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

Percentage Accurate: 73.2% → 81.8%

Time: 39.7s

Alternatives: 23

Speedup: 0.5×

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

Specification

Math

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

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: 73.2% 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: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. *-commutative 55.1%

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

   5. Simplified 55.1%

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

4. Final simplification 85.3%

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

Alternative 2: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := t_1 + t_2\\ t_5 := t_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -2750:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -6.3 \cdot 10^{-180}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -2.15 \cdot 10^{-279}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + t_2\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-117}:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{+36}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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))))
        (t_3 (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_4 (+ t_1 t_2))
        (t_5 (- t_2 (* x (- (* t a) (* y z))))))
   (if (<= j -4e+78)
     t_3
     (if (<= j -1.35e+22)
       t_4
       (if (<= j -2750.0)
         t_3
         (if (<= j -6.3e-180)
           t_5
           (if (<= j -2.15e-279)
             t_4
             (if (<= j 5.8e-171)
               (+ (* z (* x y)) t_2)
               (if (<= j 9.2e-117)
                 (+ t_1 (* y (- (* x z) (* i j))))
                 (if (<= j 7.8e+36) t_5 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_4 = t_1 + t_2;
	double t_5 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -4e+78) {
		tmp = t_3;
	} else if (j <= -1.35e+22) {
		tmp = t_4;
	} else if (j <= -2750.0) {
		tmp = t_3;
	} else if (j <= -6.3e-180) {
		tmp = t_5;
	} else if (j <= -2.15e-279) {
		tmp = t_4;
	} else if (j <= 5.8e-171) {
		tmp = (z * (x * y)) + t_2;
	} else if (j <= 9.2e-117) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else if (j <= 7.8e+36) {
		tmp = t_5;
	} 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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_4 = t_1 + t_2
    t_5 = t_2 - (x * ((t * a) - (y * z)))
    if (j <= (-4d+78)) then
        tmp = t_3
    else if (j <= (-1.35d+22)) then
        tmp = t_4
    else if (j <= (-2750.0d0)) then
        tmp = t_3
    else if (j <= (-6.3d-180)) then
        tmp = t_5
    else if (j <= (-2.15d-279)) then
        tmp = t_4
    else if (j <= 5.8d-171) then
        tmp = (z * (x * y)) + t_2
    else if (j <= 9.2d-117) then
        tmp = t_1 + (y * ((x * z) - (i * j)))
    else if (j <= 7.8d+36) then
        tmp = t_5
    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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_4 = t_1 + t_2;
	double t_5 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -4e+78) {
		tmp = t_3;
	} else if (j <= -1.35e+22) {
		tmp = t_4;
	} else if (j <= -2750.0) {
		tmp = t_3;
	} else if (j <= -6.3e-180) {
		tmp = t_5;
	} else if (j <= -2.15e-279) {
		tmp = t_4;
	} else if (j <= 5.8e-171) {
		tmp = (z * (x * y)) + t_2;
	} else if (j <= 9.2e-117) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else if (j <= 7.8e+36) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	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))
	t_3 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_4 = t_1 + t_2
	t_5 = t_2 - (x * ((t * a) - (y * z)))
	tmp = 0
	if j <= -4e+78:
		tmp = t_3
	elif j <= -1.35e+22:
		tmp = t_4
	elif j <= -2750.0:
		tmp = t_3
	elif j <= -6.3e-180:
		tmp = t_5
	elif j <= -2.15e-279:
		tmp = t_4
	elif j <= 5.8e-171:
		tmp = (z * (x * y)) + t_2
	elif j <= 9.2e-117:
		tmp = t_1 + (y * ((x * z) - (i * j)))
	elif j <= 7.8e+36:
		tmp = t_5
	else:
		tmp = t_3
	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)))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_4 = Float64(t_1 + t_2)
	t_5 = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (j <= -4e+78)
		tmp = t_3;
	elseif (j <= -1.35e+22)
		tmp = t_4;
	elseif (j <= -2750.0)
		tmp = t_3;
	elseif (j <= -6.3e-180)
		tmp = t_5;
	elseif (j <= -2.15e-279)
		tmp = t_4;
	elseif (j <= 5.8e-171)
		tmp = Float64(Float64(z * Float64(x * y)) + t_2);
	elseif (j <= 9.2e-117)
		tmp = Float64(t_1 + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (j <= 7.8e+36)
		tmp = t_5;
	else
		tmp = t_3;
	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));
	t_3 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_4 = t_1 + t_2;
	t_5 = t_2 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (j <= -4e+78)
		tmp = t_3;
	elseif (j <= -1.35e+22)
		tmp = t_4;
	elseif (j <= -2750.0)
		tmp = t_3;
	elseif (j <= -6.3e-180)
		tmp = t_5;
	elseif (j <= -2.15e-279)
		tmp = t_4;
	elseif (j <= 5.8e-171)
		tmp = (z * (x * y)) + t_2;
	elseif (j <= 9.2e-117)
		tmp = t_1 + (y * ((x * z) - (i * j)));
	elseif (j <= 7.8e+36)
		tmp = t_5;
	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[(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]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 + t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+78], t$95$3, If[LessEqual[j, -1.35e+22], t$95$4, If[LessEqual[j, -2750.0], t$95$3, If[LessEqual[j, -6.3e-180], t$95$5, If[LessEqual[j, -2.15e-279], t$95$4, If[LessEqual[j, 5.8e-171], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[j, 9.2e-117], N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e+36], t$95$5, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.00000000000000003e78 or -1.3500000000000001e22 < j < -2750 or 7.80000000000000042e36 < j

   1. Initial program 83.3%

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

   3. Taylor expanded in b around 0 79.6%

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

   if -4.00000000000000003e78 < j < -1.3500000000000001e22 or -6.2999999999999996e-180 < j < -2.15000000000000003e-279

   1. Initial program 70.7%

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

   3. Taylor expanded in y around 0 87.3%

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

      1. cancel-sign-sub-inv 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-*r* 87.3%

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

      4. *-commutative 87.3%

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

      5. distribute-rgt-in 90.0%

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

      6. +-commutative 90.0%

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

      7. mul-1-neg 90.0%

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

      8. unsub-neg 90.0%

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

      9. *-commutative 90.0%

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

      10. *-commutative 90.0%

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

      11. distribute-lft-neg-in 90.0%

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

      12. distribute-rgt-neg-in 90.0%

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

      13. neg-sub0 90.0%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      14. associate--r- 90.0%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      15. neg-sub0 90.0%

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

      16. +-commutative 90.0%

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

      17. sub-neg 90.0%

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

   5. Simplified 90.0%

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

   if -2750 < j < -6.2999999999999996e-180 or 9.19999999999999978e-117 < j < 7.80000000000000042e36

   1. Initial program 81.0%

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

   3. Taylor expanded in j around 0 79.8%

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

   if -2.15000000000000003e-279 < j < 5.7999999999999997e-171

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 71.5%

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

      2. pow3 71.5%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.5%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 71.5%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 78.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 78.0%

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

      2. associate-*r* 78.0%

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

      3. fma-neg 81.3%

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

      4. *-lft-identity 81.3%

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

      5. *-commutative 81.3%

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

      6. *-commutative 81.3%

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

      7. fma-neg 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around inf 78.2%

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

      1. associate-*r* 81.4%

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

   10. Simplified 81.4%

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

   if 5.7999999999999997e-171 < j < 9.19999999999999978e-117

   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. Add Preprocessing

   3. Taylor expanded in b around 0 46.0%

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

   4. Taylor expanded in y around 0 81.6%

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

      1. associate-+r+ 81.6%

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

      2. mul-1-neg 81.6%

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

      3. *-commutative 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. distribute-lft-in 81.6%

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

      6. +-commutative 81.6%

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

      7. *-commutative 81.6%

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

      8. sub-neg 81.6%

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

      9. *-commutative 81.6%

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

      10. +-commutative 81.6%

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

      11. mul-1-neg 81.6%

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

      12. unsub-neg 81.6%

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

      13. *-commutative 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2750:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -6.3 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq -2.15 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) + t_1\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.3 \lor \neg \left(b \leq 1.35 \cdot 10^{+63}\right) \land b \leq 1.36 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= b -5.4e+23)
     t_2
     (if (<= b -6.5e-52)
       t_3
       (if (<= b -1.05e-108)
         (- (+ (* b (* t i)) t_1) (* b (* z c)))
         (if (or (<= b 3.3) (and (not (<= b 1.35e+63)) (<= b 1.36e+80)))
           (+ (* a (- (* c j) (* x t))) t_3)
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -5.4e+23) {
		tmp = t_2;
	} else if (b <= -6.5e-52) {
		tmp = t_3;
	} else if (b <= -1.05e-108) {
		tmp = ((b * (t * i)) + t_1) - (b * (z * c));
	} else if ((b <= 3.3) || (!(b <= 1.35e+63) && (b <= 1.36e+80))) {
		tmp = (a * ((c * j) - (x * t))) + t_3;
	} 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)
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    t_3 = y * ((x * z) - (i * j))
    if (b <= (-5.4d+23)) then
        tmp = t_2
    else if (b <= (-6.5d-52)) then
        tmp = t_3
    else if (b <= (-1.05d-108)) then
        tmp = ((b * (t * i)) + t_1) - (b * (z * c))
    else if ((b <= 3.3d0) .or. (.not. (b <= 1.35d+63)) .and. (b <= 1.36d+80)) then
        tmp = (a * ((c * j) - (x * t))) + t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -5.4e+23) {
		tmp = t_2;
	} else if (b <= -6.5e-52) {
		tmp = t_3;
	} else if (b <= -1.05e-108) {
		tmp = ((b * (t * i)) + t_1) - (b * (z * c));
	} else if ((b <= 3.3) || (!(b <= 1.35e+63) && (b <= 1.36e+80))) {
		tmp = (a * ((c * j) - (x * t))) + t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if b <= -5.4e+23:
		tmp = t_2
	elif b <= -6.5e-52:
		tmp = t_3
	elif b <= -1.05e-108:
		tmp = ((b * (t * i)) + t_1) - (b * (z * c))
	elif (b <= 3.3) or (not (b <= 1.35e+63) and (b <= 1.36e+80)):
		tmp = (a * ((c * j) - (x * t))) + t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (b <= -5.4e+23)
		tmp = t_2;
	elseif (b <= -6.5e-52)
		tmp = t_3;
	elseif (b <= -1.05e-108)
		tmp = Float64(Float64(Float64(b * Float64(t * i)) + t_1) - Float64(b * Float64(z * c)));
	elseif ((b <= 3.3) || (!(b <= 1.35e+63) && (b <= 1.36e+80)))
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (b <= -5.4e+23)
		tmp = t_2;
	elseif (b <= -6.5e-52)
		tmp = t_3;
	elseif (b <= -1.05e-108)
		tmp = ((b * (t * i)) + t_1) - (b * (z * c));
	elseif ((b <= 3.3) || (~((b <= 1.35e+63)) && (b <= 1.36e+80)))
		tmp = (a * ((c * j) - (x * t))) + t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e+23], t$95$2, If[LessEqual[b, -6.5e-52], t$95$3, If[LessEqual[b, -1.05e-108], N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3.3], And[N[Not[LessEqual[b, 1.35e+63]], $MachinePrecision], LessEqual[b, 1.36e+80]]], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.3999999999999997e23 or 3.2999999999999998 < b < 1.35000000000000009e63 or 1.36000000000000013e80 < b

   1. Initial program 81.3%

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

      1. add-cube-cbrt 81.2%

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

      2. pow3 81.2%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.2%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.2%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 72.2%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 72.2%

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

      2. associate-*r* 72.2%

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

      3. fma-neg 74.7%

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

      4. *-lft-identity 74.7%

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

      5. *-commutative 74.7%

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

      6. *-commutative 74.7%

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

      7. fma-neg 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around inf 66.0%

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

      1. associate-*r* 69.1%

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

   10. Simplified 69.1%

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

   if -5.3999999999999997e23 < b < -6.5e-52

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. unsub-neg 86.0%

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

      4. *-commutative 86.0%

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

   5. Simplified 86.0%

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

   if -6.5e-52 < b < -1.05e-108

   1. Initial program 85.4%

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

      1. add-cube-cbrt 85.4%

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

      2. pow3 85.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 85.4%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 85.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 64.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 64.8%

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

      2. associate-*r* 64.8%

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

      3. fma-neg 64.8%

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

      4. *-lft-identity 64.8%

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

      5. *-commutative 64.8%

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

      6. *-commutative 64.8%

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

      7. fma-neg 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in i around 0 64.9%

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

   9. Taylor expanded in y around inf 64.4%

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

       1. associate-*r* 71.6%

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

   11. Simplified 71.7%

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

   if -1.05e-108 < b < 3.2999999999999998 or 1.35000000000000009e63 < b < 1.36000000000000013e80

   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. Add Preprocessing

   3. Taylor expanded in b around 0 74.2%

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

   4. Taylor expanded in y around 0 71.9%

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

      1. associate-+r+ 71.9%

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

      2. mul-1-neg 71.9%

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

      3. *-commutative 71.9%

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

      4. distribute-rgt-neg-in 71.9%

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

      5. distribute-lft-in 74.7%

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

      6. +-commutative 74.7%

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

      7. *-commutative 74.7%

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

      8. sub-neg 74.7%

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

      9. *-commutative 74.7%

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

      10. +-commutative 74.7%

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

      11. mul-1-neg 74.7%

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

      12. unsub-neg 74.7%

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

      13. *-commutative 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) + z \cdot \left(x \cdot y\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.3 \lor \neg \left(b \leq 1.35 \cdot 10^{+63}\right) \land b \leq 1.36 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;j \leq -3500:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) + t_3\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-279}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + t_1\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;t_4 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (- t_1 (* x (- (* t a) (* y z)))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (* a (- (* c j) (* x t)))))
   (if (<= j -3500.0)
     (- (+ (* b (* t i)) t_3) (* b (* z c)))
     (if (<= j -5.7e-180)
       t_2
       (if (<= j -2.5e-279)
         (+ t_4 t_1)
         (if (<= j 2.2e-173)
           (+ (* z (* x y)) t_1)
           (if (<= j 1.05e-116)
             (+ t_4 (* y (- (* x z) (* i j))))
             (if (<= j 1.6e+29) t_2 (+ t_3 (* x (- (* y z) (* t a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = a * ((c * j) - (x * t));
	double tmp;
	if (j <= -3500.0) {
		tmp = ((b * (t * i)) + t_3) - (b * (z * c));
	} else if (j <= -5.7e-180) {
		tmp = t_2;
	} else if (j <= -2.5e-279) {
		tmp = t_4 + t_1;
	} else if (j <= 2.2e-173) {
		tmp = (z * (x * y)) + t_1;
	} else if (j <= 1.05e-116) {
		tmp = t_4 + (y * ((x * z) - (i * j)));
	} else if (j <= 1.6e+29) {
		tmp = t_2;
	} else {
		tmp = t_3 + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = t_1 - (x * ((t * a) - (y * z)))
    t_3 = j * ((a * c) - (y * i))
    t_4 = a * ((c * j) - (x * t))
    if (j <= (-3500.0d0)) then
        tmp = ((b * (t * i)) + t_3) - (b * (z * c))
    else if (j <= (-5.7d-180)) then
        tmp = t_2
    else if (j <= (-2.5d-279)) then
        tmp = t_4 + t_1
    else if (j <= 2.2d-173) then
        tmp = (z * (x * y)) + t_1
    else if (j <= 1.05d-116) then
        tmp = t_4 + (y * ((x * z) - (i * j)))
    else if (j <= 1.6d+29) then
        tmp = t_2
    else
        tmp = t_3 + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = a * ((c * j) - (x * t));
	double tmp;
	if (j <= -3500.0) {
		tmp = ((b * (t * i)) + t_3) - (b * (z * c));
	} else if (j <= -5.7e-180) {
		tmp = t_2;
	} else if (j <= -2.5e-279) {
		tmp = t_4 + t_1;
	} else if (j <= 2.2e-173) {
		tmp = (z * (x * y)) + t_1;
	} else if (j <= 1.05e-116) {
		tmp = t_4 + (y * ((x * z) - (i * j)));
	} else if (j <= 1.6e+29) {
		tmp = t_2;
	} else {
		tmp = t_3 + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = t_1 - (x * ((t * a) - (y * z)))
	t_3 = j * ((a * c) - (y * i))
	t_4 = a * ((c * j) - (x * t))
	tmp = 0
	if j <= -3500.0:
		tmp = ((b * (t * i)) + t_3) - (b * (z * c))
	elif j <= -5.7e-180:
		tmp = t_2
	elif j <= -2.5e-279:
		tmp = t_4 + t_1
	elif j <= 2.2e-173:
		tmp = (z * (x * y)) + t_1
	elif j <= 1.05e-116:
		tmp = t_4 + (y * ((x * z) - (i * j)))
	elif j <= 1.6e+29:
		tmp = t_2
	else:
		tmp = t_3 + (x * ((y * z) - (t * a)))
	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(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (j <= -3500.0)
		tmp = Float64(Float64(Float64(b * Float64(t * i)) + t_3) - Float64(b * Float64(z * c)));
	elseif (j <= -5.7e-180)
		tmp = t_2;
	elseif (j <= -2.5e-279)
		tmp = Float64(t_4 + t_1);
	elseif (j <= 2.2e-173)
		tmp = Float64(Float64(z * Float64(x * y)) + t_1);
	elseif (j <= 1.05e-116)
		tmp = Float64(t_4 + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (j <= 1.6e+29)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	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 = t_1 - (x * ((t * a) - (y * z)));
	t_3 = j * ((a * c) - (y * i));
	t_4 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (j <= -3500.0)
		tmp = ((b * (t * i)) + t_3) - (b * (z * c));
	elseif (j <= -5.7e-180)
		tmp = t_2;
	elseif (j <= -2.5e-279)
		tmp = t_4 + t_1;
	elseif (j <= 2.2e-173)
		tmp = (z * (x * y)) + t_1;
	elseif (j <= 1.05e-116)
		tmp = t_4 + (y * ((x * z) - (i * j)));
	elseif (j <= 1.6e+29)
		tmp = t_2;
	else
		tmp = t_3 + (x * ((y * z) - (t * a)));
	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[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3500.0], N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.7e-180], t$95$2, If[LessEqual[j, -2.5e-279], N[(t$95$4 + t$95$1), $MachinePrecision], If[LessEqual[j, 2.2e-173], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 1.05e-116], N[(t$95$4 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e+29], t$95$2, N[(t$95$3 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3500

   1. Initial program 84.7%

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

      1. add-cube-cbrt 84.6%

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

      2. pow3 84.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 84.6%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 84.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 80.7%

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

   if -3500 < j < -5.69999999999999977e-180 or 1.05e-116 < j < 1.59999999999999993e29

   1. Initial program 81.0%

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

   3. Taylor expanded in j around 0 79.8%

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

   if -5.69999999999999977e-180 < j < -2.49999999999999984e-279

   1. Initial program 63.2%

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

   3. Taylor expanded in y around 0 91.5%

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

      1. cancel-sign-sub-inv 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. distribute-rgt-in 91.5%

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

      6. +-commutative 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

      9. *-commutative 91.5%

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

      10. *-commutative 91.5%

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

      11. distribute-lft-neg-in 91.5%

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

      12. distribute-rgt-neg-in 91.5%

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

      13. neg-sub0 91.5%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      14. associate--r- 91.5%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      15. neg-sub0 91.5%

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

      16. +-commutative 91.5%

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

      17. sub-neg 91.5%

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

   5. Simplified 91.5%

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

   if -2.49999999999999984e-279 < j < 2.1999999999999999e-173

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 71.5%

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

      2. pow3 71.5%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.5%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 71.5%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 78.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 78.0%

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

      2. associate-*r* 78.0%

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

      3. fma-neg 81.3%

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

      4. *-lft-identity 81.3%

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

      5. *-commutative 81.3%

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

      6. *-commutative 81.3%

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

      7. fma-neg 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around inf 78.2%

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

      1. associate-*r* 81.4%

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

   10. Simplified 81.4%

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

   if 2.1999999999999999e-173 < j < 1.05e-116

   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. Add Preprocessing

   3. Taylor expanded in b around 0 46.0%

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

   4. Taylor expanded in y around 0 81.6%

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

      1. associate-+r+ 81.6%

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

      2. mul-1-neg 81.6%

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

      3. *-commutative 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. distribute-lft-in 81.6%

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

      6. +-commutative 81.6%

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

      7. *-commutative 81.6%

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

      8. sub-neg 81.6%

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

      9. *-commutative 81.6%

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

      10. +-commutative 81.6%

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

      11. mul-1-neg 81.6%

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

      12. unsub-neg 81.6%

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

      13. *-commutative 81.6%

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

   6. Simplified 81.6%

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

   if 1.59999999999999993e29 < j

   1. Initial program 82.0%

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

   3. Taylor expanded in b around 0 82.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3500:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.34 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -5.5e+66)
     t_1
     (if (<= a 2.85e-242)
       (+ (* z (* x y)) (* b (- (* t i) (* z c))))
       (if (<= a 1.34e-135)
         (* y (- (* x z) (* i j)))
         (if (<= a 8e-66)
           (* t (- (* b i) (* x a)))
           (if (<= a 2.45e+64)
             (+ (* x (- (* y z) (* t a))) (* j (* a c)))
             (if (<= a 2.8e+102) (* i (- (* t b) (* y j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.5e+66) {
		tmp = t_1;
	} else if (a <= 2.85e-242) {
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	} else if (a <= 1.34e-135) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8e-66) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 2.45e+64) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (a <= 2.8e+102) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-5.5d+66)) then
        tmp = t_1
    else if (a <= 2.85d-242) then
        tmp = (z * (x * y)) + (b * ((t * i) - (z * c)))
    else if (a <= 1.34d-135) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 8d-66) then
        tmp = t * ((b * i) - (x * a))
    else if (a <= 2.45d+64) then
        tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
    else if (a <= 2.8d+102) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.5e+66) {
		tmp = t_1;
	} else if (a <= 2.85e-242) {
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	} else if (a <= 1.34e-135) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8e-66) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 2.45e+64) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (a <= 2.8e+102) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5.5e+66:
		tmp = t_1
	elif a <= 2.85e-242:
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)))
	elif a <= 1.34e-135:
		tmp = y * ((x * z) - (i * j))
	elif a <= 8e-66:
		tmp = t * ((b * i) - (x * a))
	elif a <= 2.45e+64:
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
	elif a <= 2.8e+102:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.5e+66)
		tmp = t_1;
	elseif (a <= 2.85e-242)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 1.34e-135)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 8e-66)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (a <= 2.45e+64)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(a * c)));
	elseif (a <= 2.8e+102)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5.5e+66)
		tmp = t_1;
	elseif (a <= 2.85e-242)
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	elseif (a <= 1.34e-135)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 8e-66)
		tmp = t * ((b * i) - (x * a));
	elseif (a <= 2.45e+64)
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	elseif (a <= 2.8e+102)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+66], t$95$1, If[LessEqual[a, 2.85e-242], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.34e-135], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-66], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+64], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+102], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -5.5e66 or 2.80000000000000018e102 < a

   1. Initial program 66.8%

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

   3. Taylor expanded in a around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -5.5e66 < a < 2.85000000000000016e-242

   1. Initial program 91.1%

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

      1. add-cube-cbrt 91.0%

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

      2. pow3 90.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 90.9%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 90.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 71.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 71.8%

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

      2. associate-*r* 71.8%

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

      3. fma-neg 72.8%

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

      4. *-lft-identity 72.8%

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

      5. *-commutative 72.8%

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

      6. *-commutative 72.8%

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

      7. fma-neg 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in y around inf 65.7%

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

      1. associate-*r* 67.8%

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

   10. Simplified 67.8%

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

   if 2.85000000000000016e-242 < a < 1.34e-135

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if 1.34e-135 < a < 7.9999999999999998e-66

   1. Initial program 76.3%

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

      1. add-cube-cbrt 75.9%

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

      2. pow3 75.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 64.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 64.1%

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

      2. associate-*r* 64.1%

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

      3. fma-neg 64.1%

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

      4. *-lft-identity 64.1%

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

      5. *-commutative 64.1%

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

      6. *-commutative 64.1%

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

      7. fma-neg 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in i around 0 64.1%

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

   9. Taylor expanded in t around inf 54.7%

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

       1. +-commutative 54.7%

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

       2. mul-1-neg 54.7%

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

       3. unsub-neg 54.7%

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

       4. *-commutative 54.7%

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

   11. Simplified 54.7%

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

   if 7.9999999999999998e-66 < a < 2.4500000000000001e64

   1. Initial program 80.8%

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

   3. Taylor expanded in b around 0 72.0%

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

   4. Taylor expanded in a around inf 72.3%

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

   if 2.4500000000000001e64 < a < 2.80000000000000018e102

   1. Initial program 35.7%

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

      1. prod-diff 34.0%

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

      2. *-commutative 34.0%

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

      3. fma-neg 34.0%

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

      4. distribute-rgt-in 34.0%

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

      5. *-commutative 34.0%

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

      6. *-commutative 34.0%

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

   4. Applied egg-rr 34.0%

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

   5. Taylor expanded in i around inf 79.8%

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

      1. sub-neg 79.8%

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

      2. mul-1-neg 79.8%

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

      3. mul-1-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. remove-double-neg 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in i around 0 79.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.34 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-242}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) + z \cdot \left(x \cdot y\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.1e+66)
     t_1
     (if (<= a 6.5e-242)
       (- (+ (* b (* t i)) (* z (* x y))) (* b (* z c)))
       (if (<= a 1.32e-135)
         (* y (- (* x z) (* i j)))
         (if (<= a 1.25e-65)
           (* t (- (* b i) (* x a)))
           (if (<= a 2.35e+64)
             (+ (* x (- (* y z) (* t a))) (* j (* a c)))
             (if (<= a 7.2e+101) (* i (- (* t b) (* y j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.1e+66) {
		tmp = t_1;
	} else if (a <= 6.5e-242) {
		tmp = ((b * (t * i)) + (z * (x * y))) - (b * (z * c));
	} else if (a <= 1.32e-135) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.25e-65) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 2.35e+64) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (a <= 7.2e+101) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.1d+66)) then
        tmp = t_1
    else if (a <= 6.5d-242) then
        tmp = ((b * (t * i)) + (z * (x * y))) - (b * (z * c))
    else if (a <= 1.32d-135) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 1.25d-65) then
        tmp = t * ((b * i) - (x * a))
    else if (a <= 2.35d+64) then
        tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
    else if (a <= 7.2d+101) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.1e+66) {
		tmp = t_1;
	} else if (a <= 6.5e-242) {
		tmp = ((b * (t * i)) + (z * (x * y))) - (b * (z * c));
	} else if (a <= 1.32e-135) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.25e-65) {
		tmp = t * ((b * i) - (x * a));
	} else if (a <= 2.35e+64) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (a <= 7.2e+101) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.1e+66:
		tmp = t_1
	elif a <= 6.5e-242:
		tmp = ((b * (t * i)) + (z * (x * y))) - (b * (z * c))
	elif a <= 1.32e-135:
		tmp = y * ((x * z) - (i * j))
	elif a <= 1.25e-65:
		tmp = t * ((b * i) - (x * a))
	elif a <= 2.35e+64:
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
	elif a <= 7.2e+101:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e+66)
		tmp = t_1;
	elseif (a <= 6.5e-242)
		tmp = Float64(Float64(Float64(b * Float64(t * i)) + Float64(z * Float64(x * y))) - Float64(b * Float64(z * c)));
	elseif (a <= 1.32e-135)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 1.25e-65)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (a <= 2.35e+64)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(a * c)));
	elseif (a <= 7.2e+101)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e+66)
		tmp = t_1;
	elseif (a <= 6.5e-242)
		tmp = ((b * (t * i)) + (z * (x * y))) - (b * (z * c));
	elseif (a <= 1.32e-135)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 1.25e-65)
		tmp = t * ((b * i) - (x * a));
	elseif (a <= 2.35e+64)
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	elseif (a <= 7.2e+101)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+66], t$95$1, If[LessEqual[a, 6.5e-242], N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e-135], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-65], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+64], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+101], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.09999999999999994e66 or 7.20000000000000058e101 < a

   1. Initial program 66.8%

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

   3. Taylor expanded in a around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -4.09999999999999994e66 < a < 6.4999999999999998e-242

   1. Initial program 91.1%

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

      1. add-cube-cbrt 91.0%

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

      2. pow3 90.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 90.9%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 90.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 71.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 71.8%

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

      2. associate-*r* 71.8%

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

      3. fma-neg 72.8%

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

      4. *-lft-identity 72.8%

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

      5. *-commutative 72.8%

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

      6. *-commutative 72.8%

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

      7. fma-neg 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in i around 0 71.8%

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

   9. Taylor expanded in y around inf 65.7%

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

       1. associate-*r* 67.8%

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

   11. Simplified 67.8%

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

   if 6.4999999999999998e-242 < a < 1.32000000000000007e-135

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if 1.32000000000000007e-135 < a < 1.24999999999999996e-65

   1. Initial program 76.3%

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

      1. add-cube-cbrt 75.9%

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

      2. pow3 75.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 64.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 64.1%

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

      2. associate-*r* 64.1%

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

      3. fma-neg 64.1%

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

      4. *-lft-identity 64.1%

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

      5. *-commutative 64.1%

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

      6. *-commutative 64.1%

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

      7. fma-neg 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in i around 0 64.1%

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

   9. Taylor expanded in t around inf 54.7%

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

       1. +-commutative 54.7%

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

       2. mul-1-neg 54.7%

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

       3. unsub-neg 54.7%

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

       4. *-commutative 54.7%

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

   11. Simplified 54.7%

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

   if 1.24999999999999996e-65 < a < 2.35000000000000015e64

   1. Initial program 80.8%

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

   3. Taylor expanded in b around 0 72.0%

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

   4. Taylor expanded in a around inf 72.3%

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

   if 2.35000000000000015e64 < a < 7.20000000000000058e101

   1. Initial program 35.7%

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

      1. prod-diff 34.0%

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

      2. *-commutative 34.0%

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

      3. fma-neg 34.0%

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

      4. distribute-rgt-in 34.0%

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

      5. *-commutative 34.0%

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

      6. *-commutative 34.0%

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

   4. Applied egg-rr 34.0%

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

   5. Taylor expanded in i around inf 79.8%

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

      1. sub-neg 79.8%

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

      2. mul-1-neg 79.8%

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

      3. mul-1-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. remove-double-neg 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in i around 0 79.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-242}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) + z \cdot \left(x \cdot y\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.55e+45)
     t_2
     (if (<= a -1.3e-123)
       (* z (- (* x y) (* b c)))
       (if (<= a -1.35e-167)
         t_1
         (if (<= a 2.35e-239)
           (* b (- (* t i) (* z c)))
           (if (<= a 5.2e+49)
             (* y (- (* x z) (* i j)))
             (if (<= a 8e+101) 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.55e+45) {
		tmp = t_2;
	} else if (a <= -1.3e-123) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= -1.35e-167) {
		tmp = t_1;
	} else if (a <= 2.35e-239) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 5.2e+49) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8e+101) {
		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 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.55d+45)) then
        tmp = t_2
    else if (a <= (-1.3d-123)) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= (-1.35d-167)) then
        tmp = t_1
    else if (a <= 2.35d-239) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 5.2d+49) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 8d+101) 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.55e+45) {
		tmp = t_2;
	} else if (a <= -1.3e-123) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= -1.35e-167) {
		tmp = t_1;
	} else if (a <= 2.35e-239) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 5.2e+49) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.55e+45:
		tmp = t_2
	elif a <= -1.3e-123:
		tmp = z * ((x * y) - (b * c))
	elif a <= -1.35e-167:
		tmp = t_1
	elif a <= 2.35e-239:
		tmp = b * ((t * i) - (z * c))
	elif a <= 5.2e+49:
		tmp = y * ((x * z) - (i * j))
	elif a <= 8e+101:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.55e+45)
		tmp = t_2;
	elseif (a <= -1.3e-123)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= -1.35e-167)
		tmp = t_1;
	elseif (a <= 2.35e-239)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 5.2e+49)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 8e+101)
		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 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.55e+45)
		tmp = t_2;
	elseif (a <= -1.3e-123)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= -1.35e-167)
		tmp = t_1;
	elseif (a <= 2.35e-239)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 5.2e+49)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 8e+101)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e+45], t$95$2, If[LessEqual[a, -1.3e-123], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e-167], t$95$1, If[LessEqual[a, 2.35e-239], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+49], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+101], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5499999999999999e45 or 7.9999999999999998e101 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in a around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -2.5499999999999999e45 < a < -1.29999999999999998e-123

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -1.29999999999999998e-123 < a < -1.35e-167 or 5.19999999999999977e49 < a < 7.9999999999999998e101

   1. Initial program 65.5%

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

      1. prod-diff 64.9%

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

      2. *-commutative 64.9%

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

      3. fma-neg 64.9%

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

      4. distribute-rgt-in 60.9%

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

      5. *-commutative 60.9%

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

      6. *-commutative 60.9%

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

   4. Applied egg-rr 60.9%

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

   5. Taylor expanded in i around inf 65.6%

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

      1. sub-neg 65.6%

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

      2. mul-1-neg 65.6%

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

      3. mul-1-neg 65.6%

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

      4. *-commutative 65.6%

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

      5. remove-double-neg 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in i around 0 65.6%

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

   if -1.35e-167 < a < 2.3500000000000001e-239

   1. Initial program 90.6%

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

   3. Taylor expanded in b around inf 59.9%

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

   if 2.3500000000000001e-239 < a < 5.19999999999999977e49

   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. Add Preprocessing

   3. Taylor expanded in y around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. *-commutative 55.5%

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

   5. Simplified 55.5%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-239}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-108} \lor \neg \left(b \leq 1.75 \cdot 10^{-23}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (+ t_2 (* b (- (* t i) (* z c))))))
   (if (<= b -5e+43)
     t_3
     (if (<= b -5.1e-49)
       t_1
       (if (or (<= b -1e-108) (not (<= b 1.75e-23))) t_3 (+ t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -5e+43) {
		tmp = t_3;
	} else if (b <= -5.1e-49) {
		tmp = t_1;
	} else if ((b <= -1e-108) || !(b <= 1.75e-23)) {
		tmp = t_3;
	} else {
		tmp = t_2 + 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 = y * ((x * z) - (i * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = t_2 + (b * ((t * i) - (z * c)))
    if (b <= (-5d+43)) then
        tmp = t_3
    else if (b <= (-5.1d-49)) then
        tmp = t_1
    else if ((b <= (-1d-108)) .or. (.not. (b <= 1.75d-23))) then
        tmp = t_3
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -5e+43) {
		tmp = t_3;
	} else if (b <= -5.1e-49) {
		tmp = t_1;
	} else if ((b <= -1e-108) || !(b <= 1.75e-23)) {
		tmp = t_3;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = t_2 + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -5e+43:
		tmp = t_3
	elif b <= -5.1e-49:
		tmp = t_1
	elif (b <= -1e-108) or not (b <= 1.75e-23):
		tmp = t_3
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -5e+43)
		tmp = t_3;
	elseif (b <= -5.1e-49)
		tmp = t_1;
	elseif ((b <= -1e-108) || !(b <= 1.75e-23))
		tmp = t_3;
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = t_2 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -5e+43)
		tmp = t_3;
	elseif (b <= -5.1e-49)
		tmp = t_1;
	elseif ((b <= -1e-108) || ~((b <= 1.75e-23)))
		tmp = t_3;
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+43], t$95$3, If[LessEqual[b, -5.1e-49], t$95$1, If[Or[LessEqual[b, -1e-108], N[Not[LessEqual[b, 1.75e-23]], $MachinePrecision]], t$95$3, N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.0000000000000004e43 or -5.10000000000000026e-49 < b < -1.00000000000000004e-108 or 1.74999999999999997e-23 < b

   1. Initial program 81.1%

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

   3. Taylor expanded in y around 0 73.4%

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

      1. cancel-sign-sub-inv 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 73.4%

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

      4. *-commutative 73.4%

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

      5. distribute-rgt-in 74.1%

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

      6. +-commutative 74.1%

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

      7. mul-1-neg 74.1%

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

      8. unsub-neg 74.1%

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

      9. *-commutative 74.1%

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

      10. *-commutative 74.1%

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

      11. distribute-lft-neg-in 74.1%

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

      12. distribute-rgt-neg-in 74.1%

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

      13. neg-sub0 74.1%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      14. associate--r- 74.1%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      15. neg-sub0 74.1%

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

      16. +-commutative 74.1%

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

      17. sub-neg 74.1%

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

   5. Simplified 74.1%

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

   if -5.0000000000000004e43 < b < -5.10000000000000026e-49

   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. Add Preprocessing

   3. Taylor expanded in y around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   if -1.00000000000000004e-108 < b < 1.74999999999999997e-23

   1. Initial program 73.1%

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

   3. Taylor expanded in b around 0 72.7%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. associate-+r+ 71.2%

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

      2. mul-1-neg 71.2%

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

      3. *-commutative 71.2%

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

      4. distribute-rgt-neg-in 71.2%

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

      5. distribute-lft-in 74.3%

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

      6. +-commutative 74.3%

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

      7. *-commutative 74.3%

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

      8. sub-neg 74.3%

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

      9. *-commutative 74.3%

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

      10. +-commutative 74.3%

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

      11. mul-1-neg 74.3%

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

      12. unsub-neg 74.3%

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

      13. *-commutative 74.3%

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

   6. Simplified 74.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-108} \lor \neg \left(b \leq 1.75 \cdot 10^{-23}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-125} \lor \neg \left(b \leq 1.18 \cdot 10^{-23}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))
   (if (<= b -5e+43)
     t_1
     (if (<= b -1.45e-49)
       (* y (- (* x z) (* i j)))
       (if (or (<= b -1.12e-125) (not (<= b 1.18e-23)))
         t_1
         (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -5e+43) {
		tmp = t_1;
	} else if (b <= -1.45e-49) {
		tmp = y * ((x * z) - (i * j));
	} else if ((b <= -1.12e-125) || !(b <= 1.18e-23)) {
		tmp = t_1;
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    if (b <= (-5d+43)) then
        tmp = t_1
    else if (b <= (-1.45d-49)) then
        tmp = y * ((x * z) - (i * j))
    else if ((b <= (-1.12d-125)) .or. (.not. (b <= 1.18d-23))) then
        tmp = t_1
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -5e+43) {
		tmp = t_1;
	} else if (b <= -1.45e-49) {
		tmp = y * ((x * z) - (i * j));
	} else if ((b <= -1.12e-125) || !(b <= 1.18e-23)) {
		tmp = t_1;
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -5e+43:
		tmp = t_1
	elif b <= -1.45e-49:
		tmp = y * ((x * z) - (i * j))
	elif (b <= -1.12e-125) or not (b <= 1.18e-23):
		tmp = t_1
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -5e+43)
		tmp = t_1;
	elseif (b <= -1.45e-49)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif ((b <= -1.12e-125) || !(b <= 1.18e-23))
		tmp = t_1;
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	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))) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -5e+43)
		tmp = t_1;
	elseif (b <= -1.45e-49)
		tmp = y * ((x * z) - (i * j));
	elseif ((b <= -1.12e-125) || ~((b <= 1.18e-23)))
		tmp = t_1;
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+43], t$95$1, If[LessEqual[b, -1.45e-49], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.12e-125], N[Not[LessEqual[b, 1.18e-23]], $MachinePrecision]], t$95$1, N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.0000000000000004e43 or -1.45e-49 < b < -1.11999999999999997e-125 or 1.18e-23 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 71.9%

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

      1. cancel-sign-sub-inv 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-*r* 71.9%

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

      4. *-commutative 71.9%

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

      5. distribute-rgt-in 73.3%

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

      6. +-commutative 73.3%

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

      7. mul-1-neg 73.3%

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

      8. unsub-neg 73.3%

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

      9. *-commutative 73.3%

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

      10. *-commutative 73.3%

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

      11. distribute-lft-neg-in 73.3%

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

      12. distribute-rgt-neg-in 73.3%

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

      13. neg-sub0 73.3%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      14. associate--r- 73.3%

          \[\leadsto a \cdot \left(j \cdot c - x \cdot t\right) + b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      15. neg-sub0 73.3%

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

      16. +-commutative 73.3%

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

      17. sub-neg 73.3%

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

   5. Simplified 73.3%

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

   if -5.0000000000000004e43 < b < -1.45e-49

   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. Add Preprocessing

   3. Taylor expanded in y around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   if -1.11999999999999997e-125 < b < 1.18e-23

   1. Initial program 76.6%

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

   3. Taylor expanded in b around 0 76.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-125} \lor \neg \left(b \leq 1.18 \cdot 10^{-23}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-152}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-100}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= z -3.2e+99)
     t_1
     (if (<= z -2.9e-152)
       (* (* x t) (- a))
       (if (<= z 2.7e-278)
         (* a (* c j))
         (if (<= z 3.2e-100)
           (* i (* t b))
           (if (<= z 3.5e+176)
             (* x (* y z))
             (if (<= z 7.1e+224) t_1 (* 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 = c * (z * -b);
	double tmp;
	if (z <= -3.2e+99) {
		tmp = t_1;
	} else if (z <= -2.9e-152) {
		tmp = (x * t) * -a;
	} else if (z <= 2.7e-278) {
		tmp = a * (c * j);
	} else if (z <= 3.2e-100) {
		tmp = i * (t * b);
	} else if (z <= 3.5e+176) {
		tmp = x * (y * z);
	} else if (z <= 7.1e+224) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = c * (z * -b)
    if (z <= (-3.2d+99)) then
        tmp = t_1
    else if (z <= (-2.9d-152)) then
        tmp = (x * t) * -a
    else if (z <= 2.7d-278) then
        tmp = a * (c * j)
    else if (z <= 3.2d-100) then
        tmp = i * (t * b)
    else if (z <= 3.5d+176) then
        tmp = x * (y * z)
    else if (z <= 7.1d+224) then
        tmp = t_1
    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 = c * (z * -b);
	double tmp;
	if (z <= -3.2e+99) {
		tmp = t_1;
	} else if (z <= -2.9e-152) {
		tmp = (x * t) * -a;
	} else if (z <= 2.7e-278) {
		tmp = a * (c * j);
	} else if (z <= 3.2e-100) {
		tmp = i * (t * b);
	} else if (z <= 3.5e+176) {
		tmp = x * (y * z);
	} else if (z <= 7.1e+224) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if z <= -3.2e+99:
		tmp = t_1
	elif z <= -2.9e-152:
		tmp = (x * t) * -a
	elif z <= 2.7e-278:
		tmp = a * (c * j)
	elif z <= 3.2e-100:
		tmp = i * (t * b)
	elif z <= 3.5e+176:
		tmp = x * (y * z)
	elif z <= 7.1e+224:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (z <= -3.2e+99)
		tmp = t_1;
	elseif (z <= -2.9e-152)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (z <= 2.7e-278)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 3.2e-100)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 3.5e+176)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 7.1e+224)
		tmp = t_1;
	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 = c * (z * -b);
	tmp = 0.0;
	if (z <= -3.2e+99)
		tmp = t_1;
	elseif (z <= -2.9e-152)
		tmp = (x * t) * -a;
	elseif (z <= 2.7e-278)
		tmp = a * (c * j);
	elseif (z <= 3.2e-100)
		tmp = i * (t * b);
	elseif (z <= 3.5e+176)
		tmp = x * (y * z);
	elseif (z <= 7.1e+224)
		tmp = t_1;
	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[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+99], t$95$1, If[LessEqual[z, -2.9e-152], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[z, 2.7e-278], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-100], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+176], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.1e+224], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.19999999999999999e99 or 3.50000000000000003e176 < z < 7.0999999999999998e224

   1. Initial program 62.3%

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

      1. add-cube-cbrt 62.1%

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

      2. pow3 62.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 62.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 62.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 62.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 62.5%

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

      2. associate-*r* 62.5%

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

      3. fma-neg 66.1%

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

      4. *-lft-identity 66.1%

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

      5. *-commutative 66.1%

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

      6. *-commutative 66.1%

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

      7. fma-neg 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in i around 0 62.5%

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

   9. Taylor expanded in c around inf 47.7%

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

       1. *-commutative 47.7%

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

       2. associate-*r* 49.1%

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

       3. associate-*r* 49.1%

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

       4. *-commutative 49.1%

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

       5. mul-1-neg 49.1%

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

       6. distribute-rgt-neg-in 49.1%

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

   11. Simplified 49.1%

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

   if -3.19999999999999999e99 < z < -2.9000000000000001e-152

   1. Initial program 80.8%

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

   3. Taylor expanded in a around inf 37.4%

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

      1. +-commutative 37.4%

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

      2. mul-1-neg 37.4%

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

      3. unsub-neg 37.4%

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

      4. *-commutative 37.4%

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

      5. *-commutative 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in j around 0 26.6%

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

      1. mul-1-neg 26.6%

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

      2. *-commutative 26.6%

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

      3. distribute-rgt-neg-in 26.6%

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

   8. Simplified 26.6%

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

   if -2.9000000000000001e-152 < z < 2.7000000000000001e-278

   1. Initial program 81.4%

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

      1. add-cube-cbrt 81.4%

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

      2. pow3 81.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.4%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 45.7%

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

      1. *-commutative 45.7%

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

   7. Simplified 45.7%

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

   if 2.7000000000000001e-278 < z < 3.20000000000000017e-100

   1. Initial program 88.3%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 88.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in y around 0 39.9%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. associate-*l* 40.0%

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

      4. *-commutative 40.0%

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

   10. Simplified 40.0%

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

   if 3.20000000000000017e-100 < z < 3.50000000000000003e176

   1. Initial program 92.1%

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

      1. add-cube-cbrt 91.8%

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

      2. pow3 91.8%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 91.8%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 91.8%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 78.6%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 78.6%

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

      2. associate-*r* 78.6%

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

      3. fma-neg 78.6%

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

      4. *-lft-identity 78.6%

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

      5. *-commutative 78.6%

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

      6. *-commutative 78.6%

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

      7. fma-neg 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 35.7%

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

   if 7.0999999999999998e224 < z

   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. Add Preprocessing

   3. Taylor expanded in z around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in y around inf 55.6%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+99}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-152}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-100}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{+224}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 27000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -6.4e+43)
     t_1
     (if (<= b -9.5e-49)
       (* y (- (* x z) (* i j)))
       (if (<= b -3.3e-125)
         (* c (- (* a j) (* z b)))
         (if (<= b 27000000.0)
           (+ (* x (- (* y z) (* t a))) (* j (* a 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.4e+43) {
		tmp = t_1;
	} else if (b <= -9.5e-49) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -3.3e-125) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 27000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-6.4d+43)) then
        tmp = t_1
    else if (b <= (-9.5d-49)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= (-3.3d-125)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 27000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.4e+43) {
		tmp = t_1;
	} else if (b <= -9.5e-49) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= -3.3e-125) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 27000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -6.4e+43:
		tmp = t_1
	elif b <= -9.5e-49:
		tmp = y * ((x * z) - (i * j))
	elif b <= -3.3e-125:
		tmp = c * ((a * j) - (z * b))
	elif b <= 27000000.0:
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.4e+43)
		tmp = t_1;
	elseif (b <= -9.5e-49)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= -3.3e-125)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 27000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(a * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.4e+43)
		tmp = t_1;
	elseif (b <= -9.5e-49)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= -3.3e-125)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 27000000.0)
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+43], t$95$1, If[LessEqual[b, -9.5e-49], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.3e-125], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 27000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.40000000000000029e43 or 2.7e7 < b

   1. Initial program 80.9%

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

   3. Taylor expanded in b around inf 61.6%

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

   if -6.40000000000000029e43 < b < -9.50000000000000006e-49

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -9.50000000000000006e-49 < b < -3.3000000000000001e-125

   1. Initial program 65.7%

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

   3. Taylor expanded in c around inf 65.9%

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

   if -3.3000000000000001e-125 < b < 2.7e7

   1. Initial program 75.6%

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

   3. Taylor expanded in b around 0 75.3%

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

   4. Taylor expanded in a around inf 64.0%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 27000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-144}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-217}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 2.36 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3e+14)
     t_1
     (if (<= a -6.8e-144)
       (* c (* z (- b)))
       (if (<= a -2.1e-217)
         (* i (* t b))
         (if (<= a 2.36e-240)
           (* b (* z (- c)))
           (if (<= a 2.9e-40) (* y (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3e+14) {
		tmp = t_1;
	} else if (a <= -6.8e-144) {
		tmp = c * (z * -b);
	} else if (a <= -2.1e-217) {
		tmp = i * (t * b);
	} else if (a <= 2.36e-240) {
		tmp = b * (z * -c);
	} else if (a <= 2.9e-40) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-3d+14)) then
        tmp = t_1
    else if (a <= (-6.8d-144)) then
        tmp = c * (z * -b)
    else if (a <= (-2.1d-217)) then
        tmp = i * (t * b)
    else if (a <= 2.36d-240) then
        tmp = b * (z * -c)
    else if (a <= 2.9d-40) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3e+14) {
		tmp = t_1;
	} else if (a <= -6.8e-144) {
		tmp = c * (z * -b);
	} else if (a <= -2.1e-217) {
		tmp = i * (t * b);
	} else if (a <= 2.36e-240) {
		tmp = b * (z * -c);
	} else if (a <= 2.9e-40) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3e+14:
		tmp = t_1
	elif a <= -6.8e-144:
		tmp = c * (z * -b)
	elif a <= -2.1e-217:
		tmp = i * (t * b)
	elif a <= 2.36e-240:
		tmp = b * (z * -c)
	elif a <= 2.9e-40:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3e+14)
		tmp = t_1;
	elseif (a <= -6.8e-144)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (a <= -2.1e-217)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 2.36e-240)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 2.9e-40)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3e+14)
		tmp = t_1;
	elseif (a <= -6.8e-144)
		tmp = c * (z * -b);
	elseif (a <= -2.1e-217)
		tmp = i * (t * b);
	elseif (a <= 2.36e-240)
		tmp = b * (z * -c);
	elseif (a <= 2.9e-40)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+14], t$95$1, If[LessEqual[a, -6.8e-144], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-217], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.36e-240], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-40], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3e14 or 2.8999999999999999e-40 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

      5. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if -3e14 < a < -6.80000000000000035e-144

   1. Initial program 89.5%

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

      1. add-cube-cbrt 89.5%

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

      2. pow3 89.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 89.4%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 89.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 73.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 73.0%

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

      2. associate-*r* 73.0%

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

      3. fma-neg 73.0%

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

      4. *-lft-identity 73.0%

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

      5. *-commutative 73.0%

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

      6. *-commutative 73.0%

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

      7. fma-neg 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in i around 0 73.0%

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

   9. Taylor expanded in c around inf 37.7%

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

       1. *-commutative 37.7%

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

       2. associate-*r* 44.3%

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

       3. associate-*r* 44.3%

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

       4. *-commutative 44.3%

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

       5. mul-1-neg 44.3%

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

       6. distribute-rgt-neg-in 44.3%

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

   11. Simplified 44.3%

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

   if -6.80000000000000035e-144 < a < -2.1e-217

   1. Initial program 87.4%

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

      1. add-cube-cbrt 87.3%

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

      2. pow3 87.3%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 87.3%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 87.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 55.8%

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

      1. distribute-lft-out-- 55.8%

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

      2. *-commutative 55.8%

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

      3. *-commutative 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in y around 0 39.1%

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

      1. associate-*r* 43.0%

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

      2. *-commutative 43.0%

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

      3. associate-*l* 39.1%

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

      4. *-commutative 39.1%

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

   10. Simplified 39.1%

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

   if -2.1e-217 < a < 2.3599999999999999e-240

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 89.2%

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

      2. pow3 89.2%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 89.2%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 89.2%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in z around inf 42.4%

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

      1. associate-*r* 42.4%

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

      2. neg-mul-1 42.4%

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

      3. *-commutative 42.4%

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

   7. Simplified 42.4%

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

   if 2.3599999999999999e-240 < a < 2.8999999999999999e-40

   1. Initial program 79.3%

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

      1. add-cube-cbrt 78.8%

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

      2. pow3 78.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.9%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 78.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 56.6%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 56.6%

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

      2. associate-*r* 56.6%

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

      3. fma-neg 58.7%

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

      4. *-lft-identity 58.7%

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

      5. *-commutative 58.7%

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

      6. *-commutative 58.7%

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

      7. fma-neg 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in y around inf 37.3%

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

      1. *-commutative 37.3%

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

      2. associate-*r* 37.3%

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

   10. Simplified 37.3%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-144}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-217}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 2.36 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.2e+16)
     t_2
     (if (<= a 3e-222)
       (* b (- (* t i) (* z c)))
       (if (<= a 8e-66)
         t_1
         (if (<= a 1.2e+56)
           (* c (- (* a j) (* z b)))
           (if (<= a 1.65e+102) 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.2e+16) {
		tmp = t_2;
	} else if (a <= 3e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 8e-66) {
		tmp = t_1;
	} else if (a <= 1.2e+56) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.65e+102) {
		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 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.2d+16)) then
        tmp = t_2
    else if (a <= 3d-222) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 8d-66) then
        tmp = t_1
    else if (a <= 1.2d+56) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 1.65d+102) 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.2e+16) {
		tmp = t_2;
	} else if (a <= 3e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 8e-66) {
		tmp = t_1;
	} else if (a <= 1.2e+56) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.65e+102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.2e+16:
		tmp = t_2
	elif a <= 3e-222:
		tmp = b * ((t * i) - (z * c))
	elif a <= 8e-66:
		tmp = t_1
	elif a <= 1.2e+56:
		tmp = c * ((a * j) - (z * b))
	elif a <= 1.65e+102:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.2e+16)
		tmp = t_2;
	elseif (a <= 3e-222)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 8e-66)
		tmp = t_1;
	elseif (a <= 1.2e+56)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 1.65e+102)
		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 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.2e+16)
		tmp = t_2;
	elseif (a <= 3e-222)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 8e-66)
		tmp = t_1;
	elseif (a <= 1.2e+56)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 1.65e+102)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+16], t$95$2, If[LessEqual[a, 3e-222], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-66], t$95$1, If[LessEqual[a, 1.2e+56], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+102], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2e16 or 1.64999999999999999e102 < a

   1. Initial program 70.8%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -1.2e16 < a < 3.0000000000000003e-222

   1. Initial program 89.6%

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

   3. Taylor expanded in b around inf 56.4%

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

   if 3.0000000000000003e-222 < a < 7.9999999999999998e-66 or 1.20000000000000007e56 < a < 1.64999999999999999e102

   1. Initial program 69.3%

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

      1. prod-diff 69.0%

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

      2. *-commutative 69.0%

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

      3. fma-neg 69.0%

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

      4. distribute-rgt-in 66.7%

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

      5. *-commutative 66.7%

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

      6. *-commutative 66.7%

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

   4. Applied egg-rr 66.7%

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

   5. Taylor expanded in i around inf 53.9%

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

      1. sub-neg 53.9%

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

      2. mul-1-neg 53.9%

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

      3. mul-1-neg 53.9%

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

      4. *-commutative 53.9%

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

      5. remove-double-neg 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in i around 0 53.9%

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

   if 7.9999999999999998e-66 < a < 1.20000000000000007e56

   1. Initial program 79.8%

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

   3. Taylor expanded in c around inf 46.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+56}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-138}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.7e+15)
     t_2
     (if (<= a 9.6e-203)
       t_1
       (if (<= a 4.7e-138) (* (* i j) (- y)) (if (<= a 8.2e+110) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.7e+15) {
		tmp = t_2;
	} else if (a <= 9.6e-203) {
		tmp = t_1;
	} else if (a <= 4.7e-138) {
		tmp = (i * j) * -y;
	} else if (a <= 8.2e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.7d+15)) then
        tmp = t_2
    else if (a <= 9.6d-203) then
        tmp = t_1
    else if (a <= 4.7d-138) then
        tmp = (i * j) * -y
    else if (a <= 8.2d+110) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.7e+15) {
		tmp = t_2;
	} else if (a <= 9.6e-203) {
		tmp = t_1;
	} else if (a <= 4.7e-138) {
		tmp = (i * j) * -y;
	} else if (a <= 8.2e+110) {
		tmp = t_1;
	} 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 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.7e+15:
		tmp = t_2
	elif a <= 9.6e-203:
		tmp = t_1
	elif a <= 4.7e-138:
		tmp = (i * j) * -y
	elif a <= 8.2e+110:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.7e+15)
		tmp = t_2;
	elseif (a <= 9.6e-203)
		tmp = t_1;
	elseif (a <= 4.7e-138)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (a <= 8.2e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.7e+15)
		tmp = t_2;
	elseif (a <= 9.6e-203)
		tmp = t_1;
	elseif (a <= 4.7e-138)
		tmp = (i * j) * -y;
	elseif (a <= 8.2e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+15], t$95$2, If[LessEqual[a, 9.6e-203], t$95$1, If[LessEqual[a, 4.7e-138], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[a, 8.2e+110], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e15 or 8.1999999999999997e110 < a

   1. Initial program 70.2%

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

   3. Taylor expanded in a around inf 68.1%

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

      1. +-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. *-commutative 68.1%

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

      5. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if -2.7e15 < a < 9.5999999999999994e-203 or 4.7000000000000001e-138 < a < 8.1999999999999997e110

   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. Add Preprocessing

   3. Taylor expanded in b around inf 50.6%

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

   if 9.5999999999999994e-203 < a < 4.7000000000000001e-138

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 71.9%

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

      2. pow3 71.9%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.9%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 71.9%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around inf 37.0%

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

      1. mul-1-neg 37.0%

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

      2. associate-*r* 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

      4. *-commutative 50.7%

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

   7. Simplified 50.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-138}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-217}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -5.4e+14)
     t_1
     (if (<= a 5e-217)
       (* b (- (* t i) (* z c)))
       (if (<= a 2.4e+60)
         (* x (- (* y z) (* t a)))
         (if (<= a 6.5e+101) (* i (- (* t b) (* y j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.4e+14) {
		tmp = t_1;
	} else if (a <= 5e-217) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 2.4e+60) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 6.5e+101) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-5.4d+14)) then
        tmp = t_1
    else if (a <= 5d-217) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 2.4d+60) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= 6.5d+101) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.4e+14) {
		tmp = t_1;
	} else if (a <= 5e-217) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 2.4e+60) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 6.5e+101) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5.4e+14:
		tmp = t_1
	elif a <= 5e-217:
		tmp = b * ((t * i) - (z * c))
	elif a <= 2.4e+60:
		tmp = x * ((y * z) - (t * a))
	elif a <= 6.5e+101:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.4e+14)
		tmp = t_1;
	elseif (a <= 5e-217)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 2.4e+60)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= 6.5e+101)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5.4e+14)
		tmp = t_1;
	elseif (a <= 5e-217)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 2.4e+60)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= 6.5e+101)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e+14], t$95$1, If[LessEqual[a, 5e-217], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+60], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+101], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.4e14 or 6.50000000000000016e101 < a

   1. Initial program 70.8%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -5.4e14 < a < 5.0000000000000002e-217

   1. Initial program 89.7%

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

   3. Taylor expanded in b around inf 55.9%

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

   if 5.0000000000000002e-217 < a < 2.4e60

   1. Initial program 78.3%

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

      1. prod-diff 78.3%

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

      2. *-commutative 78.3%

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

      3. fma-neg 78.3%

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

      4. distribute-rgt-in 76.4%

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

      5. *-commutative 76.4%

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

      6. *-commutative 76.4%

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

   4. Applied egg-rr 76.4%

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

   5. Taylor expanded in x around inf 47.7%

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

      1. neg-mul-1 47.7%

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

      2. +-commutative 47.7%

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

      3. sub-neg 47.7%

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

   7. Simplified 47.7%

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

   if 2.4e60 < a < 6.50000000000000016e101

   1. Initial program 35.7%

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

      1. prod-diff 34.0%

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

      2. *-commutative 34.0%

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

      3. fma-neg 34.0%

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

      4. distribute-rgt-in 34.0%

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

      5. *-commutative 34.0%

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

      6. *-commutative 34.0%

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

   4. Applied egg-rr 34.0%

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

   5. Taylor expanded in i around inf 79.8%

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

      1. sub-neg 79.8%

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

      2. mul-1-neg 79.8%

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

      3. mul-1-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. remove-double-neg 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in i around 0 79.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-217}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -5e+15)
     t_1
     (if (<= a 6.6e-241)
       (* b (- (* t i) (* z c)))
       (if (<= a 3.8e+54)
         (* y (- (* x z) (* i j)))
         (if (<= a 8.4e+101) (* i (- (* t b) (* y j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5e+15) {
		tmp = t_1;
	} else if (a <= 6.6e-241) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 3.8e+54) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8.4e+101) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-5d+15)) then
        tmp = t_1
    else if (a <= 6.6d-241) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 3.8d+54) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 8.4d+101) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5e+15) {
		tmp = t_1;
	} else if (a <= 6.6e-241) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 3.8e+54) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8.4e+101) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5e+15:
		tmp = t_1
	elif a <= 6.6e-241:
		tmp = b * ((t * i) - (z * c))
	elif a <= 3.8e+54:
		tmp = y * ((x * z) - (i * j))
	elif a <= 8.4e+101:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5e+15)
		tmp = t_1;
	elseif (a <= 6.6e-241)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 3.8e+54)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 8.4e+101)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5e+15)
		tmp = t_1;
	elseif (a <= 6.6e-241)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 3.8e+54)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 8.4e+101)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+15], t$95$1, If[LessEqual[a, 6.6e-241], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+54], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e+101], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5e15 or 8.4000000000000001e101 < a

   1. Initial program 70.8%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -5e15 < a < 6.5999999999999998e-241

   1. Initial program 88.8%

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

   3. Taylor expanded in b around inf 57.4%

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

   if 6.5999999999999998e-241 < a < 3.8000000000000002e54

   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. Add Preprocessing

   3. Taylor expanded in y around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if 3.8000000000000002e54 < a < 8.4000000000000001e101

   1. Initial program 42.1%

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

      1. prod-diff 40.6%

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

      2. *-commutative 40.6%

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

      3. fma-neg 40.6%

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

      4. distribute-rgt-in 30.6%

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

      5. *-commutative 30.6%

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

      6. *-commutative 30.6%

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

   4. Applied egg-rr 30.6%

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

   5. Taylor expanded in i around inf 72.6%

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

      1. sub-neg 72.6%

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

      2. mul-1-neg 72.6%

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

      3. mul-1-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. remove-double-neg 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in i around 0 72.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.1e+99)
   (* z (* b (- c)))
   (if (<= z -3.5e-152)
     (* (* x t) (- a))
     (if (<= z 5.6e-278)
       (* a (* c j))
       (if (<= z 4.4e-101) (* i (* t b)) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.1e+99) {
		tmp = z * (b * -c);
	} else if (z <= -3.5e-152) {
		tmp = (x * t) * -a;
	} else if (z <= 5.6e-278) {
		tmp = a * (c * j);
	} else if (z <= 4.4e-101) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.1d+99)) then
        tmp = z * (b * -c)
    else if (z <= (-3.5d-152)) then
        tmp = (x * t) * -a
    else if (z <= 5.6d-278) then
        tmp = a * (c * j)
    else if (z <= 4.4d-101) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.1e+99) {
		tmp = z * (b * -c);
	} else if (z <= -3.5e-152) {
		tmp = (x * t) * -a;
	} else if (z <= 5.6e-278) {
		tmp = a * (c * j);
	} else if (z <= 4.4e-101) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.1e+99:
		tmp = z * (b * -c)
	elif z <= -3.5e-152:
		tmp = (x * t) * -a
	elif z <= 5.6e-278:
		tmp = a * (c * j)
	elif z <= 4.4e-101:
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.1e+99)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (z <= -3.5e-152)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (z <= 5.6e-278)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 4.4e-101)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.1e+99)
		tmp = z * (b * -c);
	elseif (z <= -3.5e-152)
		tmp = (x * t) * -a;
	elseif (z <= 5.6e-278)
		tmp = a * (c * j);
	elseif (z <= 4.4e-101)
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.1e+99], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-152], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[z, 5.6e-278], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-101], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.1000000000000001e99

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in y around 0 47.6%

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

      1. neg-mul-1 47.6%

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

      2. distribute-rgt-neg-in 47.6%

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

   8. Simplified 47.6%

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

   if -2.1000000000000001e99 < z < -3.5000000000000001e-152

   1. Initial program 80.8%

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

   3. Taylor expanded in a around inf 37.4%

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

      1. +-commutative 37.4%

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

      2. mul-1-neg 37.4%

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

      3. unsub-neg 37.4%

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

      4. *-commutative 37.4%

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

      5. *-commutative 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in j around 0 26.6%

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

      1. mul-1-neg 26.6%

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

      2. *-commutative 26.6%

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

      3. distribute-rgt-neg-in 26.6%

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

   8. Simplified 26.6%

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

   if -3.5000000000000001e-152 < z < 5.60000000000000015e-278

   1. Initial program 81.4%

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

      1. add-cube-cbrt 81.4%

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

      2. pow3 81.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.4%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 45.7%

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

      1. *-commutative 45.7%

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

   7. Simplified 45.7%

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

   if 5.60000000000000015e-278 < z < 4.3999999999999998e-101

   1. Initial program 88.3%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 88.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in y around 0 39.9%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. associate-*l* 40.0%

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

      4. *-commutative 40.0%

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

   10. Simplified 40.0%

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

   if 4.3999999999999998e-101 < z

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 77.1%

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

      2. pow3 77.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 77.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 71.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 71.4%

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

      2. associate-*r* 71.4%

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

      3. fma-neg 73.9%

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

      4. *-lft-identity 73.9%

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

      5. *-commutative 73.9%

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

      6. *-commutative 73.9%

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

      7. fma-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around inf 39.3%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.4e+99)
   (* z (* b (- c)))
   (if (<= z -3.5e-260)
     (* i (- (* y j)))
     (if (<= z 4.2e-277)
       (* a (* c j))
       (if (<= z 1.5e-101) (* i (* t b)) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.4e+99) {
		tmp = z * (b * -c);
	} else if (z <= -3.5e-260) {
		tmp = i * -(y * j);
	} else if (z <= 4.2e-277) {
		tmp = a * (c * j);
	} else if (z <= 1.5e-101) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.4d+99)) then
        tmp = z * (b * -c)
    else if (z <= (-3.5d-260)) then
        tmp = i * -(y * j)
    else if (z <= 4.2d-277) then
        tmp = a * (c * j)
    else if (z <= 1.5d-101) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.4e+99) {
		tmp = z * (b * -c);
	} else if (z <= -3.5e-260) {
		tmp = i * -(y * j);
	} else if (z <= 4.2e-277) {
		tmp = a * (c * j);
	} else if (z <= 1.5e-101) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.4e+99:
		tmp = z * (b * -c)
	elif z <= -3.5e-260:
		tmp = i * -(y * j)
	elif z <= 4.2e-277:
		tmp = a * (c * j)
	elif z <= 1.5e-101:
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.4e+99)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (z <= -3.5e-260)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (z <= 4.2e-277)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1.5e-101)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.4e+99)
		tmp = z * (b * -c);
	elseif (z <= -3.5e-260)
		tmp = i * -(y * j);
	elseif (z <= 4.2e-277)
		tmp = a * (c * j);
	elseif (z <= 1.5e-101)
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.4e+99], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-260], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 4.2e-277], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-101], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.39999999999999984e99

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in y around 0 47.6%

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

      1. neg-mul-1 47.6%

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

      2. distribute-rgt-neg-in 47.6%

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

   8. Simplified 47.6%

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

   if -3.39999999999999984e99 < z < -3.5e-260

   1. Initial program 79.0%

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

      1. add-cube-cbrt 78.9%

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

      2. pow3 78.8%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.8%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 78.8%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in y around inf 32.0%

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

      1. associate-*r* 32.0%

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

      2. neg-mul-1 32.0%

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

      3. *-commutative 32.0%

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

   7. Simplified 32.0%

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

   if -3.5e-260 < z < 4.1999999999999999e-277

   1. Initial program 87.4%

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

      1. add-cube-cbrt 87.3%

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

      2. pow3 87.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 87.4%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 87.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 61.6%

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

      1. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   if 4.1999999999999999e-277 < z < 1.5000000000000002e-101

   1. Initial program 88.3%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 88.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in y around 0 39.9%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. associate-*l* 40.0%

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

      4. *-commutative 40.0%

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

   10. Simplified 40.0%

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

   if 1.5000000000000002e-101 < z

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 77.1%

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

      2. pow3 77.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 77.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 71.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 71.4%

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

      2. associate-*r* 71.4%

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

      3. fma-neg 73.9%

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

      4. *-lft-identity 73.9%

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

      5. *-commutative 73.9%

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

      6. *-commutative 73.9%

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

      7. fma-neg 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around inf 39.3%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -7.5e-96)
     t_1
     (if (<= z 4.3e-280)
       (* a (* c j))
       (if (<= z 1.3e-99) (* i (* t b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -7.5e-96) {
		tmp = t_1;
	} else if (z <= 4.3e-280) {
		tmp = a * (c * j);
	} else if (z <= 1.3e-99) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (z <= (-7.5d-96)) then
        tmp = t_1
    else if (z <= 4.3d-280) then
        tmp = a * (c * j)
    else if (z <= 1.3d-99) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -7.5e-96) {
		tmp = t_1;
	} else if (z <= 4.3e-280) {
		tmp = a * (c * j);
	} else if (z <= 1.3e-99) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -7.5e-96:
		tmp = t_1
	elif z <= 4.3e-280:
		tmp = a * (c * j)
	elif z <= 1.3e-99:
		tmp = i * (t * b)
	else:
		tmp = t_1
	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 (z <= -7.5e-96)
		tmp = t_1;
	elseif (z <= 4.3e-280)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1.3e-99)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -7.5e-96)
		tmp = t_1;
	elseif (z <= 4.3e-280)
		tmp = a * (c * j);
	elseif (z <= 1.3e-99)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-96], t$95$1, If[LessEqual[z, 4.3e-280], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-99], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e-96 or 1.30000000000000003e-99 < z

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 74.2%

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

      2. pow3 74.2%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.2%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 74.2%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 66.2%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 66.2%

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

      2. associate-*r* 66.2%

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

      3. fma-neg 68.1%

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

      4. *-lft-identity 68.1%

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

      5. *-commutative 68.1%

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

      6. *-commutative 68.1%

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

      7. fma-neg 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in y around inf 30.0%

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

   if -7.5e-96 < z < 4.2999999999999999e-280

   1. Initial program 81.4%

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

      1. add-cube-cbrt 81.3%

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

      2. pow3 81.3%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.3%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 40.8%

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

      1. *-commutative 40.8%

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

   7. Simplified 40.8%

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

   if 4.2999999999999999e-280 < z < 1.30000000000000003e-99

   1. Initial program 88.3%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 88.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 50.6%

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

      1. distribute-lft-out-- 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in y around 0 39.9%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. associate-*l* 40.0%

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

      4. *-commutative 40.0%

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

   10. Simplified 40.0%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -5.5e-94)
   (* y (* x z))
   (if (<= z 1.7e-277)
     (* a (* c j))
     (if (<= z 1.15e-99) (* i (* t b)) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.5e-94) {
		tmp = y * (x * z);
	} else if (z <= 1.7e-277) {
		tmp = a * (c * j);
	} else if (z <= 1.15e-99) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-5.5d-94)) then
        tmp = y * (x * z)
    else if (z <= 1.7d-277) then
        tmp = a * (c * j)
    else if (z <= 1.15d-99) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.5e-94) {
		tmp = y * (x * z);
	} else if (z <= 1.7e-277) {
		tmp = a * (c * j);
	} else if (z <= 1.15e-99) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -5.5e-94:
		tmp = y * (x * z)
	elif z <= 1.7e-277:
		tmp = a * (c * j)
	elif z <= 1.15e-99:
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -5.5e-94)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 1.7e-277)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1.15e-99)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -5.5e-94)
		tmp = y * (x * z);
	elseif (z <= 1.7e-277)
		tmp = a * (c * j);
	elseif (z <= 1.15e-99)
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -5.5e-94], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-277], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-99], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999989e-94

   1. Initial program 71.5%

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

      1. add-cube-cbrt 71.3%

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

      2. pow3 71.3%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.3%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 71.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 61.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 61.1%

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

      2. associate-*r* 61.1%

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

      3. fma-neg 62.3%

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

      4. *-lft-identity 62.3%

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

      5. *-commutative 62.3%

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

      6. *-commutative 62.3%

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

      7. fma-neg 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around inf 20.8%

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

      1. *-commutative 20.8%

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

      2. associate-*r* 25.7%

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

   10. Simplified 25.7%

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

   if -5.49999999999999989e-94 < z < 1.69999999999999991e-277

   1. Initial program 81.4%

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

      1. add-cube-cbrt 81.3%

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

      2. pow3 81.3%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.3%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 81.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 40.8%

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

      1. *-commutative 40.8%

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

   7. Simplified 40.8%

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

   if 1.69999999999999991e-277 < z < 1.1499999999999999e-99

   1. Initial program 88.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 88.1%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 88.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 88.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 50.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 50.6%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 50.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 50.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   7. Simplified 50.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 39.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 39.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*l* 40.0%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

      4. *-commutative 40.0%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   10. Simplified 40.0%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.1499999999999999e-99 < z

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 77.1%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 77.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.1%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 77.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 71.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 71.4%

         \[\leadsto \color{blue}{1} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 71.4%

         \[\leadsto \color{blue}{\left(1 \cdot x\right) \cdot \left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. fma-neg 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 \cdot x, y \cdot z - a \cdot t, -b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      4. *-lft-identity 73.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x}, y \cdot z - a \cdot t, -b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      6. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, -b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

      7. fma-neg 71.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \]

   7. Simplified 71.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \]

   8. Taylor expanded in y around inf 39.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-58} \lor \neg \left(a \leq 1.95 \cdot 10^{+102}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.2e-58) (not (<= a 1.95e+102))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.2e-58) || !(a <= 1.95e+102)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-2.2d-58)) .or. (.not. (a <= 1.95d+102))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.2e-58) || !(a <= 1.95e+102)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.2e-58) or not (a <= 1.95e+102):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.2e-58) || !(a <= 1.95e+102))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.2e-58) || ~((a <= 1.95e+102)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.2e-58], N[Not[LessEqual[a, 1.95e+102]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.20000000000000006e-58 or 1.9499999999999999e102 < a

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 72.5%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 72.5%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 72.5%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 72.5%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 35.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 35.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -2.20000000000000006e-58 < a < 1.9499999999999999e102

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 82.2%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 82.2%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 82.2%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 82.2%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 27.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   7. Simplified 27.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-58} \lor \neg \left(a \leq 1.95 \cdot 10^{+102}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2400:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -8.5e+101)
   (* i (* t b))
   (if (<= t 2400.0) (* a (* c j)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8.5e+101) {
		tmp = i * (t * b);
	} else if (t <= 2400.0) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-8.5d+101)) then
        tmp = i * (t * b)
    else if (t <= 2400.0d0) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8.5e+101) {
		tmp = i * (t * b);
	} else if (t <= 2400.0) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -8.5e+101:
		tmp = i * (t * b)
	elif t <= 2400.0:
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -8.5e+101)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 2400.0)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -8.5e+101)
		tmp = i * (t * b);
	elseif (t <= 2400.0)
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -8.5e+101], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2400.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5000000000000001e101

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 66.2%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 66.2%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 66.2%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.2%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 50.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 50.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 50.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 50.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   7. Simplified 50.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 36.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 38.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*l* 41.8%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

      4. *-commutative 41.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   10. Simplified 41.8%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -8.5000000000000001e101 < t < 2400

   1. Initial program 83.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 83.6%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 83.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 83.6%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 83.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in a around inf 23.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 23.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 23.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if 2400 < t

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 70.5%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 70.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.4%

         \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 70.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in t around inf 40.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   7. Simplified 40.6%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 2400:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-cube-cbrt 78.0%

      \[\leadsto \left(\color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. pow3 78.0%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. *-commutative 78.0%

      \[\leadsto \left({\left(\sqrt[3]{x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right)}\right)}^{3} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

4. Applied egg-rr 78.0%

   \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - a \cdot t\right)}\right)}^{3}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

5. Taylor expanded in a around inf 19.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
6. Step-by-step derivation

   1. *-commutative 19.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

7. Simplified 19.3%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

8. Final simplification 19.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
9. Add Preprocessing

Developer target: 58.7% 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 2024017 
(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)))))