42) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if ((j <= 8e+154) || !(j <= 1.15e+246)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + t_1
	tmp = 0
	if j <= -5.8e+33:
		tmp = t_3
	elif j <= -1.05e-52:
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)))
	elif j <= 1.32e-42:
		tmp = t_2 + (b * ((t * i) - (z * c)))
	elif (j <= 8e+154) or not (j <= 1.15e+246):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (j <= -5.8e+33)
		tmp = t_3;
	elseif (j <= -1.05e-52)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(a * j) - Float64(z * b))));
	elseif (j <= 1.32e-42)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif ((j <= 8e+154) || !(j <= 1.15e+246))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (j <= -5.8e+33)
		tmp = t_3;
	elseif (j <= -1.05e-52)
		tmp = (y * ((x * z) - (i * j))) + (c * ((a * j) - (z * b)));
	elseif (j <= 1.32e-42)
		tmp = t_2 + (b * ((t * i) - (z * c)));
	elseif ((j <= 8e+154) || ~((j <= 1.15e+246)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[j, -5.8e+33], t$95$3, If[LessEqual[j, -1.05e-52], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.32e-42], N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 8e+154], N[Not[LessEqual[j, 1.15e+246]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.80000000000000049e33 or 1.32000000000000006e-42 < j < 8.0000000000000003e154 or 1.15000000000000007e246 < j

   1. Initial program 73.0%

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

   2. Taylor expanded in b around 0 77.7%

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

   if -5.80000000000000049e33 < j < -1.0499999999999999e-52

   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 c around -inf 86.8%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in t around 0 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

      4. *-commutative 91.1%

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

      5. associate-*r* 87.1%

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

      6. associate-*r* 87.1%

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

      7. associate-*r* 87.1%

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

      8. distribute-rgt-in 91.4%

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

      9. +-commutative 91.4%

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

      10. mul-1-neg 91.4%

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

      11. unsub-neg 91.4%

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

      12. +-commutative 91.4%

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

      13. mul-1-neg 91.4%

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

      14. unsub-neg 91.4%

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

   7. Simplified 91.4%

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

   if -1.0499999999999999e-52 < j < 1.32000000000000006e-42

   1. Initial program 75.2%

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

   2. Taylor expanded in j around 0 74.6%

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

      1. *-commutative 74.6%

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

      2. *-commutative 74.6%

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

   4. Simplified 74.6%

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

   if 8.0000000000000003e154 < j < 1.15000000000000007e246

   1. Initial program 50.3%

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

   2. Taylor expanded in j around inf 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+154} \lor \neg \left(j \leq 1.15 \cdot 10^{+246}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - z \cdot \left(b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5.6 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+34}:\\ \;\;\;\;t_3 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+269}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* z (* b c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -1.2e+63)
     t_3
     (if (<= j -5.6e-89)
       t_2
       (if (<= j -6.4e-197)
         (- (* z (- (* x y) (* b c))) (* j (* y i)))
         (if (<= j 3.3e-42)
           t_2
           (if (<= j 1.25e+34)
             (+ t_3 (* x (* y z)))
             (if (<= j 4.5e+65) t_2 (if (<= j 7e+269) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.2e+63) {
		tmp = t_3;
	} else if (j <= -5.6e-89) {
		tmp = t_2;
	} else if (j <= -6.4e-197) {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	} else if (j <= 3.3e-42) {
		tmp = t_2;
	} else if (j <= 1.25e+34) {
		tmp = t_3 + (x * (y * z));
	} else if (j <= 4.5e+65) {
		tmp = t_2;
	} else if (j <= 7e+269) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (z * (b * c))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-1.2d+63)) then
        tmp = t_3
    else if (j <= (-5.6d-89)) then
        tmp = t_2
    else if (j <= (-6.4d-197)) then
        tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
    else if (j <= 3.3d-42) then
        tmp = t_2
    else if (j <= 1.25d+34) then
        tmp = t_3 + (x * (y * z))
    else if (j <= 4.5d+65) then
        tmp = t_2
    else if (j <= 7d+269) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.2e+63) {
		tmp = t_3;
	} else if (j <= -5.6e-89) {
		tmp = t_2;
	} else if (j <= -6.4e-197) {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	} else if (j <= 3.3e-42) {
		tmp = t_2;
	} else if (j <= 1.25e+34) {
		tmp = t_3 + (x * (y * z));
	} else if (j <= 4.5e+65) {
		tmp = t_2;
	} else if (j <= 7e+269) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (z * (b * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.2e+63:
		tmp = t_3
	elif j <= -5.6e-89:
		tmp = t_2
	elif j <= -6.4e-197:
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
	elif j <= 3.3e-42:
		tmp = t_2
	elif j <= 1.25e+34:
		tmp = t_3 + (x * (y * z))
	elif j <= 4.5e+65:
		tmp = t_2
	elif j <= 7e+269:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(z * Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.2e+63)
		tmp = t_3;
	elseif (j <= -5.6e-89)
		tmp = t_2;
	elseif (j <= -6.4e-197)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(y * i)));
	elseif (j <= 3.3e-42)
		tmp = t_2;
	elseif (j <= 1.25e+34)
		tmp = Float64(t_3 + Float64(x * Float64(y * z)));
	elseif (j <= 4.5e+65)
		tmp = t_2;
	elseif (j <= 7e+269)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (z * (b * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.2e+63)
		tmp = t_3;
	elseif (j <= -5.6e-89)
		tmp = t_2;
	elseif (j <= -6.4e-197)
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	elseif (j <= 3.3e-42)
		tmp = t_2;
	elseif (j <= 1.25e+34)
		tmp = t_3 + (x * (y * z));
	elseif (j <= 4.5e+65)
		tmp = t_2;
	elseif (j <= 7e+269)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e+63], t$95$3, If[LessEqual[j, -5.6e-89], t$95$2, If[LessEqual[j, -6.4e-197], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e-42], t$95$2, If[LessEqual[j, 1.25e+34], N[(t$95$3 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e+65], t$95$2, If[LessEqual[j, 7e+269], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.2e63 or 4.5e65 < j < 7.0000000000000003e269

   1. Initial program 67.6%

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

   2. Taylor expanded in j around inf 74.8%

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

      1. *-commutative 74.8%

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

   4. Simplified 74.8%

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

   if -1.2e63 < j < -5.5999999999999998e-89 or -6.3999999999999994e-197 < j < 3.3000000000000002e-42 or 1.25e34 < j < 4.5e65

   1. Initial program 77.3%

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

   2. Taylor expanded in j around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in c around inf 70.2%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

   7. Simplified 70.7%

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

   if -5.5999999999999998e-89 < j < -6.3999999999999994e-197

   1. Initial program 73.7%

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

   2. Taylor expanded in c around -inf 73.7%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in t around 0 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. *-commutative 62.8%

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

      5. associate-*r* 59.1%

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

      6. associate-*r* 59.1%

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

      7. associate-*r* 59.1%

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

      8. distribute-rgt-in 59.1%

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

      9. +-commutative 59.1%

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

      10. mul-1-neg 59.1%

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

      11. unsub-neg 59.1%

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

      12. +-commutative 59.1%

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

      13. mul-1-neg 59.1%

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

      14. unsub-neg 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in a around 0 46.5%

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

   10. Simplified 67.7%

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

   if 3.3000000000000002e-42 < j < 1.25e34

   1. Initial program 79.5%

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

   2. Taylor expanded in y around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in b around 0 60.5%

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

   if 7.0000000000000003e269 < j

   1. Initial program 37.3%

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

   2. Taylor expanded in x around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. *-commutative 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.6 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+269}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 7: 56.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - z \cdot \left(b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+262}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* z (* b c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -8.5e+62)
     t_3
     (if (<= j -1.55e-89)
       t_2
       (if (<= j -4.1e-197)
         (- (* z (- (* x y) (* b c))) (* j (* y i)))
         (if (<= j 3.7e-98)
           t_2
           (if (<= j 1.4e+34)
             (- (* c (- (* a j) (* z b))) (* i (* y j)))
             (if (<= j 9.5e+66) t_2 (if (<= j 2.4e+262) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -8.5e+62) {
		tmp = t_3;
	} else if (j <= -1.55e-89) {
		tmp = t_2;
	} else if (j <= -4.1e-197) {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	} else if (j <= 3.7e-98) {
		tmp = t_2;
	} else if (j <= 1.4e+34) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else if (j <= 9.5e+66) {
		tmp = t_2;
	} else if (j <= 2.4e+262) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (z * (b * c))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-8.5d+62)) then
        tmp = t_3
    else if (j <= (-1.55d-89)) then
        tmp = t_2
    else if (j <= (-4.1d-197)) then
        tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
    else if (j <= 3.7d-98) then
        tmp = t_2
    else if (j <= 1.4d+34) then
        tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
    else if (j <= 9.5d+66) then
        tmp = t_2
    else if (j <= 2.4d+262) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -8.5e+62) {
		tmp = t_3;
	} else if (j <= -1.55e-89) {
		tmp = t_2;
	} else if (j <= -4.1e-197) {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	} else if (j <= 3.7e-98) {
		tmp = t_2;
	} else if (j <= 1.4e+34) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else if (j <= 9.5e+66) {
		tmp = t_2;
	} else if (j <= 2.4e+262) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (z * (b * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -8.5e+62:
		tmp = t_3
	elif j <= -1.55e-89:
		tmp = t_2
	elif j <= -4.1e-197:
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
	elif j <= 3.7e-98:
		tmp = t_2
	elif j <= 1.4e+34:
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
	elif j <= 9.5e+66:
		tmp = t_2
	elif j <= 2.4e+262:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(z * Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -8.5e+62)
		tmp = t_3;
	elseif (j <= -1.55e-89)
		tmp = t_2;
	elseif (j <= -4.1e-197)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(y * i)));
	elseif (j <= 3.7e-98)
		tmp = t_2;
	elseif (j <= 1.4e+34)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(i * Float64(y * j)));
	elseif (j <= 9.5e+66)
		tmp = t_2;
	elseif (j <= 2.4e+262)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (z * (b * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -8.5e+62)
		tmp = t_3;
	elseif (j <= -1.55e-89)
		tmp = t_2;
	elseif (j <= -4.1e-197)
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	elseif (j <= 3.7e-98)
		tmp = t_2;
	elseif (j <= 1.4e+34)
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	elseif (j <= 9.5e+66)
		tmp = t_2;
	elseif (j <= 2.4e+262)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.5e+62], t$95$3, If[LessEqual[j, -1.55e-89], t$95$2, If[LessEqual[j, -4.1e-197], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-98], t$95$2, If[LessEqual[j, 1.4e+34], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+66], t$95$2, If[LessEqual[j, 2.4e+262], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.4999999999999997e62 or 9.50000000000000051e66 < j < 2.39999999999999983e262

   1. Initial program 67.6%

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

   2. Taylor expanded in j around inf 75.2%

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

      1. *-commutative 75.2%

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

   4. Simplified 75.2%

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

   if -8.4999999999999997e62 < j < -1.54999999999999998e-89 or -4.1e-197 < j < 3.7e-98 or 1.40000000000000004e34 < j < 9.50000000000000051e66

   1. Initial program 77.4%

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

   2. Taylor expanded in j around 0 77.3%

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

      1. *-commutative 77.3%

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

      2. *-commutative 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in c around inf 70.6%

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

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -1.54999999999999998e-89 < j < -4.1e-197

   1. Initial program 73.7%

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

   2. Taylor expanded in c around -inf 73.7%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in t around 0 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. *-commutative 62.8%

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

      5. associate-*r* 59.1%

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

      6. associate-*r* 59.1%

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

      7. associate-*r* 59.1%

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

      8. distribute-rgt-in 59.1%

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

      9. +-commutative 59.1%

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

      10. mul-1-neg 59.1%

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

      11. unsub-neg 59.1%

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

      12. +-commutative 59.1%

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

      13. mul-1-neg 59.1%

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

      14. unsub-neg 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in a around 0 46.5%

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

   10. Simplified 67.7%

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

   if 3.7e-98 < j < 1.40000000000000004e34

   1. Initial program 78.0%

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

   2. Taylor expanded in c around -inf 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in t around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-*r* 66.4%

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

      6. associate-*r* 61.1%

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

      7. associate-*r* 61.1%

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

      8. distribute-rgt-in 61.1%

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

      9. +-commutative 61.1%

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

      10. mul-1-neg 61.1%

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

      11. unsub-neg 61.1%

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

      12. +-commutative 61.1%

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

      13. mul-1-neg 61.1%

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

      14. unsub-neg 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in x around 0 61.8%

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

      1. associate-*r* 61.8%

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

      2. neg-mul-1 61.8%

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

      3. *-commutative 61.8%

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

   10. Simplified 61.8%

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

   if 2.39999999999999983e262 < j

   1. Initial program 45.3%

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

   2. Taylor expanded in x around inf 91.0%

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

      1. *-commutative 91.0%

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

      2. *-commutative 91.0%

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

   4. Simplified 91.0%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+262}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 8: 59.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{-31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* a (* x t))))
        (t_2 (- (* x (- (* y z) (* t a))) (* z (* b c))))
        (t_3 (+ (* j (- (* a c) (* y i))) (* x (* y z)))))
   (if (<= x -8.6e+64)
     t_2
     (if (<= x -6.1e-31)
       t_3
       (if (<= x -5.1e-155)
         t_1
         (if (<= x -5.5e-215)
           t_3
           (if (<= x 1.4e-260)
             t_1
             (if (<= x 4.2e+19)
               (- (* c (- (* a j) (* z b))) (* i (* y j)))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) - (a * (x * t));
	double t_2 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double t_3 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double tmp;
	if (x <= -8.6e+64) {
		tmp = t_2;
	} else if (x <= -6.1e-31) {
		tmp = t_3;
	} else if (x <= -5.1e-155) {
		tmp = t_1;
	} else if (x <= -5.5e-215) {
		tmp = t_3;
	} else if (x <= 1.4e-260) {
		tmp = t_1;
	} else if (x <= 4.2e+19) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) - (a * (x * t))
    t_2 = (x * ((y * z) - (t * a))) - (z * (b * c))
    t_3 = (j * ((a * c) - (y * i))) + (x * (y * z))
    if (x <= (-8.6d+64)) then
        tmp = t_2
    else if (x <= (-6.1d-31)) then
        tmp = t_3
    else if (x <= (-5.1d-155)) then
        tmp = t_1
    else if (x <= (-5.5d-215)) then
        tmp = t_3
    else if (x <= 1.4d-260) then
        tmp = t_1
    else if (x <= 4.2d+19) then
        tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) - (a * (x * t));
	double t_2 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double t_3 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double tmp;
	if (x <= -8.6e+64) {
		tmp = t_2;
	} else if (x <= -6.1e-31) {
		tmp = t_3;
	} else if (x <= -5.1e-155) {
		tmp = t_1;
	} else if (x <= -5.5e-215) {
		tmp = t_3;
	} else if (x <= 1.4e-260) {
		tmp = t_1;
	} else if (x <= 4.2e+19) {
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (a * (x * t))
	t_2 = (x * ((y * z) - (t * a))) - (z * (b * c))
	t_3 = (j * ((a * c) - (y * i))) + (x * (y * z))
	tmp = 0
	if x <= -8.6e+64:
		tmp = t_2
	elif x <= -6.1e-31:
		tmp = t_3
	elif x <= -5.1e-155:
		tmp = t_1
	elif x <= -5.5e-215:
		tmp = t_3
	elif x <= 1.4e-260:
		tmp = t_1
	elif x <= 4.2e+19:
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(x * t)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	tmp = 0.0
	if (x <= -8.6e+64)
		tmp = t_2;
	elseif (x <= -6.1e-31)
		tmp = t_3;
	elseif (x <= -5.1e-155)
		tmp = t_1;
	elseif (x <= -5.5e-215)
		tmp = t_3;
	elseif (x <= 1.4e-260)
		tmp = t_1;
	elseif (x <= 4.2e+19)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(i * Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((t * i) - (z * c))) - (a * (x * t));
	t_2 = (x * ((y * z) - (t * a))) - (z * (b * c));
	t_3 = (j * ((a * c) - (y * i))) + (x * (y * z));
	tmp = 0.0;
	if (x <= -8.6e+64)
		tmp = t_2;
	elseif (x <= -6.1e-31)
		tmp = t_3;
	elseif (x <= -5.1e-155)
		tmp = t_1;
	elseif (x <= -5.5e-215)
		tmp = t_3;
	elseif (x <= 1.4e-260)
		tmp = t_1;
	elseif (x <= 4.2e+19)
		tmp = (c * ((a * j) - (z * b))) - (i * (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+64], t$95$2, If[LessEqual[x, -6.1e-31], t$95$3, If[LessEqual[x, -5.1e-155], t$95$1, If[LessEqual[x, -5.5e-215], t$95$3, If[LessEqual[x, 1.4e-260], t$95$1, If[LessEqual[x, 4.2e+19], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.5999999999999995e64 or 4.2e19 < x

   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 j around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in c around inf 69.7%

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

      1. associate-*r* 71.4%

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

      2. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   if -8.5999999999999995e64 < x < -6.0999999999999998e-31 or -5.0999999999999996e-155 < x < -5.50000000000000004e-215

   1. Initial program 72.3%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*l* 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in b around 0 78.1%

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

   if -6.0999999999999998e-31 < x < -5.0999999999999996e-155 or -5.50000000000000004e-215 < x < 1.3999999999999999e-260

   1. Initial program 72.9%

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

   2. Taylor expanded in j around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in y around 0 69.1%

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

   if 1.3999999999999999e-260 < x < 4.2e19

   1. Initial program 71.6%

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

   2. Taylor expanded in c around -inf 69.1%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around 0 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*r* 67.5%

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

      6. associate-*r* 67.8%

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

      7. associate-*r* 67.8%

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

      8. distribute-rgt-in 69.7%

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

      9. +-commutative 69.7%

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

      10. mul-1-neg 69.7%

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

      11. unsub-neg 69.7%

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

      12. +-commutative 69.7%

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

      13. mul-1-neg 69.7%

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

      14. unsub-neg 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in x around 0 66.0%

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

      1. associate-*r* 66.0%

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

      2. neg-mul-1 66.0%

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

      3. *-commutative 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 9: 69.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-42}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{+154} \lor \neg \left(j \leq 8.5 \cdot 10^{+245}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 t_1)))
   (if (<= j -1.55e+63)
     t_3
     (if (<= j 2.55e-42)
       (+ t_2 (* b (- (* t i) (* z c))))
       (if (or (<= j 2.05e+154) (not (<= j 8.5e+245))) 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double tmp;
	if (j <= -1.55e+63) {
		tmp = t_3;
	} else if (j <= 2.55e-42) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if ((j <= 2.05e+154) || !(j <= 8.5e+245)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + t_1
    if (j <= (-1.55d+63)) then
        tmp = t_3
    else if (j <= 2.55d-42) then
        tmp = t_2 + (b * ((t * i) - (z * c)))
    else if ((j <= 2.05d+154) .or. (.not. (j <= 8.5d+245))) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double tmp;
	if (j <= -1.55e+63) {
		tmp = t_3;
	} else if (j <= 2.55e-42) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if ((j <= 2.05e+154) || !(j <= 8.5e+245)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + t_1
	tmp = 0
	if j <= -1.55e+63:
		tmp = t_3
	elif j <= 2.55e-42:
		tmp = t_2 + (b * ((t * i) - (z * c)))
	elif (j <= 2.05e+154) or not (j <= 8.5e+245):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (j <= -1.55e+63)
		tmp = t_3;
	elseif (j <= 2.55e-42)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif ((j <= 2.05e+154) || !(j <= 8.5e+245))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (j <= -1.55e+63)
		tmp = t_3;
	elseif (j <= 2.55e-42)
		tmp = t_2 + (b * ((t * i) - (z * c)));
	elseif ((j <= 2.05e+154) || ~((j <= 8.5e+245)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[j, -1.55e+63], t$95$3, If[LessEqual[j, 2.55e-42], N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 2.05e+154], N[Not[LessEqual[j, 8.5e+245]], $MachinePrecision]], t$95$3, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.55e63 or 2.55e-42 < j < 2.05e154 or 8.49999999999999971e245 < j

   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 b around 0 77.0%

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

   if -1.55e63 < j < 2.55e-42

   1. Initial program 75.6%

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

   2. Taylor expanded in j around 0 74.4%

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

      1. *-commutative 74.4%

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

      2. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   if 2.05e154 < j < 8.49999999999999971e245

   1. Initial program 50.3%

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

   2. Taylor expanded in j around inf 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{+154} \lor \neg \left(j \leq 8.5 \cdot 10^{+245}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 10: 63.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* j (- (* a c) (* y i))))))
   (if (<= z -1.6e+161)
     (- (* z (- (* x y) (* b c))) (* j (* y i)))
     (if (<= z -2.45e-259)
       t_2
       (if (<= z 2.1e-273)
         (* i (- (* t b) (* y j)))
         (if (<= z 2.1e-26) t_2 (- t_1 (* z (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (j * ((a * c) - (y * i)));
	double tmp;
	if (z <= -1.6e+161) {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	} else if (z <= -2.45e-259) {
		tmp = t_2;
	} else if (z <= 2.1e-273) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 2.1e-26) {
		tmp = t_2;
	} else {
		tmp = t_1 - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (j * ((a * c) - (y * i)))
    if (z <= (-1.6d+161)) then
        tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
    else if (z <= (-2.45d-259)) then
        tmp = t_2
    else if (z <= 2.1d-273) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 2.1d-26) then
        tmp = t_2
    else
        tmp = t_1 - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (j * ((a * c) - (y * i)));
	double tmp;
	if (z <= -1.6e+161) {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	} else if (z <= -2.45e-259) {
		tmp = t_2;
	} else if (z <= 2.1e-273) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 2.1e-26) {
		tmp = t_2;
	} else {
		tmp = t_1 - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (j * ((a * c) - (y * i)))
	tmp = 0
	if z <= -1.6e+161:
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
	elif z <= -2.45e-259:
		tmp = t_2
	elif z <= 2.1e-273:
		tmp = i * ((t * b) - (y * j))
	elif z <= 2.1e-26:
		tmp = t_2
	else:
		tmp = t_1 - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (z <= -1.6e+161)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(y * i)));
	elseif (z <= -2.45e-259)
		tmp = t_2;
	elseif (z <= 2.1e-273)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 2.1e-26)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (z <= -1.6e+161)
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	elseif (z <= -2.45e-259)
		tmp = t_2;
	elseif (z <= 2.1e-273)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 2.1e-26)
		tmp = t_2;
	else
		tmp = t_1 - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+161], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.45e-259], t$95$2, If[LessEqual[z, 2.1e-273], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-26], t$95$2, N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.60000000000000001e161

   1. Initial program 56.8%

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

   2. Taylor expanded in c around -inf 47.3%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in t around 0 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. associate-*r* 48.0%

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

      6. associate-*r* 48.0%

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

      7. associate-*r* 48.0%

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

      8. distribute-rgt-in 48.0%

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

      9. +-commutative 48.0%

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

      10. mul-1-neg 48.0%

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

      11. unsub-neg 48.0%

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

      12. +-commutative 48.0%

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

      13. mul-1-neg 48.0%

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

      14. unsub-neg 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in a around 0 57.7%

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

   10. Simplified 73.4%

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

   if -1.60000000000000001e161 < z < -2.45000000000000011e-259 or 2.1000000000000002e-273 < z < 2.10000000000000008e-26

   1. Initial program 83.0%

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

   2. Taylor expanded in b around 0 71.9%

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

   if -2.45000000000000011e-259 < z < 2.1000000000000002e-273

   1. Initial program 47.3%

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

   2. Taylor expanded in c around -inf 47.3%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in i around inf 82.9%

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

      1. +-commutative 82.9%

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

      2. mul-1-neg 82.9%

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

      3. unsub-neg 82.9%

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

   7. Simplified 82.9%

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

   if 2.10000000000000008e-26 < z

   1. Initial program 64.6%

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

   2. Taylor expanded in j around 0 69.2%

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

      1. *-commutative 69.2%

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

      2. *-commutative 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in c around inf 63.5%

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

      1. associate-*r* 67.9%

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

      2. *-commutative 67.9%

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

   7. Simplified 67.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]

Alternative 11: 51.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-287}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= j -7.5e+59)
     t_2
     (if (<= j -6e-52)
       t_1
       (if (<= j -2.5e-79)
         (* a (- (* c j) (* x t)))
         (if (<= j -5.5e-167)
           t_1
           (if (<= j -3e-287)
             t_3
             (if (<= j 4.3e-231)
               (* b (- (* t i) (* z c)))
               (if (<= j 3.6e-93)
                 t_3
                 (if (<= j 3.1e-19) (* 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 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -7.5e+59) {
		tmp = t_2;
	} else if (j <= -6e-52) {
		tmp = t_1;
	} else if (j <= -2.5e-79) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -5.5e-167) {
		tmp = t_1;
	} else if (j <= -3e-287) {
		tmp = t_3;
	} else if (j <= 4.3e-231) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 3.6e-93) {
		tmp = t_3;
	} else if (j <= 3.1e-19) {
		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) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (j <= (-7.5d+59)) then
        tmp = t_2
    else if (j <= (-6d-52)) then
        tmp = t_1
    else if (j <= (-2.5d-79)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-5.5d-167)) then
        tmp = t_1
    else if (j <= (-3d-287)) then
        tmp = t_3
    else if (j <= 4.3d-231) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 3.6d-93) then
        tmp = t_3
    else if (j <= 3.1d-19) 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 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -7.5e+59) {
		tmp = t_2;
	} else if (j <= -6e-52) {
		tmp = t_1;
	} else if (j <= -2.5e-79) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -5.5e-167) {
		tmp = t_1;
	} else if (j <= -3e-287) {
		tmp = t_3;
	} else if (j <= 4.3e-231) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 3.6e-93) {
		tmp = t_3;
	} else if (j <= 3.1e-19) {
		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 = j * ((a * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -7.5e+59:
		tmp = t_2
	elif j <= -6e-52:
		tmp = t_1
	elif j <= -2.5e-79:
		tmp = a * ((c * j) - (x * t))
	elif j <= -5.5e-167:
		tmp = t_1
	elif j <= -3e-287:
		tmp = t_3
	elif j <= 4.3e-231:
		tmp = b * ((t * i) - (z * c))
	elif j <= 3.6e-93:
		tmp = t_3
	elif j <= 3.1e-19:
		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(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -7.5e+59)
		tmp = t_2;
	elseif (j <= -6e-52)
		tmp = t_1;
	elseif (j <= -2.5e-79)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -5.5e-167)
		tmp = t_1;
	elseif (j <= -3e-287)
		tmp = t_3;
	elseif (j <= 4.3e-231)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 3.6e-93)
		tmp = t_3;
	elseif (j <= 3.1e-19)
		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 = j * ((a * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -7.5e+59)
		tmp = t_2;
	elseif (j <= -6e-52)
		tmp = t_1;
	elseif (j <= -2.5e-79)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -5.5e-167)
		tmp = t_1;
	elseif (j <= -3e-287)
		tmp = t_3;
	elseif (j <= 4.3e-231)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 3.6e-93)
		tmp = t_3;
	elseif (j <= 3.1e-19)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.5e+59], t$95$2, If[LessEqual[j, -6e-52], t$95$1, If[LessEqual[j, -2.5e-79], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.5e-167], t$95$1, If[LessEqual[j, -3e-287], t$95$3, If[LessEqual[j, 4.3e-231], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e-93], t$95$3, If[LessEqual[j, 3.1e-19], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -7.4999999999999996e59 or 3.0999999999999999e-19 < j

   1. Initial program 69.5%

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

   2. Taylor expanded in j around inf 67.0%

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

      1. *-commutative 67.0%

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

   4. Simplified 67.0%

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

   if -7.4999999999999996e59 < j < -6e-52 or -2.5e-79 < j < -5.5000000000000003e-167

   1. Initial program 77.2%

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

   2. Taylor expanded in z around inf 73.5%

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

      1. *-commutative 73.5%

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

   4. Simplified 73.5%

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

   if -6e-52 < j < -2.5e-79

   1. Initial program 89.2%

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

   2. Taylor expanded in a around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

   4. Simplified 63.4%

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

   if -5.5000000000000003e-167 < j < -2.99999999999999992e-287 or 4.29999999999999998e-231 < j < 3.6000000000000002e-93

   1. Initial program 69.2%

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

   2. Taylor expanded in x around inf 57.1%

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

      1. *-commutative 57.1%

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

      2. *-commutative 57.1%

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

   4. Simplified 57.1%

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

   if -2.99999999999999992e-287 < j < 4.29999999999999998e-231

   1. Initial program 78.5%

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

   2. Taylor expanded in b around inf 60.6%

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

   if 3.6000000000000002e-93 < j < 3.0999999999999999e-19

   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. Taylor expanded in c around inf 87.5%

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

      1. *-commutative 87.5%

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

   4. Simplified 87.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-167}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 12: 51.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.56 \cdot 10^{-252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -2.9e+62)
     t_3
     (if (<= j -3.9e-56)
       t_2
       (if (<= j -1.45e-81)
         t_1
         (if (<= j -1.56e-252)
           t_2
           (if (<= j 5.9e-255)
             t_1
             (if (<= j 1.85e-178)
               t_2
               (if (<= j 1.7e-111)
                 t_1
                 (if (<= j 5.2e-30) (* c (- (* a j) (* z b))) 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) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.9e+62) {
		tmp = t_3;
	} else if (j <= -3.9e-56) {
		tmp = t_2;
	} else if (j <= -1.45e-81) {
		tmp = t_1;
	} else if (j <= -1.56e-252) {
		tmp = t_2;
	} else if (j <= 5.9e-255) {
		tmp = t_1;
	} else if (j <= 1.85e-178) {
		tmp = t_2;
	} else if (j <= 1.7e-111) {
		tmp = t_1;
	} else if (j <= 5.2e-30) {
		tmp = c * ((a * j) - (z * b));
	} 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) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-2.9d+62)) then
        tmp = t_3
    else if (j <= (-3.9d-56)) then
        tmp = t_2
    else if (j <= (-1.45d-81)) then
        tmp = t_1
    else if (j <= (-1.56d-252)) then
        tmp = t_2
    else if (j <= 5.9d-255) then
        tmp = t_1
    else if (j <= 1.85d-178) then
        tmp = t_2
    else if (j <= 1.7d-111) then
        tmp = t_1
    else if (j <= 5.2d-30) then
        tmp = c * ((a * j) - (z * b))
    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) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.9e+62) {
		tmp = t_3;
	} else if (j <= -3.9e-56) {
		tmp = t_2;
	} else if (j <= -1.45e-81) {
		tmp = t_1;
	} else if (j <= -1.56e-252) {
		tmp = t_2;
	} else if (j <= 5.9e-255) {
		tmp = t_1;
	} else if (j <= 1.85e-178) {
		tmp = t_2;
	} else if (j <= 1.7e-111) {
		tmp = t_1;
	} else if (j <= 5.2e-30) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.9e+62:
		tmp = t_3
	elif j <= -3.9e-56:
		tmp = t_2
	elif j <= -1.45e-81:
		tmp = t_1
	elif j <= -1.56e-252:
		tmp = t_2
	elif j <= 5.9e-255:
		tmp = t_1
	elif j <= 1.85e-178:
		tmp = t_2
	elif j <= 1.7e-111:
		tmp = t_1
	elif j <= 5.2e-30:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.9e+62)
		tmp = t_3;
	elseif (j <= -3.9e-56)
		tmp = t_2;
	elseif (j <= -1.45e-81)
		tmp = t_1;
	elseif (j <= -1.56e-252)
		tmp = t_2;
	elseif (j <= 5.9e-255)
		tmp = t_1;
	elseif (j <= 1.85e-178)
		tmp = t_2;
	elseif (j <= 1.7e-111)
		tmp = t_1;
	elseif (j <= 5.2e-30)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.9e+62)
		tmp = t_3;
	elseif (j <= -3.9e-56)
		tmp = t_2;
	elseif (j <= -1.45e-81)
		tmp = t_1;
	elseif (j <= -1.56e-252)
		tmp = t_2;
	elseif (j <= 5.9e-255)
		tmp = t_1;
	elseif (j <= 1.85e-178)
		tmp = t_2;
	elseif (j <= 1.7e-111)
		tmp = t_1;
	elseif (j <= 5.2e-30)
		tmp = c * ((a * j) - (z * b));
	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[(N[(b * i), $MachinePrecision] - N[(x * a), $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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+62], t$95$3, If[LessEqual[j, -3.9e-56], t$95$2, If[LessEqual[j, -1.45e-81], t$95$1, If[LessEqual[j, -1.56e-252], t$95$2, If[LessEqual[j, 5.9e-255], t$95$1, If[LessEqual[j, 1.85e-178], t$95$2, If[LessEqual[j, 1.7e-111], t$95$1, If[LessEqual[j, 5.2e-30], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.89999999999999984e62 or 5.19999999999999973e-30 < j

   1. Initial program 69.5%

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

   2. Taylor expanded in j around inf 67.0%

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

      1. *-commutative 67.0%

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

   4. Simplified 67.0%

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

   if -2.89999999999999984e62 < j < -3.9e-56 or -1.44999999999999994e-81 < j < -1.56e-252 or 5.9000000000000001e-255 < j < 1.85000000000000002e-178

   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 z around inf 67.8%

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

      1. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -3.9e-56 < j < -1.44999999999999994e-81 or -1.56e-252 < j < 5.9000000000000001e-255 or 1.85000000000000002e-178 < j < 1.69999999999999998e-111

   1. Initial program 82.2%

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

   2. Taylor expanded in t around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

   4. Simplified 63.7%

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

   if 1.69999999999999998e-111 < j < 5.19999999999999973e-30

   1. Initial program 67.4%

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

   2. Taylor expanded in c around inf 67.5%

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

      1. *-commutative 67.5%

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

   4. Simplified 67.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.56 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-255}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 13: 56.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -0.00045:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -1.45e+50)
     t_1
     (if (<= t -0.00045)
       (* c (- (* a j) (* z b)))
       (if (<= t -1.5e-45)
         t_1
         (if (<= t -2.15e-69)
           (* z (- (* x y) (* b c)))
           (if (<= t 4.5e-12)
             (+ (* j (- (* a c) (* y i))) (* x (* y z)))
             (if (<= t 3.2e+81)
               (* b (- (* t i) (* z c)))
               (if (<= t 3.3e+148) (* a (- (* c j) (* x t))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.45e+50) {
		tmp = t_1;
	} else if (t <= -0.00045) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -1.5e-45) {
		tmp = t_1;
	} else if (t <= -2.15e-69) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 4.5e-12) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (t <= 3.2e+81) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= 3.3e+148) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-1.45d+50)) then
        tmp = t_1
    else if (t <= (-0.00045d0)) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= (-1.5d-45)) then
        tmp = t_1
    else if (t <= (-2.15d-69)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 4.5d-12) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else if (t <= 3.2d+81) then
        tmp = b * ((t * i) - (z * c))
    else if (t <= 3.3d+148) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.45e+50) {
		tmp = t_1;
	} else if (t <= -0.00045) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= -1.5e-45) {
		tmp = t_1;
	} else if (t <= -2.15e-69) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 4.5e-12) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (t <= 3.2e+81) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= 3.3e+148) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.45e+50:
		tmp = t_1
	elif t <= -0.00045:
		tmp = c * ((a * j) - (z * b))
	elif t <= -1.5e-45:
		tmp = t_1
	elif t <= -2.15e-69:
		tmp = z * ((x * y) - (b * c))
	elif t <= 4.5e-12:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	elif t <= 3.2e+81:
		tmp = b * ((t * i) - (z * c))
	elif t <= 3.3e+148:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.45e+50)
		tmp = t_1;
	elseif (t <= -0.00045)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= -1.5e-45)
		tmp = t_1;
	elseif (t <= -2.15e-69)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 4.5e-12)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (t <= 3.2e+81)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (t <= 3.3e+148)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.45e+50)
		tmp = t_1;
	elseif (t <= -0.00045)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= -1.5e-45)
		tmp = t_1;
	elseif (t <= -2.15e-69)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 4.5e-12)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	elseif (t <= 3.2e+81)
		tmp = b * ((t * i) - (z * c));
	elseif (t <= 3.3e+148)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+50], t$95$1, If[LessEqual[t, -0.00045], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-45], t$95$1, If[LessEqual[t, -2.15e-69], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-12], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+81], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+148], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.45e50 or -4.4999999999999999e-4 < t < -1.50000000000000005e-45 or 3.3000000000000001e148 < t

   1. Initial program 56.5%

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

   2. Taylor expanded in t around inf 70.5%

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

      1. distribute-lft-out-- 70.5%

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

   4. Simplified 70.5%

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

   if -1.45e50 < t < -4.4999999999999999e-4

   1. Initial program 73.5%

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

   2. Taylor expanded in c around inf 73.9%

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

      1. *-commutative 73.9%

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

   4. Simplified 73.9%

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

   if -1.50000000000000005e-45 < t < -2.15e-69

   1. Initial program 69.8%

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

   2. Taylor expanded in z around inf 75.5%

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

      1. *-commutative 75.5%

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

   4. Simplified 75.5%

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

   if -2.15e-69 < t < 4.49999999999999981e-12

   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 y around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*l* 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in b around 0 66.0%

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

   if 4.49999999999999981e-12 < t < 3.2e81

   1. Initial program 93.9%

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

   2. Taylor expanded in b around inf 67.8%

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

   if 3.2e81 < t < 3.3000000000000001e148

   1. Initial program 67.3%

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

   2. Taylor expanded in a around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   4. Simplified 51.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -0.00045:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 14: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.757 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-159}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.757e+50)
     t_2
     (if (<= i 1e-289)
       t_1
       (if (<= i 8.5e-159)
         (* c (- (* a j) (* z b)))
         (if (<= i 1.3e-39)
           t_1
           (if (<= i 2.2e+18)
             (* x (* y z))
             (if (<= i 5.5e+45)
               (* (* x t) (- a))
               (if (<= i 2.1e+108) (* y (* x z)) 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.757e+50) {
		tmp = t_2;
	} else if (i <= 1e-289) {
		tmp = t_1;
	} else if (i <= 8.5e-159) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.3e-39) {
		tmp = t_1;
	} else if (i <= 2.2e+18) {
		tmp = x * (y * z);
	} else if (i <= 5.5e+45) {
		tmp = (x * t) * -a;
	} else if (i <= 2.1e+108) {
		tmp = y * (x * z);
	} 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 = i * ((t * b) - (y * j))
    if (i <= (-1.757d+50)) then
        tmp = t_2
    else if (i <= 1d-289) then
        tmp = t_1
    else if (i <= 8.5d-159) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.3d-39) then
        tmp = t_1
    else if (i <= 2.2d+18) then
        tmp = x * (y * z)
    else if (i <= 5.5d+45) then
        tmp = (x * t) * -a
    else if (i <= 2.1d+108) then
        tmp = y * (x * z)
    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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.757e+50) {
		tmp = t_2;
	} else if (i <= 1e-289) {
		tmp = t_1;
	} else if (i <= 8.5e-159) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.3e-39) {
		tmp = t_1;
	} else if (i <= 2.2e+18) {
		tmp = x * (y * z);
	} else if (i <= 5.5e+45) {
		tmp = (x * t) * -a;
	} else if (i <= 2.1e+108) {
		tmp = y * (x * z);
	} 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 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.757e+50:
		tmp = t_2
	elif i <= 1e-289:
		tmp = t_1
	elif i <= 8.5e-159:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.3e-39:
		tmp = t_1
	elif i <= 2.2e+18:
		tmp = x * (y * z)
	elif i <= 5.5e+45:
		tmp = (x * t) * -a
	elif i <= 2.1e+108:
		tmp = y * (x * z)
	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(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.757e+50)
		tmp = t_2;
	elseif (i <= 1e-289)
		tmp = t_1;
	elseif (i <= 8.5e-159)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.3e-39)
		tmp = t_1;
	elseif (i <= 2.2e+18)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 5.5e+45)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (i <= 2.1e+108)
		tmp = Float64(y * Float64(x * z));
	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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.757e+50)
		tmp = t_2;
	elseif (i <= 1e-289)
		tmp = t_1;
	elseif (i <= 8.5e-159)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.3e-39)
		tmp = t_1;
	elseif (i <= 2.2e+18)
		tmp = x * (y * z);
	elseif (i <= 5.5e+45)
		tmp = (x * t) * -a;
	elseif (i <= 2.1e+108)
		tmp = y * (x * z);
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.757e+50], t$95$2, If[LessEqual[i, 1e-289], t$95$1, If[LessEqual[i, 8.5e-159], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-39], t$95$1, If[LessEqual[i, 2.2e+18], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+45], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[i, 2.1e+108], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.7569999999999999e50 or 2.1000000000000001e108 < i

   1. Initial program 60.9%

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

   2. Taylor expanded in c around -inf 59.8%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in i around inf 59.6%

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

      1. +-commutative 59.6%

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

      2. mul-1-neg 59.6%

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

      3. unsub-neg 59.6%

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

   7. Simplified 59.6%

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

   if -1.7569999999999999e50 < i < 1e-289 or 8.4999999999999998e-159 < i < 1.3e-39

   1. Initial program 84.0%

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

   2. Taylor expanded in a around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

   4. Simplified 56.2%

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

   if 1e-289 < i < 8.4999999999999998e-159

   1. Initial program 87.9%

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

   2. Taylor expanded in c around inf 49.6%

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

      1. *-commutative 49.6%

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

   4. Simplified 49.6%

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

   if 1.3e-39 < i < 2.2e18

   1. Initial program 77.4%

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

   2. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in z around inf 55.5%

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

   if 2.2e18 < i < 5.5000000000000001e45

   1. Initial program 66.7%

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

   2. Taylor expanded in a around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

   4. Simplified 56.7%

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

   5. Taylor expanded in c around 0 57.1%

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

      1. neg-mul-1 57.1%

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

      2. distribute-rgt-neg-in 57.1%

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

   7. Simplified 57.1%

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

   if 5.5000000000000001e45 < i < 2.1000000000000001e108

   1. Initial program 46.2%

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

   2. Taylor expanded in 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%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

   7. Simplified 58.4%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.757 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 10^{-289}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-159}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 15: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - z \cdot \left(b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;t_3 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+269}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* z (* b c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -9.2e+61)
     t_3
     (if (<= j 1.9e-42)
       t_2
       (if (<= j 3.3e+35)
         (+ t_3 (* x (* y z)))
         (if (<= j 3.7e+65) t_2 (if (<= j 7e+269) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.2e+61) {
		tmp = t_3;
	} else if (j <= 1.9e-42) {
		tmp = t_2;
	} else if (j <= 3.3e+35) {
		tmp = t_3 + (x * (y * z));
	} else if (j <= 3.7e+65) {
		tmp = t_2;
	} else if (j <= 7e+269) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (z * (b * c))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-9.2d+61)) then
        tmp = t_3
    else if (j <= 1.9d-42) then
        tmp = t_2
    else if (j <= 3.3d+35) then
        tmp = t_3 + (x * (y * z))
    else if (j <= 3.7d+65) then
        tmp = t_2
    else if (j <= 7d+269) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.2e+61) {
		tmp = t_3;
	} else if (j <= 1.9e-42) {
		tmp = t_2;
	} else if (j <= 3.3e+35) {
		tmp = t_3 + (x * (y * z));
	} else if (j <= 3.7e+65) {
		tmp = t_2;
	} else if (j <= 7e+269) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (z * (b * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -9.2e+61:
		tmp = t_3
	elif j <= 1.9e-42:
		tmp = t_2
	elif j <= 3.3e+35:
		tmp = t_3 + (x * (y * z))
	elif j <= 3.7e+65:
		tmp = t_2
	elif j <= 7e+269:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(z * Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9.2e+61)
		tmp = t_3;
	elseif (j <= 1.9e-42)
		tmp = t_2;
	elseif (j <= 3.3e+35)
		tmp = Float64(t_3 + Float64(x * Float64(y * z)));
	elseif (j <= 3.7e+65)
		tmp = t_2;
	elseif (j <= 7e+269)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (z * (b * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -9.2e+61)
		tmp = t_3;
	elseif (j <= 1.9e-42)
		tmp = t_2;
	elseif (j <= 3.3e+35)
		tmp = t_3 + (x * (y * z));
	elseif (j <= 3.7e+65)
		tmp = t_2;
	elseif (j <= 7e+269)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.2e+61], t$95$3, If[LessEqual[j, 1.9e-42], t$95$2, If[LessEqual[j, 3.3e+35], N[(t$95$3 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e+65], t$95$2, If[LessEqual[j, 7e+269], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.1999999999999998e61 or 3.69999999999999995e65 < j < 7.0000000000000003e269

   1. Initial program 67.6%

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

   2. Taylor expanded in j around inf 74.8%

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

      1. *-commutative 74.8%

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

   4. Simplified 74.8%

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

   if -9.1999999999999998e61 < j < 1.90000000000000009e-42 or 3.3000000000000002e35 < j < 3.69999999999999995e65

   1. Initial program 76.8%

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

   2. Taylor expanded in j around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

   4. Simplified 75.1%

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

   5. Taylor expanded in c around inf 66.5%

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

      1. associate-*r* 67.5%

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

      2. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if 1.90000000000000009e-42 < j < 3.3000000000000002e35

   1. Initial program 79.5%

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

   2. Taylor expanded in y around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in b around 0 60.5%

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

   if 7.0000000000000003e269 < j

   1. Initial program 37.3%

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

   2. Taylor expanded in x around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. *-commutative 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+269}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 16: 29.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* t (- a)))))
   (if (<= z -1.7e+139)
     (* x (* y z))
     (if (<= z -5500000000.0)
       t_1
       (if (<= z -3.6e-52)
         t_2
         (if (<= z -1.65e-287)
           t_1
           (if (<= z 1.4e-249)
             (* i (- (* y j)))
             (if (<= z 3.4e-41)
               t_2
               (if (<= z 6.6e+87)
                 (* y (* x z))
                 (if (<= z 3.8e+119) (* z (* c (- b))) (* z (* x y))))))))))))

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 t_2 = x * (t * -a);
	double tmp;
	if (z <= -1.7e+139) {
		tmp = x * (y * z);
	} else if (z <= -5500000000.0) {
		tmp = t_1;
	} else if (z <= -3.6e-52) {
		tmp = t_2;
	} else if (z <= -1.65e-287) {
		tmp = t_1;
	} else if (z <= 1.4e-249) {
		tmp = i * -(y * j);
	} else if (z <= 3.4e-41) {
		tmp = t_2;
	} else if (z <= 6.6e+87) {
		tmp = y * (x * z);
	} else if (z <= 3.8e+119) {
		tmp = z * (c * -b);
	} else {
		tmp = z * (x * y);
	}
	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)
    t_2 = x * (t * -a)
    if (z <= (-1.7d+139)) then
        tmp = x * (y * z)
    else if (z <= (-5500000000.0d0)) then
        tmp = t_1
    else if (z <= (-3.6d-52)) then
        tmp = t_2
    else if (z <= (-1.65d-287)) then
        tmp = t_1
    else if (z <= 1.4d-249) then
        tmp = i * -(y * j)
    else if (z <= 3.4d-41) then
        tmp = t_2
    else if (z <= 6.6d+87) then
        tmp = y * (x * z)
    else if (z <= 3.8d+119) then
        tmp = z * (c * -b)
    else
        tmp = z * (x * y)
    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 t_2 = x * (t * -a);
	double tmp;
	if (z <= -1.7e+139) {
		tmp = x * (y * z);
	} else if (z <= -5500000000.0) {
		tmp = t_1;
	} else if (z <= -3.6e-52) {
		tmp = t_2;
	} else if (z <= -1.65e-287) {
		tmp = t_1;
	} else if (z <= 1.4e-249) {
		tmp = i * -(y * j);
	} else if (z <= 3.4e-41) {
		tmp = t_2;
	} else if (z <= 6.6e+87) {
		tmp = y * (x * z);
	} else if (z <= 3.8e+119) {
		tmp = z * (c * -b);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (t * -a)
	tmp = 0
	if z <= -1.7e+139:
		tmp = x * (y * z)
	elif z <= -5500000000.0:
		tmp = t_1
	elif z <= -3.6e-52:
		tmp = t_2
	elif z <= -1.65e-287:
		tmp = t_1
	elif z <= 1.4e-249:
		tmp = i * -(y * j)
	elif z <= 3.4e-41:
		tmp = t_2
	elif z <= 6.6e+87:
		tmp = y * (x * z)
	elif z <= 3.8e+119:
		tmp = z * (c * -b)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (z <= -1.7e+139)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -5500000000.0)
		tmp = t_1;
	elseif (z <= -3.6e-52)
		tmp = t_2;
	elseif (z <= -1.65e-287)
		tmp = t_1;
	elseif (z <= 1.4e-249)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (z <= 3.4e-41)
		tmp = t_2;
	elseif (z <= 6.6e+87)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 3.8e+119)
		tmp = Float64(z * Float64(c * Float64(-b)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (t * -a);
	tmp = 0.0;
	if (z <= -1.7e+139)
		tmp = x * (y * z);
	elseif (z <= -5500000000.0)
		tmp = t_1;
	elseif (z <= -3.6e-52)
		tmp = t_2;
	elseif (z <= -1.65e-287)
		tmp = t_1;
	elseif (z <= 1.4e-249)
		tmp = i * -(y * j);
	elseif (z <= 3.4e-41)
		tmp = t_2;
	elseif (z <= 6.6e+87)
		tmp = y * (x * z);
	elseif (z <= 3.8e+119)
		tmp = z * (c * -b);
	else
		tmp = z * (x * y);
	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]}, Block[{t$95$2 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+139], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5500000000.0], t$95$1, If[LessEqual[z, -3.6e-52], t$95$2, If[LessEqual[z, -1.65e-287], t$95$1, If[LessEqual[z, 1.4e-249], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.4e-41], t$95$2, If[LessEqual[z, 6.6e+87], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+119], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.7000000000000001e139

   1. Initial program 57.7%

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

   2. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. *-commutative 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in z around inf 52.4%

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

   if -1.7000000000000001e139 < z < -5.5e9 or -3.59999999999999988e-52 < z < -1.64999999999999987e-287

   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 a around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in c around inf 42.3%

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

      1. *-commutative 42.3%

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

   7. Simplified 42.3%

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

   if -5.5e9 < z < -3.59999999999999988e-52 or 1.4e-249 < z < 3.3999999999999998e-41

   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 x around inf 49.1%

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

      1. *-commutative 49.1%

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

      2. *-commutative 49.1%

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

   4. Simplified 49.1%

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

   5. Taylor expanded in z around 0 39.4%

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

      1. neg-mul-1 39.4%

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

      2. distribute-lft-neg-in 39.4%

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

      3. *-commutative 39.4%

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

   7. Simplified 39.4%

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

   if -1.64999999999999987e-287 < z < 1.4e-249

   1. Initial program 65.4%

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

   2. Taylor expanded in c around -inf 60.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in i around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in b around 0 51.1%

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

      1. associate-*r* 51.1%

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

      2. neg-mul-1 51.1%

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

      3. *-commutative 51.1%

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

   10. Simplified 51.1%

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

   if 3.3999999999999998e-41 < z < 6.6000000000000003e87

   1. Initial program 76.0%

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

   2. Taylor expanded in y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. *-commutative 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in z around inf 45.0%

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

      1. *-commutative 45.0%

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

   7. Simplified 45.0%

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

   if 6.6000000000000003e87 < z < 3.7999999999999999e119

   1. Initial program 43.7%

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

   2. Taylor expanded in c around -inf 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. +-commutative 85.7%

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

      2. mul-1-neg 85.7%

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

      3. unsub-neg 85.7%

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

      4. *-commutative 85.7%

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

      5. associate-*r* 85.7%

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

      6. associate-*r* 85.7%

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

      7. associate-*r* 85.7%

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

      8. distribute-rgt-in 85.7%

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

      9. +-commutative 85.7%

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

      10. mul-1-neg 85.7%

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

      11. unsub-neg 85.7%

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

      12. +-commutative 85.7%

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

      13. mul-1-neg 85.7%

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

      14. unsub-neg 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in b around inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. associate-*r* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

   10. Simplified 73.2%

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

   if 3.7999999999999999e119 < z

   1. Initial program 63.4%

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

   2. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

      2. *-commutative 53.3%

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

      3. associate-*l* 58.4%

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

   4. Simplified 58.4%

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

      1. associate-+l- 58.4%

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

      2. associate-*r* 53.3%

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

      3. fma-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. *-commutative 53.3%

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

   6. Applied egg-rr 53.3%

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

   7. Taylor expanded in x around inf 46.1%

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

      1. *-commutative 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*l* 46.2%

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

   9. Simplified 46.2%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5500000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-287}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 46.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -46000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -4.5e+147)
     t_2
     (if (<= b -46000000.0)
       t_1
       (if (<= b -6e-220)
         (* x (* y z))
         (if (<= b 1.02e-161)
           t_1
           (if (<= b 1.85e-103)
             (* y (* x z))
             (if (<= b 1.7e+116) 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 <= -4.5e+147) {
		tmp = t_2;
	} else if (b <= -46000000.0) {
		tmp = t_1;
	} else if (b <= -6e-220) {
		tmp = x * (y * z);
	} else if (b <= 1.02e-161) {
		tmp = t_1;
	} else if (b <= 1.85e-103) {
		tmp = y * (x * z);
	} else if (b <= 1.7e+116) {
		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 <= (-4.5d+147)) then
        tmp = t_2
    else if (b <= (-46000000.0d0)) then
        tmp = t_1
    else if (b <= (-6d-220)) then
        tmp = x * (y * z)
    else if (b <= 1.02d-161) then
        tmp = t_1
    else if (b <= 1.85d-103) then
        tmp = y * (x * z)
    else if (b <= 1.7d+116) 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 <= -4.5e+147) {
		tmp = t_2;
	} else if (b <= -46000000.0) {
		tmp = t_1;
	} else if (b <= -6e-220) {
		tmp = x * (y * z);
	} else if (b <= 1.02e-161) {
		tmp = t_1;
	} else if (b <= 1.85e-103) {
		tmp = y * (x * z);
	} else if (b <= 1.7e+116) {
		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 <= -4.5e+147:
		tmp = t_2
	elif b <= -46000000.0:
		tmp = t_1
	elif b <= -6e-220:
		tmp = x * (y * z)
	elif b <= 1.02e-161:
		tmp = t_1
	elif b <= 1.85e-103:
		tmp = y * (x * z)
	elif b <= 1.7e+116:
		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 <= -4.5e+147)
		tmp = t_2;
	elseif (b <= -46000000.0)
		tmp = t_1;
	elseif (b <= -6e-220)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.02e-161)
		tmp = t_1;
	elseif (b <= 1.85e-103)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.7e+116)
		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 <= -4.5e+147)
		tmp = t_2;
	elseif (b <= -46000000.0)
		tmp = t_1;
	elseif (b <= -6e-220)
		tmp = x * (y * z);
	elseif (b <= 1.02e-161)
		tmp = t_1;
	elseif (b <= 1.85e-103)
		tmp = y * (x * z);
	elseif (b <= 1.7e+116)
		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, -4.5e+147], t$95$2, If[LessEqual[b, -46000000.0], t$95$1, If[LessEqual[b, -6e-220], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-161], t$95$1, If[LessEqual[b, 1.85e-103], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+116], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.50000000000000008e147 or 1.70000000000000011e116 < b

   1. Initial program 69.5%

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

   2. Taylor expanded in b around inf 68.5%

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

   if -4.50000000000000008e147 < b < -4.6e7 or -6.00000000000000035e-220 < b < 1.0199999999999999e-161 or 1.85e-103 < b < 1.70000000000000011e116

   1. Initial program 75.8%

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

   2. Taylor expanded in a around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

   4. Simplified 49.3%

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

   if -4.6e7 < b < -6.00000000000000035e-220

   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 x around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-commutative 59.7%

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

   4. Simplified 59.7%

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

   5. Taylor expanded in z around inf 43.6%

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

   if 1.0199999999999999e-161 < b < 1.85e-103

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 79.0%

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

      1. +-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. unsub-neg 79.0%

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

      4. *-commutative 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. *-commutative 57.1%

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

   7. Simplified 57.1%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -46000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 18: 53.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -5.2e+50)
     t_3
     (if (<= x -2.9e-34)
       t_2
       (if (<= x 7.8e-205)
         t_1
         (if (<= x 6.5e-44)
           t_2
           (if (<= x 1.65e-19) t_1 (if (<= x 5.4e+19) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.2e+50) {
		tmp = t_3;
	} else if (x <= -2.9e-34) {
		tmp = t_2;
	} else if (x <= 7.8e-205) {
		tmp = t_1;
	} else if (x <= 6.5e-44) {
		tmp = t_2;
	} else if (x <= 1.65e-19) {
		tmp = t_1;
	} else if (x <= 5.4e+19) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-5.2d+50)) then
        tmp = t_3
    else if (x <= (-2.9d-34)) then
        tmp = t_2
    else if (x <= 7.8d-205) then
        tmp = t_1
    else if (x <= 6.5d-44) then
        tmp = t_2
    else if (x <= 1.65d-19) then
        tmp = t_1
    else if (x <= 5.4d+19) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.2e+50) {
		tmp = t_3;
	} else if (x <= -2.9e-34) {
		tmp = t_2;
	} else if (x <= 7.8e-205) {
		tmp = t_1;
	} else if (x <= 6.5e-44) {
		tmp = t_2;
	} else if (x <= 1.65e-19) {
		tmp = t_1;
	} else if (x <= 5.4e+19) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.2e+50:
		tmp = t_3
	elif x <= -2.9e-34:
		tmp = t_2
	elif x <= 7.8e-205:
		tmp = t_1
	elif x <= 6.5e-44:
		tmp = t_2
	elif x <= 1.65e-19:
		tmp = t_1
	elif x <= 5.4e+19:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.2e+50)
		tmp = t_3;
	elseif (x <= -2.9e-34)
		tmp = t_2;
	elseif (x <= 7.8e-205)
		tmp = t_1;
	elseif (x <= 6.5e-44)
		tmp = t_2;
	elseif (x <= 1.65e-19)
		tmp = t_1;
	elseif (x <= 5.4e+19)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5.2e+50)
		tmp = t_3;
	elseif (x <= -2.9e-34)
		tmp = t_2;
	elseif (x <= 7.8e-205)
		tmp = t_1;
	elseif (x <= 6.5e-44)
		tmp = t_2;
	elseif (x <= 1.65e-19)
		tmp = t_1;
	elseif (x <= 5.4e+19)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+50], t$95$3, If[LessEqual[x, -2.9e-34], t$95$2, If[LessEqual[x, 7.8e-205], t$95$1, If[LessEqual[x, 6.5e-44], t$95$2, If[LessEqual[x, 1.65e-19], t$95$1, If[LessEqual[x, 5.4e+19], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2000000000000004e50 or 5.4e19 < x

   1. Initial program 73.5%

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

   2. Taylor expanded in x around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   if -5.2000000000000004e50 < x < -2.9000000000000002e-34 or 7.80000000000000036e-205 < x < 6.5e-44 or 1.6499999999999999e-19 < x < 5.4e19

   1. Initial program 73.6%

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

   2. Taylor expanded in j around inf 62.5%

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

      1. *-commutative 62.5%

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

   4. Simplified 62.5%

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

   if -2.9000000000000002e-34 < x < 7.80000000000000036e-205 or 6.5e-44 < x < 1.6499999999999999e-19

   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 b around inf 59.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 19: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-285}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* t (- a)))))
   (if (<= z -3.6e+137)
     (* x (* y z))
     (if (<= z -200000000.0)
       t_1
       (if (<= z -2.7e-49)
         t_2
         (if (<= z -2.15e-260)
           t_1
           (if (<= z 1.45e-285)
             (* b (* t i))
             (if (<= z 3.5e-257)
               (* c (* a j))
               (if (<= z 1.62e-41) t_2 (* y (* x z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (t * -a);
	double tmp;
	if (z <= -3.6e+137) {
		tmp = x * (y * z);
	} else if (z <= -200000000.0) {
		tmp = t_1;
	} else if (z <= -2.7e-49) {
		tmp = t_2;
	} else if (z <= -2.15e-260) {
		tmp = t_1;
	} else if (z <= 1.45e-285) {
		tmp = b * (t * i);
	} else if (z <= 3.5e-257) {
		tmp = c * (a * j);
	} else if (z <= 1.62e-41) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = x * (t * -a)
    if (z <= (-3.6d+137)) then
        tmp = x * (y * z)
    else if (z <= (-200000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.7d-49)) then
        tmp = t_2
    else if (z <= (-2.15d-260)) then
        tmp = t_1
    else if (z <= 1.45d-285) then
        tmp = b * (t * i)
    else if (z <= 3.5d-257) then
        tmp = c * (a * j)
    else if (z <= 1.62d-41) then
        tmp = t_2
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (t * -a);
	double tmp;
	if (z <= -3.6e+137) {
		tmp = x * (y * z);
	} else if (z <= -200000000.0) {
		tmp = t_1;
	} else if (z <= -2.7e-49) {
		tmp = t_2;
	} else if (z <= -2.15e-260) {
		tmp = t_1;
	} else if (z <= 1.45e-285) {
		tmp = b * (t * i);
	} else if (z <= 3.5e-257) {
		tmp = c * (a * j);
	} else if (z <= 1.62e-41) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (t * -a)
	tmp = 0
	if z <= -3.6e+137:
		tmp = x * (y * z)
	elif z <= -200000000.0:
		tmp = t_1
	elif z <= -2.7e-49:
		tmp = t_2
	elif z <= -2.15e-260:
		tmp = t_1
	elif z <= 1.45e-285:
		tmp = b * (t * i)
	elif z <= 3.5e-257:
		tmp = c * (a * j)
	elif z <= 1.62e-41:
		tmp = t_2
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (z <= -3.6e+137)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -200000000.0)
		tmp = t_1;
	elseif (z <= -2.7e-49)
		tmp = t_2;
	elseif (z <= -2.15e-260)
		tmp = t_1;
	elseif (z <= 1.45e-285)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 3.5e-257)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 1.62e-41)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (t * -a);
	tmp = 0.0;
	if (z <= -3.6e+137)
		tmp = x * (y * z);
	elseif (z <= -200000000.0)
		tmp = t_1;
	elseif (z <= -2.7e-49)
		tmp = t_2;
	elseif (z <= -2.15e-260)
		tmp = t_1;
	elseif (z <= 1.45e-285)
		tmp = b * (t * i);
	elseif (z <= 3.5e-257)
		tmp = c * (a * j);
	elseif (z <= 1.62e-41)
		tmp = t_2;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+137], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -200000000.0], t$95$1, If[LessEqual[z, -2.7e-49], t$95$2, If[LessEqual[z, -2.15e-260], t$95$1, If[LessEqual[z, 1.45e-285], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-257], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e-41], t$95$2, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.6e137

   1. Initial program 57.7%

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

   2. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. *-commutative 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in z around inf 52.4%

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

   if -3.6e137 < z < -2e8 or -2.7e-49 < z < -2.15000000000000011e-260

   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 a around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

   4. Simplified 56.4%

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

   5. Taylor expanded in c around inf 43.1%

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

      1. *-commutative 43.1%

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

   7. Simplified 43.1%

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

   if -2e8 < z < -2.7e-49 or 3.50000000000000029e-257 < z < 1.6199999999999999e-41

   1. Initial program 83.2%

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

   2. Taylor expanded in x around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. *-commutative 47.5%

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

   4. Simplified 47.5%

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

   5. Taylor expanded in z around 0 38.1%

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

      1. neg-mul-1 38.1%

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

      2. distribute-lft-neg-in 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if -2.15000000000000011e-260 < z < 1.45e-285

   1. Initial program 54.6%

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

   2. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*l* 69.4%

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

   4. Simplified 69.4%

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

      1. associate-+l- 69.4%

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

      2. associate-*r* 77.1%

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

      3. fma-neg 77.1%

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

      4. *-commutative 77.1%

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

      5. *-commutative 77.1%

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

   6. Applied egg-rr 77.1%

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

   7. Taylor expanded in t around inf 47.3%

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

   if 1.45e-285 < z < 3.50000000000000029e-257

   1. Initial program 66.5%

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

   2. Taylor expanded in y around 0 65.3%

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

   3. Taylor expanded in j around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-*l* 57.6%

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

      3. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   if 1.6199999999999999e-41 < z

   1. Initial program 66.5%

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

   2. Taylor expanded in y around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

   4. Simplified 48.0%

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

   5. Taylor expanded in z around inf 42.8%

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

      1. *-commutative 42.8%

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

   7. Simplified 42.8%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -200000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-285}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 20: 29.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -25000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* t (- a)))))
   (if (<= z -1.46e+138)
     (* x (* y z))
     (if (<= z -25000000.0)
       t_1
       (if (<= z -2.5e-51)
         t_2
         (if (<= z -9e-292)
           t_1
           (if (<= z 1.25e-249)
             (* i (- (* y j)))
             (if (<= z 3.8e-42) t_2 (* y (* x z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (t * -a);
	double tmp;
	if (z <= -1.46e+138) {
		tmp = x * (y * z);
	} else if (z <= -25000000.0) {
		tmp = t_1;
	} else if (z <= -2.5e-51) {
		tmp = t_2;
	} else if (z <= -9e-292) {
		tmp = t_1;
	} else if (z <= 1.25e-249) {
		tmp = i * -(y * j);
	} else if (z <= 3.8e-42) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = x * (t * -a)
    if (z <= (-1.46d+138)) then
        tmp = x * (y * z)
    else if (z <= (-25000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.5d-51)) then
        tmp = t_2
    else if (z <= (-9d-292)) then
        tmp = t_1
    else if (z <= 1.25d-249) then
        tmp = i * -(y * j)
    else if (z <= 3.8d-42) then
        tmp = t_2
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (t * -a);
	double tmp;
	if (z <= -1.46e+138) {
		tmp = x * (y * z);
	} else if (z <= -25000000.0) {
		tmp = t_1;
	} else if (z <= -2.5e-51) {
		tmp = t_2;
	} else if (z <= -9e-292) {
		tmp = t_1;
	} else if (z <= 1.25e-249) {
		tmp = i * -(y * j);
	} else if (z <= 3.8e-42) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (t * -a)
	tmp = 0
	if z <= -1.46e+138:
		tmp = x * (y * z)
	elif z <= -25000000.0:
		tmp = t_1
	elif z <= -2.5e-51:
		tmp = t_2
	elif z <= -9e-292:
		tmp = t_1
	elif z <= 1.25e-249:
		tmp = i * -(y * j)
	elif z <= 3.8e-42:
		tmp = t_2
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (z <= -1.46e+138)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -25000000.0)
		tmp = t_1;
	elseif (z <= -2.5e-51)
		tmp = t_2;
	elseif (z <= -9e-292)
		tmp = t_1;
	elseif (z <= 1.25e-249)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (z <= 3.8e-42)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (t * -a);
	tmp = 0.0;
	if (z <= -1.46e+138)
		tmp = x * (y * z);
	elseif (z <= -25000000.0)
		tmp = t_1;
	elseif (z <= -2.5e-51)
		tmp = t_2;
	elseif (z <= -9e-292)
		tmp = t_1;
	elseif (z <= 1.25e-249)
		tmp = i * -(y * j);
	elseif (z <= 3.8e-42)
		tmp = t_2;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.46e+138], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -25000000.0], t$95$1, If[LessEqual[z, -2.5e-51], t$95$2, If[LessEqual[z, -9e-292], t$95$1, If[LessEqual[z, 1.25e-249], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.8e-42], t$95$2, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.45999999999999995e138

   1. Initial program 57.7%

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

   2. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. *-commutative 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in z around inf 52.4%

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

   if -1.45999999999999995e138 < z < -2.5e7 or -2.50000000000000002e-51 < z < -8.99999999999999913e-292

   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 a around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in c around inf 42.3%

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

      1. *-commutative 42.3%

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

   7. Simplified 42.3%

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

   if -2.5e7 < z < -2.50000000000000002e-51 or 1.24999999999999997e-249 < z < 3.80000000000000017e-42

   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 x around inf 49.1%

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

      1. *-commutative 49.1%

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

      2. *-commutative 49.1%

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

   4. Simplified 49.1%

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

   5. Taylor expanded in z around 0 39.4%

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

      1. neg-mul-1 39.4%

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

      2. distribute-lft-neg-in 39.4%

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

      3. *-commutative 39.4%

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

   7. Simplified 39.4%

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

   if -8.99999999999999913e-292 < z < 1.24999999999999997e-249

   1. Initial program 65.4%

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

   2. Taylor expanded in c around -inf 60.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in i around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in b around 0 51.1%

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

      1. associate-*r* 51.1%

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

      2. neg-mul-1 51.1%

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

      3. *-commutative 51.1%

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

   10. Simplified 51.1%

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

   if 3.80000000000000017e-42 < z

   1. Initial program 66.5%

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

   2. Taylor expanded in y around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

   4. Simplified 48.0%

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

   5. Taylor expanded in z around inf 42.8%

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

      1. *-commutative 42.8%

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

   7. Simplified 42.8%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -25000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 21: 39.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= z -3.8e+138)
     (* x (* y z))
     (if (<= z -1.8e-298)
       t_1
       (if (<= z 3.5e-272)
         (* i (- (* y j)))
         (if (<= z 9.5e-42) t_1 (* y (* x z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -3.8e+138) {
		tmp = x * (y * z);
	} else if (z <= -1.8e-298) {
		tmp = t_1;
	} else if (z <= 3.5e-272) {
		tmp = i * -(y * j);
	} else if (z <= 9.5e-42) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (z <= (-3.8d+138)) then
        tmp = x * (y * z)
    else if (z <= (-1.8d-298)) then
        tmp = t_1
    else if (z <= 3.5d-272) then
        tmp = i * -(y * j)
    else if (z <= 9.5d-42) then
        tmp = t_1
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -3.8e+138) {
		tmp = x * (y * z);
	} else if (z <= -1.8e-298) {
		tmp = t_1;
	} else if (z <= 3.5e-272) {
		tmp = i * -(y * j);
	} else if (z <= 9.5e-42) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if z <= -3.8e+138:
		tmp = x * (y * z)
	elif z <= -1.8e-298:
		tmp = t_1
	elif z <= 3.5e-272:
		tmp = i * -(y * j)
	elif z <= 9.5e-42:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (z <= -3.8e+138)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -1.8e-298)
		tmp = t_1;
	elseif (z <= 3.5e-272)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (z <= 9.5e-42)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (z <= -3.8e+138)
		tmp = x * (y * z);
	elseif (z <= -1.8e-298)
		tmp = t_1;
	elseif (z <= 3.5e-272)
		tmp = i * -(y * j);
	elseif (z <= 9.5e-42)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+138], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-298], t$95$1, If[LessEqual[z, 3.5e-272], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 9.5e-42], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.80000000000000012e138

   1. Initial program 57.7%

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

   2. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. *-commutative 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in z around inf 52.4%

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

   if -3.80000000000000012e138 < z < -1.80000000000000001e-298 or 3.4999999999999997e-272 < z < 9.49999999999999948e-42

   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 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

   4. Simplified 50.6%

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

   if -1.80000000000000001e-298 < z < 3.4999999999999997e-272

   1. Initial program 50.8%

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

   2. Taylor expanded in c around -inf 50.8%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in i around inf 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

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

      3. unsub-neg 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in b around 0 67.2%

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

      1. associate-*r* 67.2%

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

      2. neg-mul-1 67.2%

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

      3. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   if 9.49999999999999948e-42 < z

   1. Initial program 66.5%

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

   2. Taylor expanded in y around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

   4. Simplified 48.0%

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

   5. Taylor expanded in z around inf 42.8%

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

      1. *-commutative 42.8%

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

   7. Simplified 42.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 22: 30.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* c (* a j))))
   (if (<= a -5.5e+70)
     t_2
     (if (<= a 5.5e+33)
       t_1
       (if (<= a 2.05e+70) (* b (* t i)) (if (<= a 8.2e+97) 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 = c * (a * j);
	double tmp;
	if (a <= -5.5e+70) {
		tmp = t_2;
	} else if (a <= 5.5e+33) {
		tmp = t_1;
	} else if (a <= 2.05e+70) {
		tmp = b * (t * i);
	} else if (a <= 8.2e+97) {
		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 = c * (a * j)
    if (a <= (-5.5d+70)) then
        tmp = t_2
    else if (a <= 5.5d+33) then
        tmp = t_1
    else if (a <= 2.05d+70) then
        tmp = b * (t * i)
    else if (a <= 8.2d+97) 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 = c * (a * j);
	double tmp;
	if (a <= -5.5e+70) {
		tmp = t_2;
	} else if (a <= 5.5e+33) {
		tmp = t_1;
	} else if (a <= 2.05e+70) {
		tmp = b * (t * i);
	} else if (a <= 8.2e+97) {
		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 = c * (a * j)
	tmp = 0
	if a <= -5.5e+70:
		tmp = t_2
	elif a <= 5.5e+33:
		tmp = t_1
	elif a <= 2.05e+70:
		tmp = b * (t * i)
	elif a <= 8.2e+97:
		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(c * Float64(a * j))
	tmp = 0.0
	if (a <= -5.5e+70)
		tmp = t_2;
	elseif (a <= 5.5e+33)
		tmp = t_1;
	elseif (a <= 2.05e+70)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 8.2e+97)
		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 = c * (a * j);
	tmp = 0.0;
	if (a <= -5.5e+70)
		tmp = t_2;
	elseif (a <= 5.5e+33)
		tmp = t_1;
	elseif (a <= 2.05e+70)
		tmp = b * (t * i);
	elseif (a <= 8.2e+97)
		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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+70], t$95$2, If[LessEqual[a, 5.5e+33], t$95$1, If[LessEqual[a, 2.05e+70], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+97], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.49999999999999986e70 or 8.19999999999999977e97 < a

   1. Initial program 64.6%

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

   2. Taylor expanded in y around 0 71.3%

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

   3. Taylor expanded in j around inf 37.5%

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

      1. *-commutative 37.5%

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

      2. associate-*l* 40.2%

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

      3. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   if -5.49999999999999986e70 < a < 5.5000000000000006e33 or 2.0500000000000001e70 < a < 8.19999999999999977e97

   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 x around inf 43.0%

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

      1. *-commutative 43.0%

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

      2. *-commutative 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in z around inf 34.8%

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

   if 5.5000000000000006e33 < a < 2.0500000000000001e70

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*l* 77.9%

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

   4. Simplified 77.9%

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

      1. associate-+l- 77.9%

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

      2. associate-*r* 77.9%

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

      3. fma-neg 77.9%

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

      4. *-commutative 77.9%

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

      5. *-commutative 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in t around inf 49.6%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 23: 30.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= a -2.7e+70)
     (* j (* a c))
     (if (<= a 5.8e+33)
       t_1
       (if (<= a 1.95e+70)
         (* b (* t i))
         (if (<= a 3.4e+99) t_1 (* c (* a j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (a <= -2.7e+70) {
		tmp = j * (a * c);
	} else if (a <= 5.8e+33) {
		tmp = t_1;
	} else if (a <= 1.95e+70) {
		tmp = b * (t * i);
	} else if (a <= 3.4e+99) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (a <= (-2.7d+70)) then
        tmp = j * (a * c)
    else if (a <= 5.8d+33) then
        tmp = t_1
    else if (a <= 1.95d+70) then
        tmp = b * (t * i)
    else if (a <= 3.4d+99) then
        tmp = t_1
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (a <= -2.7e+70) {
		tmp = j * (a * c);
	} else if (a <= 5.8e+33) {
		tmp = t_1;
	} else if (a <= 1.95e+70) {
		tmp = b * (t * i);
	} else if (a <= 3.4e+99) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if a <= -2.7e+70:
		tmp = j * (a * c)
	elif a <= 5.8e+33:
		tmp = t_1
	elif a <= 1.95e+70:
		tmp = b * (t * i)
	elif a <= 3.4e+99:
		tmp = t_1
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (a <= -2.7e+70)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= 5.8e+33)
		tmp = t_1;
	elseif (a <= 1.95e+70)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 3.4e+99)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (a <= -2.7e+70)
		tmp = j * (a * c);
	elseif (a <= 5.8e+33)
		tmp = t_1;
	elseif (a <= 1.95e+70)
		tmp = b * (t * i);
	elseif (a <= 3.4e+99)
		tmp = t_1;
	else
		tmp = c * (a * j);
	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]}, If[LessEqual[a, -2.7e+70], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+33], t$95$1, If[LessEqual[a, 1.95e+70], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+99], t$95$1, N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7e70

   1. Initial program 71.2%

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

   2. Taylor expanded in y around 0 76.5%

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

   3. Taylor expanded in j around inf 39.4%

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

      1. associate-*r* 43.0%

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

   5. Simplified 43.0%

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

   if -2.7e70 < a < 5.80000000000000049e33 or 1.94999999999999987e70 < a < 3.39999999999999984e99

   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 x around inf 43.0%

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

      1. *-commutative 43.0%

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

      2. *-commutative 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in z around inf 34.8%

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

   if 5.80000000000000049e33 < a < 1.94999999999999987e70

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*l* 77.9%

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

   4. Simplified 77.9%

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

      1. associate-+l- 77.9%

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

      2. associate-*r* 77.9%

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

      3. fma-neg 77.9%

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

      4. *-commutative 77.9%

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

      5. *-commutative 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in t around inf 49.6%

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

   if 3.39999999999999984e99 < a

   1. Initial program 57.3%

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

   2. Taylor expanded in y around 0 65.5%

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

   3. Taylor expanded in j around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*l* 40.9%

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

      3. *-commutative 40.9%

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

   5. Simplified 40.9%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 24: 29.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+49} \lor \neg \left(t \leq 3.7 \cdot 10^{-20}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -7.6e+49) (not (<= t 3.7e-20))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -7.6e+49) || !(t <= 3.7e-20)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-7.6d+49)) .or. (.not. (t <= 3.7d-20))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -7.6e+49) || !(t <= 3.7e-20)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -7.6e+49) or not (t <= 3.7e-20):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -7.6e+49) || !(t <= 3.7e-20))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -7.6e+49) || ~((t <= 3.7e-20)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -7.6e+49], N[Not[LessEqual[t, 3.7e-20]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5999999999999997e49 or 3.7000000000000001e-20 < t

   1. Initial program 64.3%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*l* 51.8%

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

   4. Simplified 51.8%

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

      1. associate-+l- 51.8%

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

      2. associate-*r* 51.8%

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

      3. fma-neg 52.7%

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

      4. *-commutative 52.7%

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

      5. *-commutative 52.7%

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

   6. Applied egg-rr 52.7%

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

   7. Taylor expanded in t around inf 33.5%

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

   if -7.5999999999999997e49 < t < 3.7000000000000001e-20

   1. Initial program 79.6%

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

   2. Taylor expanded in a around inf 34.8%

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

      1. +-commutative 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. Simplified 34.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   5. Taylor expanded in c around inf 26.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 26.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 26.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+49} \lor \neg \left(t \leq 3.7 \cdot 10^{-20}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 25: 22.3% 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 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 a around inf 36.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
3. Step-by-step derivation

   1. +-commutative 36.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

4. Simplified 36.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

5. Taylor expanded in c around inf 21.4%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
6. Step-by-step derivation

   1. *-commutative 21.4%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

7. Simplified 21.4%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Final simplification 21.4%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.6% 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 2023308 
(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)))))