Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 81.7%

Time: 37.4s

Alternatives: 26

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   4. Simplified 48.4%

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

4. Final simplification 86.9%

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

Alternative 2: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -0.0023:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-255}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* a (- (* b i) (* x t))))
        (t_4 (* b (- (* a i) (* z c))))
        (t_5 (* y (- (* x z) (* i j)))))
   (if (<= y -1.05e+49)
     t_5
     (if (<= y -0.0023)
       t_4
       (if (<= y -1.65e-49)
         t_5
         (if (<= y -1.12e-135)
           t_2
           (if (<= y -8.5e-255)
             t_4
             (if (<= y -9.2e-303)
               t_1
               (if (<= y 1.9e-236)
                 t_3
                 (if (<= y 3.4e-227)
                   t_1
                   (if (<= y 1.9e-84)
                     t_3
                     (if (<= y 4e-51)
                       t_2
                       (if (<= y 5.9e-22)
                         (* i (- (* a b) (* y j)))
                         t_5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double t_4 = b * ((a * i) - (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+49) {
		tmp = t_5;
	} else if (y <= -0.0023) {
		tmp = t_4;
	} else if (y <= -1.65e-49) {
		tmp = t_5;
	} else if (y <= -1.12e-135) {
		tmp = t_2;
	} else if (y <= -8.5e-255) {
		tmp = t_4;
	} else if (y <= -9.2e-303) {
		tmp = t_1;
	} else if (y <= 1.9e-236) {
		tmp = t_3;
	} else if (y <= 3.4e-227) {
		tmp = t_1;
	} else if (y <= 1.9e-84) {
		tmp = t_3;
	} else if (y <= 4e-51) {
		tmp = t_2;
	} else if (y <= 5.9e-22) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_5;
	}
	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 = t * ((c * j) - (x * a))
    t_2 = c * ((t * j) - (z * b))
    t_3 = a * ((b * i) - (x * t))
    t_4 = b * ((a * i) - (z * c))
    t_5 = y * ((x * z) - (i * j))
    if (y <= (-1.05d+49)) then
        tmp = t_5
    else if (y <= (-0.0023d0)) then
        tmp = t_4
    else if (y <= (-1.65d-49)) then
        tmp = t_5
    else if (y <= (-1.12d-135)) then
        tmp = t_2
    else if (y <= (-8.5d-255)) then
        tmp = t_4
    else if (y <= (-9.2d-303)) then
        tmp = t_1
    else if (y <= 1.9d-236) then
        tmp = t_3
    else if (y <= 3.4d-227) then
        tmp = t_1
    else if (y <= 1.9d-84) then
        tmp = t_3
    else if (y <= 4d-51) then
        tmp = t_2
    else if (y <= 5.9d-22) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double t_4 = b * ((a * i) - (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+49) {
		tmp = t_5;
	} else if (y <= -0.0023) {
		tmp = t_4;
	} else if (y <= -1.65e-49) {
		tmp = t_5;
	} else if (y <= -1.12e-135) {
		tmp = t_2;
	} else if (y <= -8.5e-255) {
		tmp = t_4;
	} else if (y <= -9.2e-303) {
		tmp = t_1;
	} else if (y <= 1.9e-236) {
		tmp = t_3;
	} else if (y <= 3.4e-227) {
		tmp = t_1;
	} else if (y <= 1.9e-84) {
		tmp = t_3;
	} else if (y <= 4e-51) {
		tmp = t_2;
	} else if (y <= 5.9e-22) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = c * ((t * j) - (z * b))
	t_3 = a * ((b * i) - (x * t))
	t_4 = b * ((a * i) - (z * c))
	t_5 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.05e+49:
		tmp = t_5
	elif y <= -0.0023:
		tmp = t_4
	elif y <= -1.65e-49:
		tmp = t_5
	elif y <= -1.12e-135:
		tmp = t_2
	elif y <= -8.5e-255:
		tmp = t_4
	elif y <= -9.2e-303:
		tmp = t_1
	elif y <= 1.9e-236:
		tmp = t_3
	elif y <= 3.4e-227:
		tmp = t_1
	elif y <= 1.9e-84:
		tmp = t_3
	elif y <= 4e-51:
		tmp = t_2
	elif y <= 5.9e-22:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_4 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_5 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.05e+49)
		tmp = t_5;
	elseif (y <= -0.0023)
		tmp = t_4;
	elseif (y <= -1.65e-49)
		tmp = t_5;
	elseif (y <= -1.12e-135)
		tmp = t_2;
	elseif (y <= -8.5e-255)
		tmp = t_4;
	elseif (y <= -9.2e-303)
		tmp = t_1;
	elseif (y <= 1.9e-236)
		tmp = t_3;
	elseif (y <= 3.4e-227)
		tmp = t_1;
	elseif (y <= 1.9e-84)
		tmp = t_3;
	elseif (y <= 4e-51)
		tmp = t_2;
	elseif (y <= 5.9e-22)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = c * ((t * j) - (z * b));
	t_3 = a * ((b * i) - (x * t));
	t_4 = b * ((a * i) - (z * c));
	t_5 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.05e+49)
		tmp = t_5;
	elseif (y <= -0.0023)
		tmp = t_4;
	elseif (y <= -1.65e-49)
		tmp = t_5;
	elseif (y <= -1.12e-135)
		tmp = t_2;
	elseif (y <= -8.5e-255)
		tmp = t_4;
	elseif (y <= -9.2e-303)
		tmp = t_1;
	elseif (y <= 1.9e-236)
		tmp = t_3;
	elseif (y <= 3.4e-227)
		tmp = t_1;
	elseif (y <= 1.9e-84)
		tmp = t_3;
	elseif (y <= 4e-51)
		tmp = t_2;
	elseif (y <= 5.9e-22)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+49], t$95$5, If[LessEqual[y, -0.0023], t$95$4, If[LessEqual[y, -1.65e-49], t$95$5, If[LessEqual[y, -1.12e-135], t$95$2, If[LessEqual[y, -8.5e-255], t$95$4, If[LessEqual[y, -9.2e-303], t$95$1, If[LessEqual[y, 1.9e-236], t$95$3, If[LessEqual[y, 3.4e-227], t$95$1, If[LessEqual[y, 1.9e-84], t$95$3, If[LessEqual[y, 4e-51], t$95$2, If[LessEqual[y, 5.9e-22], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.05000000000000005e49 or -0.0023 < y < -1.65e-49 or 5.90000000000000008e-22 < y

   1. Initial program 73.1%

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

   2. Taylor expanded in y around inf 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

   4. Simplified 68.8%

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

   if -1.05000000000000005e49 < y < -0.0023 or -1.12e-135 < y < -8.49999999999999982e-255

   1. Initial program 80.8%

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

   2. Taylor expanded in b around inf 70.2%

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

      1. *-commutative 70.2%

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

   4. Simplified 70.2%

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

   if -1.65e-49 < y < -1.12e-135 or 1.89999999999999993e-84 < y < 4e-51

   1. Initial program 91.9%

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

   2. Taylor expanded in c around inf 78.5%

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

   if -8.49999999999999982e-255 < y < -9.19999999999999981e-303 or 1.9e-236 < y < 3.39999999999999979e-227

   1. Initial program 69.8%

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

   2. Taylor expanded in t around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. unsub-neg 86.0%

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

      4. *-commutative 86.0%

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

   4. Simplified 86.0%

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

   if -9.19999999999999981e-303 < y < 1.9e-236 or 3.39999999999999979e-227 < y < 1.89999999999999993e-84

   1. Initial program 86.7%

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

   2. Taylor expanded in a around -inf 62.2%

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

   if 4e-51 < y < 5.90000000000000008e-22

   1. Initial program 88.7%

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

   2. Taylor expanded in i around inf 89.0%

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

      1. distribute-lft-out-- 89.0%

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

      2. *-commutative 89.0%

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

   4. Simplified 89.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -0.0023:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 3: 63.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i)))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.05e+128)
     t_2
     (if (<= b -2.7e-42)
       t_1
       (if (<= b -6.6e-68)
         (* i (- (* a b) (* y j)))
         (if (<= b 1.14e-35)
           t_1
           (if (<= b 3.9e+29)
             (* a (- (* b i) (* x t)))
             (if (<= b 5.7e+200) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.05e+128) {
		tmp = t_2;
	} else if (b <= -2.7e-42) {
		tmp = t_1;
	} else if (b <= -6.6e-68) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= 1.14e-35) {
		tmp = t_1;
	} else if (b <= 3.9e+29) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= 5.7e+200) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.05d+128)) then
        tmp = t_2
    else if (b <= (-2.7d-42)) then
        tmp = t_1
    else if (b <= (-6.6d-68)) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= 1.14d-35) then
        tmp = t_1
    else if (b <= 3.9d+29) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= 5.7d+200) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.05e+128) {
		tmp = t_2;
	} else if (b <= -2.7e-42) {
		tmp = t_1;
	} else if (b <= -6.6e-68) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= 1.14e-35) {
		tmp = t_1;
	} else if (b <= 3.9e+29) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= 5.7e+200) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.05e+128:
		tmp = t_2
	elif b <= -2.7e-42:
		tmp = t_1
	elif b <= -6.6e-68:
		tmp = i * ((a * b) - (y * j))
	elif b <= 1.14e-35:
		tmp = t_1
	elif b <= 3.9e+29:
		tmp = a * ((b * i) - (x * t))
	elif b <= 5.7e+200:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.05e+128)
		tmp = t_2;
	elseif (b <= -2.7e-42)
		tmp = t_1;
	elseif (b <= -6.6e-68)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= 1.14e-35)
		tmp = t_1;
	elseif (b <= 3.9e+29)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= 5.7e+200)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.05e+128)
		tmp = t_2;
	elseif (b <= -2.7e-42)
		tmp = t_1;
	elseif (b <= -6.6e-68)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= 1.14e-35)
		tmp = t_1;
	elseif (b <= 3.9e+29)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= 5.7e+200)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+128], t$95$2, If[LessEqual[b, -2.7e-42], t$95$1, If[LessEqual[b, -6.6e-68], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.14e-35], t$95$1, If[LessEqual[b, 3.9e+29], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.7e+200], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.05e128 or 5.70000000000000007e200 < b

   1. Initial program 71.0%

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

   2. Taylor expanded in b around inf 80.2%

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

      1. *-commutative 80.2%

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

   4. Simplified 80.2%

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

   if -1.05e128 < b < -2.69999999999999999e-42 or -6.5999999999999997e-68 < b < 1.14e-35 or 3.89999999999999968e29 < b < 5.70000000000000007e200

   1. Initial program 81.4%

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

   2. Taylor expanded in b around 0 72.1%

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

   if -2.69999999999999999e-42 < b < -6.5999999999999997e-68

   1. Initial program 90.0%

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

   2. Taylor expanded in i around inf 89.9%

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

      1. distribute-lft-out-- 89.9%

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

      2. *-commutative 89.9%

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

   4. Simplified 89.9%

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

   if 1.14e-35 < b < 3.89999999999999968e29

   1. Initial program 57.0%

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

   2. Taylor expanded in a around -inf 64.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+128}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{+200}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -0.0085:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-48}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-254}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-237}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* a (- (* b i) (* x t))))
        (t_4 (* b (- (* a i) (* z c))))
        (t_5 (* y (- (* x z) (* i j)))))
   (if (<= y -1.05e+49)
     t_5
     (if (<= y -0.0085)
       t_4
       (if (<= y -1.55e-48)
         t_5
         (if (<= y -9.2e-136)
           t_2
           (if (<= y -1.52e-254)
             t_4
             (if (<= y -1.9e-301)
               t_1
               (if (<= y 4.9e-237)
                 t_3
                 (if (<= y 8e-227)
                   t_1
                   (if (<= y 2.65e-92)
                     t_3
                     (if (<= y 1.16e-50) t_2 t_5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double t_4 = b * ((a * i) - (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+49) {
		tmp = t_5;
	} else if (y <= -0.0085) {
		tmp = t_4;
	} else if (y <= -1.55e-48) {
		tmp = t_5;
	} else if (y <= -9.2e-136) {
		tmp = t_2;
	} else if (y <= -1.52e-254) {
		tmp = t_4;
	} else if (y <= -1.9e-301) {
		tmp = t_1;
	} else if (y <= 4.9e-237) {
		tmp = t_3;
	} else if (y <= 8e-227) {
		tmp = t_1;
	} else if (y <= 2.65e-92) {
		tmp = t_3;
	} else if (y <= 1.16e-50) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	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 = t * ((c * j) - (x * a))
    t_2 = c * ((t * j) - (z * b))
    t_3 = a * ((b * i) - (x * t))
    t_4 = b * ((a * i) - (z * c))
    t_5 = y * ((x * z) - (i * j))
    if (y <= (-1.05d+49)) then
        tmp = t_5
    else if (y <= (-0.0085d0)) then
        tmp = t_4
    else if (y <= (-1.55d-48)) then
        tmp = t_5
    else if (y <= (-9.2d-136)) then
        tmp = t_2
    else if (y <= (-1.52d-254)) then
        tmp = t_4
    else if (y <= (-1.9d-301)) then
        tmp = t_1
    else if (y <= 4.9d-237) then
        tmp = t_3
    else if (y <= 8d-227) then
        tmp = t_1
    else if (y <= 2.65d-92) then
        tmp = t_3
    else if (y <= 1.16d-50) then
        tmp = t_2
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double t_4 = b * ((a * i) - (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+49) {
		tmp = t_5;
	} else if (y <= -0.0085) {
		tmp = t_4;
	} else if (y <= -1.55e-48) {
		tmp = t_5;
	} else if (y <= -9.2e-136) {
		tmp = t_2;
	} else if (y <= -1.52e-254) {
		tmp = t_4;
	} else if (y <= -1.9e-301) {
		tmp = t_1;
	} else if (y <= 4.9e-237) {
		tmp = t_3;
	} else if (y <= 8e-227) {
		tmp = t_1;
	} else if (y <= 2.65e-92) {
		tmp = t_3;
	} else if (y <= 1.16e-50) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = c * ((t * j) - (z * b))
	t_3 = a * ((b * i) - (x * t))
	t_4 = b * ((a * i) - (z * c))
	t_5 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.05e+49:
		tmp = t_5
	elif y <= -0.0085:
		tmp = t_4
	elif y <= -1.55e-48:
		tmp = t_5
	elif y <= -9.2e-136:
		tmp = t_2
	elif y <= -1.52e-254:
		tmp = t_4
	elif y <= -1.9e-301:
		tmp = t_1
	elif y <= 4.9e-237:
		tmp = t_3
	elif y <= 8e-227:
		tmp = t_1
	elif y <= 2.65e-92:
		tmp = t_3
	elif y <= 1.16e-50:
		tmp = t_2
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_4 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_5 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.05e+49)
		tmp = t_5;
	elseif (y <= -0.0085)
		tmp = t_4;
	elseif (y <= -1.55e-48)
		tmp = t_5;
	elseif (y <= -9.2e-136)
		tmp = t_2;
	elseif (y <= -1.52e-254)
		tmp = t_4;
	elseif (y <= -1.9e-301)
		tmp = t_1;
	elseif (y <= 4.9e-237)
		tmp = t_3;
	elseif (y <= 8e-227)
		tmp = t_1;
	elseif (y <= 2.65e-92)
		tmp = t_3;
	elseif (y <= 1.16e-50)
		tmp = t_2;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = c * ((t * j) - (z * b));
	t_3 = a * ((b * i) - (x * t));
	t_4 = b * ((a * i) - (z * c));
	t_5 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.05e+49)
		tmp = t_5;
	elseif (y <= -0.0085)
		tmp = t_4;
	elseif (y <= -1.55e-48)
		tmp = t_5;
	elseif (y <= -9.2e-136)
		tmp = t_2;
	elseif (y <= -1.52e-254)
		tmp = t_4;
	elseif (y <= -1.9e-301)
		tmp = t_1;
	elseif (y <= 4.9e-237)
		tmp = t_3;
	elseif (y <= 8e-227)
		tmp = t_1;
	elseif (y <= 2.65e-92)
		tmp = t_3;
	elseif (y <= 1.16e-50)
		tmp = t_2;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+49], t$95$5, If[LessEqual[y, -0.0085], t$95$4, If[LessEqual[y, -1.55e-48], t$95$5, If[LessEqual[y, -9.2e-136], t$95$2, If[LessEqual[y, -1.52e-254], t$95$4, If[LessEqual[y, -1.9e-301], t$95$1, If[LessEqual[y, 4.9e-237], t$95$3, If[LessEqual[y, 8e-227], t$95$1, If[LessEqual[y, 2.65e-92], t$95$3, If[LessEqual[y, 1.16e-50], t$95$2, t$95$5]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05000000000000005e49 or -0.0085000000000000006 < y < -1.55000000000000008e-48 or 1.15999999999999989e-50 < y

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   4. Simplified 67.9%

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

   if -1.05000000000000005e49 < y < -0.0085000000000000006 or -9.19999999999999994e-136 < y < -1.52e-254

   1. Initial program 80.8%

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

   2. Taylor expanded in b around inf 70.2%

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

      1. *-commutative 70.2%

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

   4. Simplified 70.2%

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

   if -1.55000000000000008e-48 < y < -9.19999999999999994e-136 or 2.65000000000000015e-92 < y < 1.15999999999999989e-50

   1. Initial program 92.2%

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

   2. Taylor expanded in c around inf 75.6%

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

   if -1.52e-254 < y < -1.89999999999999998e-301 or 4.9000000000000001e-237 < y < 7.99999999999999956e-227

   1. Initial program 69.8%

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

   2. Taylor expanded in t around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. unsub-neg 86.0%

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

      4. *-commutative 86.0%

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

   4. Simplified 86.0%

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

   if -1.89999999999999998e-301 < y < 4.9000000000000001e-237 or 7.99999999999999956e-227 < y < 2.65000000000000015e-92

   1. Initial program 86.7%

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

   2. Taylor expanded in a around -inf 62.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -0.0085:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-136}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 5: 67.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+147} \lor \neg \left(y \leq -3.4 \cdot 10^{+59}\right) \land y \leq 7.2 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.1e+177)
   (* y (- (* x z) (* i j)))
   (if (or (<= y -8.6e+147) (and (not (<= y -3.4e+59)) (<= y 7.2e-51)))
     (+ (* b (- (* a i) (* z c))) (* t (- (* c j) (* x a))))
     (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y 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 (y <= -2.1e+177) {
		tmp = y * ((x * z) - (i * j));
	} else if ((y <= -8.6e+147) || (!(y <= -3.4e+59) && (y <= 7.2e-51))) {
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 (y <= (-2.1d+177)) then
        tmp = y * ((x * z) - (i * j))
    else if ((y <= (-8.6d+147)) .or. (.not. (y <= (-3.4d+59))) .and. (y <= 7.2d-51)) then
        tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 (y <= -2.1e+177) {
		tmp = y * ((x * z) - (i * j));
	} else if ((y <= -8.6e+147) || (!(y <= -3.4e+59) && (y <= 7.2e-51))) {
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.1e+177:
		tmp = y * ((x * z) - (i * j))
	elif (y <= -8.6e+147) or (not (y <= -3.4e+59) and (y <= 7.2e-51)):
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.1e+177)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif ((y <= -8.6e+147) || (!(y <= -3.4e+59) && (y <= 7.2e-51)))
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -2.1e+177)
		tmp = y * ((x * z) - (i * j));
	elseif ((y <= -8.6e+147) || (~((y <= -3.4e+59)) && (y <= 7.2e-51)))
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.1e+177], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.6e+147], And[N[Not[LessEqual[y, -3.4e+59]], $MachinePrecision], LessEqual[y, 7.2e-51]]], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000013e177

   1. Initial program 58.2%

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

   2. Taylor expanded in y around inf 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

   4. Simplified 85.1%

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

   if -2.10000000000000013e177 < y < -8.5999999999999997e147 or -3.40000000000000006e59 < y < 7.2000000000000001e-51

   1. Initial program 83.8%

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

   2. Taylor expanded in y around 0 75.9%

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

      1. associate-*r* 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 75.4%

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

      4. associate-*r* 75.4%

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

      5. associate-*r* 75.3%

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

      6. distribute-rgt-in 76.7%

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

      7. +-commutative 76.7%

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

      8. mul-1-neg 76.7%

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

      9. unsub-neg 76.7%

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

      10. *-commutative 76.7%

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

      11. *-commutative 76.7%

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

   4. Simplified 76.7%

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

   if -8.5999999999999997e147 < y < -3.40000000000000006e59 or 7.2000000000000001e-51 < y

   1. Initial program 77.4%

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

   2. Taylor expanded in b around 0 74.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{+147} \lor \neg \left(y \leq -3.4 \cdot 10^{+59}\right) \land y \leq 7.2 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 66.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-96}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+84}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))))
   (if (<= x -2e+245)
     (* y (- (* x z) (* i j)))
     (if (<= x -1.08e-44)
       t_1
       (if (<= x 5e-96)
         (- (+ (* c (* t j)) (* i (- (* a b) (* y j)))) (* b (* z c)))
         (if (<= x 6.4e+84)
           (+ (* b (- (* a i) (* z c))) (* t (- (* c j) (* x a))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (x <= -2e+245) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -1.08e-44) {
		tmp = t_1;
	} else if (x <= 5e-96) {
		tmp = ((c * (t * j)) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	} else if (x <= 6.4e+84) {
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    if (x <= (-2d+245)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= (-1.08d-44)) then
        tmp = t_1
    else if (x <= 5d-96) then
        tmp = ((c * (t * j)) + (i * ((a * b) - (y * j)))) - (b * (z * c))
    else if (x <= 6.4d+84) then
        tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (x <= -2e+245) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -1.08e-44) {
		tmp = t_1;
	} else if (x <= 5e-96) {
		tmp = ((c * (t * j)) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	} else if (x <= 6.4e+84) {
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if x <= -2e+245:
		tmp = y * ((x * z) - (i * j))
	elif x <= -1.08e-44:
		tmp = t_1
	elif x <= 5e-96:
		tmp = ((c * (t * j)) + (i * ((a * b) - (y * j)))) - (b * (z * c))
	elif x <= 6.4e+84:
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (x <= -2e+245)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= -1.08e-44)
		tmp = t_1;
	elseif (x <= 5e-96)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) + Float64(i * Float64(Float64(a * b) - Float64(y * j)))) - Float64(b * Float64(z * c)));
	elseif (x <= 6.4e+84)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (x <= -2e+245)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= -1.08e-44)
		tmp = t_1;
	elseif (x <= 5e-96)
		tmp = ((c * (t * j)) + (i * ((a * b) - (y * j)))) - (b * (z * c));
	elseif (x <= 6.4e+84)
		tmp = (b * ((a * i) - (z * c))) + (t * ((c * j) - (x * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+245], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.08e-44], t$95$1, If[LessEqual[x, 5e-96], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e+84], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.00000000000000009e245

   1. Initial program 55.3%

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

   2. Taylor expanded in y around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

   4. Simplified 67.4%

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

   if -2.00000000000000009e245 < x < -1.07999999999999994e-44 or 6.4000000000000002e84 < x

   1. Initial program 82.9%

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

   2. Taylor expanded in b around 0 81.3%

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

   if -1.07999999999999994e-44 < x < 4.99999999999999995e-96

   1. Initial program 78.7%

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

   2. Taylor expanded in i around -inf 74.8%

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

   3. Taylor expanded in x around 0 82.3%

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

   if 4.99999999999999995e-96 < x < 6.4000000000000002e84

   1. Initial program 78.3%

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

   2. Taylor expanded in y around 0 63.2%

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

      1. associate-*r* 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 65.4%

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

      4. associate-*r* 65.4%

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

      5. associate-*r* 69.8%

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

      6. distribute-rgt-in 72.0%

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

      7. +-commutative 72.0%

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

      8. mul-1-neg 72.0%

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

      9. unsub-neg 72.0%

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

      10. *-commutative 72.0%

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

      11. *-commutative 72.0%

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

   4. Simplified 72.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-96}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + i \cdot \left(a \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+84}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7: 29.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -132000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-54}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))) (t_2 (* y (* i (- j)))))
   (if (<= y -5.5e+205)
     t_2
     (if (<= y -3.9e+128)
       (* x (* y z))
       (if (<= y -132000000.0)
         t_2
         (if (<= y -7e-54)
           (* i (* a b))
           (if (<= y -5.2e-181)
             t_1
             (if (<= y -6e-265)
               (* a (* t (- x)))
               (if (<= y 2.6e-240)
                 (* j (* t c))
                 (if (<= y 4.5e-92)
                   (* t (* x (- a)))
                   (if (<= y 6.8e-51)
                     t_1
                     (if (<= y 3.4e+44) t_2 (* y (* x z))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = y * (i * -j);
	double tmp;
	if (y <= -5.5e+205) {
		tmp = t_2;
	} else if (y <= -3.9e+128) {
		tmp = x * (y * z);
	} else if (y <= -132000000.0) {
		tmp = t_2;
	} else if (y <= -7e-54) {
		tmp = i * (a * b);
	} else if (y <= -5.2e-181) {
		tmp = t_1;
	} else if (y <= -6e-265) {
		tmp = a * (t * -x);
	} else if (y <= 2.6e-240) {
		tmp = j * (t * c);
	} else if (y <= 4.5e-92) {
		tmp = t * (x * -a);
	} else if (y <= 6.8e-51) {
		tmp = t_1;
	} else if (y <= 3.4e+44) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * c) * -b
    t_2 = y * (i * -j)
    if (y <= (-5.5d+205)) then
        tmp = t_2
    else if (y <= (-3.9d+128)) then
        tmp = x * (y * z)
    else if (y <= (-132000000.0d0)) then
        tmp = t_2
    else if (y <= (-7d-54)) then
        tmp = i * (a * b)
    else if (y <= (-5.2d-181)) then
        tmp = t_1
    else if (y <= (-6d-265)) then
        tmp = a * (t * -x)
    else if (y <= 2.6d-240) then
        tmp = j * (t * c)
    else if (y <= 4.5d-92) then
        tmp = t * (x * -a)
    else if (y <= 6.8d-51) then
        tmp = t_1
    else if (y <= 3.4d+44) then
        tmp = t_2
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = y * (i * -j);
	double tmp;
	if (y <= -5.5e+205) {
		tmp = t_2;
	} else if (y <= -3.9e+128) {
		tmp = x * (y * z);
	} else if (y <= -132000000.0) {
		tmp = t_2;
	} else if (y <= -7e-54) {
		tmp = i * (a * b);
	} else if (y <= -5.2e-181) {
		tmp = t_1;
	} else if (y <= -6e-265) {
		tmp = a * (t * -x);
	} else if (y <= 2.6e-240) {
		tmp = j * (t * c);
	} else if (y <= 4.5e-92) {
		tmp = t * (x * -a);
	} else if (y <= 6.8e-51) {
		tmp = t_1;
	} else if (y <= 3.4e+44) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	t_2 = y * (i * -j)
	tmp = 0
	if y <= -5.5e+205:
		tmp = t_2
	elif y <= -3.9e+128:
		tmp = x * (y * z)
	elif y <= -132000000.0:
		tmp = t_2
	elif y <= -7e-54:
		tmp = i * (a * b)
	elif y <= -5.2e-181:
		tmp = t_1
	elif y <= -6e-265:
		tmp = a * (t * -x)
	elif y <= 2.6e-240:
		tmp = j * (t * c)
	elif y <= 4.5e-92:
		tmp = t * (x * -a)
	elif y <= 6.8e-51:
		tmp = t_1
	elif y <= 3.4e+44:
		tmp = t_2
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(-b))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (y <= -5.5e+205)
		tmp = t_2;
	elseif (y <= -3.9e+128)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -132000000.0)
		tmp = t_2;
	elseif (y <= -7e-54)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= -5.2e-181)
		tmp = t_1;
	elseif (y <= -6e-265)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 2.6e-240)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 4.5e-92)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 6.8e-51)
		tmp = t_1;
	elseif (y <= 3.4e+44)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	t_2 = y * (i * -j);
	tmp = 0.0;
	if (y <= -5.5e+205)
		tmp = t_2;
	elseif (y <= -3.9e+128)
		tmp = x * (y * z);
	elseif (y <= -132000000.0)
		tmp = t_2;
	elseif (y <= -7e-54)
		tmp = i * (a * b);
	elseif (y <= -5.2e-181)
		tmp = t_1;
	elseif (y <= -6e-265)
		tmp = a * (t * -x);
	elseif (y <= 2.6e-240)
		tmp = j * (t * c);
	elseif (y <= 4.5e-92)
		tmp = t * (x * -a);
	elseif (y <= 6.8e-51)
		tmp = t_1;
	elseif (y <= 3.4e+44)
		tmp = t_2;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+205], t$95$2, If[LessEqual[y, -3.9e+128], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -132000000.0], t$95$2, If[LessEqual[y, -7e-54], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-181], t$95$1, If[LessEqual[y, -6e-265], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-240], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-92], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-51], t$95$1, If[LessEqual[y, 3.4e+44], t$95$2, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -5.50000000000000004e205 or -3.8999999999999997e128 < y < -1.32e8 or 6.80000000000000005e-51 < y < 3.4e44

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in x around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. distribute-lft-neg-out 51.2%

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

      3. *-commutative 51.2%

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

   7. Simplified 51.2%

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

   if -5.50000000000000004e205 < y < -3.8999999999999997e128

   1. Initial program 52.8%

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

   2. Taylor expanded in b around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. +-commutative 58.8%

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

      4. mul-1-neg 58.8%

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

      5. *-commutative 58.8%

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

      6. *-commutative 58.8%

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

      7. fma-neg 64.7%

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

      8. fma-def 64.7%

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

      9. mul-1-neg 64.7%

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

      10. +-commutative 64.7%

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

      11. sub-neg 64.7%

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

      12. fma-udef 58.8%

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

      13. *-commutative 58.8%

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

      14. *-commutative 58.8%

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

      15. distribute-lft-neg-in 58.8%

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

      16. *-commutative 58.8%

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

   4. Simplified 64.7%

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

      1. distribute-rgt-neg-out 64.7%

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

      2. fma-neg 58.8%

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

      3. *-commutative 58.8%

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

      4. *-commutative 58.8%

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

   6. Applied egg-rr 58.8%

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

   7. Taylor expanded in z around inf 59.6%

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

   if -1.32e8 < y < -6.99999999999999964e-54

   1. Initial program 90.0%

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

   2. Taylor expanded in b around inf 41.9%

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

      1. *-commutative 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in a around inf 31.6%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. expm1-log1p-u 16.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)\right)} \]

      2. expm1-udef 6.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)} - 1} \]

      3. *-commutative 6.9%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(i \cdot b\right)}\right)} - 1 \]

   8. Applied egg-rr 6.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 16.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. expm1-log1p 31.7%

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

      3. *-commutative 31.7%

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

      4. associate-*l* 31.7%

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

   10. Simplified 31.7%

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

   if -6.99999999999999964e-54 < y < -5.19999999999999998e-181 or 4.5e-92 < y < 6.80000000000000005e-51

   1. Initial program 92.0%

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

   2. Taylor expanded in b around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in a around 0 53.2%

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

      1. neg-mul-1 53.2%

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

      2. *-commutative 53.2%

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

      3. distribute-rgt-neg-in 53.2%

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

   7. Simplified 53.2%

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

   if -5.19999999999999998e-181 < y < -5.9999999999999996e-265

   1. Initial program 65.4%

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

   2. Taylor expanded in b around 0 44.2%

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

      1. +-commutative 44.2%

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

      2. sub-neg 44.2%

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

      3. +-commutative 44.2%

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

      4. mul-1-neg 44.2%

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

      5. *-commutative 44.2%

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

      6. *-commutative 44.2%

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

      7. fma-neg 44.2%

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

      8. fma-def 44.2%

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

      9. mul-1-neg 44.2%

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

      10. +-commutative 44.2%

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

      11. sub-neg 44.2%

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

      12. fma-udef 44.2%

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

      13. *-commutative 44.2%

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

      14. *-commutative 44.2%

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

      15. distribute-lft-neg-in 44.2%

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

      16. *-commutative 44.2%

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

   4. Simplified 44.2%

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

      1. distribute-rgt-neg-out 44.2%

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

      2. fma-neg 44.2%

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

      3. *-commutative 44.2%

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

      4. *-commutative 44.2%

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

   6. Applied egg-rr 44.2%

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

   7. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. neg-mul-1 50.6%

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

   9. Simplified 50.6%

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

   if -5.9999999999999996e-265 < y < 2.59999999999999992e-240

   1. Initial program 77.6%

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

   2. Taylor expanded in c around inf 58.4%

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

   3. Taylor expanded in j around inf 46.8%

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

      1. associate-*r* 40.6%

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

      2. *-commutative 40.6%

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

      3. associate-*l* 49.7%

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

   5. Simplified 49.7%

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

   if 2.59999999999999992e-240 < y < 4.5e-92

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in c around 0 47.4%

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

      1. mul-1-neg 47.4%

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

      2. *-commutative 47.4%

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

      3. distribute-rgt-neg-in 47.4%

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

   7. Simplified 47.4%

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

   if 3.4e44 < y

   1. Initial program 74.1%

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

   2. Taylor expanded in y around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in x around inf 48.6%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -132000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-54}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-181}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-51}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 8: 29.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -340000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.26 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))) (t_2 (* i (* y (- j)))))
   (if (<= y -1.7e+206)
     t_2
     (if (<= y -9.2e+126)
       (* x (* y z))
       (if (<= y -340000000.0)
         (* y (* i (- j)))
         (if (<= y -4.2e-54)
           (* i (* a b))
           (if (<= y -1.7e-179)
             t_1
             (if (<= y -4.2e-264)
               (* a (* t (- x)))
               (if (<= y 2.26e-240)
                 (* j (* t c))
                 (if (<= y 4.8e-90)
                   (* t (* x (- a)))
                   (if (<= y 7.5e-51)
                     t_1
                     (if (<= y 2.5e+53) t_2 (* y (* x z))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = i * (y * -j);
	double tmp;
	if (y <= -1.7e+206) {
		tmp = t_2;
	} else if (y <= -9.2e+126) {
		tmp = x * (y * z);
	} else if (y <= -340000000.0) {
		tmp = y * (i * -j);
	} else if (y <= -4.2e-54) {
		tmp = i * (a * b);
	} else if (y <= -1.7e-179) {
		tmp = t_1;
	} else if (y <= -4.2e-264) {
		tmp = a * (t * -x);
	} else if (y <= 2.26e-240) {
		tmp = j * (t * c);
	} else if (y <= 4.8e-90) {
		tmp = t * (x * -a);
	} else if (y <= 7.5e-51) {
		tmp = t_1;
	} else if (y <= 2.5e+53) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * c) * -b
    t_2 = i * (y * -j)
    if (y <= (-1.7d+206)) then
        tmp = t_2
    else if (y <= (-9.2d+126)) then
        tmp = x * (y * z)
    else if (y <= (-340000000.0d0)) then
        tmp = y * (i * -j)
    else if (y <= (-4.2d-54)) then
        tmp = i * (a * b)
    else if (y <= (-1.7d-179)) then
        tmp = t_1
    else if (y <= (-4.2d-264)) then
        tmp = a * (t * -x)
    else if (y <= 2.26d-240) then
        tmp = j * (t * c)
    else if (y <= 4.8d-90) then
        tmp = t * (x * -a)
    else if (y <= 7.5d-51) then
        tmp = t_1
    else if (y <= 2.5d+53) then
        tmp = t_2
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = i * (y * -j);
	double tmp;
	if (y <= -1.7e+206) {
		tmp = t_2;
	} else if (y <= -9.2e+126) {
		tmp = x * (y * z);
	} else if (y <= -340000000.0) {
		tmp = y * (i * -j);
	} else if (y <= -4.2e-54) {
		tmp = i * (a * b);
	} else if (y <= -1.7e-179) {
		tmp = t_1;
	} else if (y <= -4.2e-264) {
		tmp = a * (t * -x);
	} else if (y <= 2.26e-240) {
		tmp = j * (t * c);
	} else if (y <= 4.8e-90) {
		tmp = t * (x * -a);
	} else if (y <= 7.5e-51) {
		tmp = t_1;
	} else if (y <= 2.5e+53) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	t_2 = i * (y * -j)
	tmp = 0
	if y <= -1.7e+206:
		tmp = t_2
	elif y <= -9.2e+126:
		tmp = x * (y * z)
	elif y <= -340000000.0:
		tmp = y * (i * -j)
	elif y <= -4.2e-54:
		tmp = i * (a * b)
	elif y <= -1.7e-179:
		tmp = t_1
	elif y <= -4.2e-264:
		tmp = a * (t * -x)
	elif y <= 2.26e-240:
		tmp = j * (t * c)
	elif y <= 4.8e-90:
		tmp = t * (x * -a)
	elif y <= 7.5e-51:
		tmp = t_1
	elif y <= 2.5e+53:
		tmp = t_2
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(-b))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -1.7e+206)
		tmp = t_2;
	elseif (y <= -9.2e+126)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -340000000.0)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (y <= -4.2e-54)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= -1.7e-179)
		tmp = t_1;
	elseif (y <= -4.2e-264)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 2.26e-240)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 4.8e-90)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 7.5e-51)
		tmp = t_1;
	elseif (y <= 2.5e+53)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (y <= -1.7e+206)
		tmp = t_2;
	elseif (y <= -9.2e+126)
		tmp = x * (y * z);
	elseif (y <= -340000000.0)
		tmp = y * (i * -j);
	elseif (y <= -4.2e-54)
		tmp = i * (a * b);
	elseif (y <= -1.7e-179)
		tmp = t_1;
	elseif (y <= -4.2e-264)
		tmp = a * (t * -x);
	elseif (y <= 2.26e-240)
		tmp = j * (t * c);
	elseif (y <= 4.8e-90)
		tmp = t * (x * -a);
	elseif (y <= 7.5e-51)
		tmp = t_1;
	elseif (y <= 2.5e+53)
		tmp = t_2;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+206], t$95$2, If[LessEqual[y, -9.2e+126], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -340000000.0], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-54], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-179], t$95$1, If[LessEqual[y, -4.2e-264], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.26e-240], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-90], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-51], t$95$1, If[LessEqual[y, 2.5e+53], t$95$2, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -1.69999999999999999e206 or 7.49999999999999976e-51 < y < 2.5000000000000002e53

   1. Initial program 75.8%

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

   2. Taylor expanded in y around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in x around 0 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

      3. *-commutative 57.3%

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

   7. Simplified 57.3%

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

   if -1.69999999999999999e206 < y < -9.2000000000000002e126

   1. Initial program 52.8%

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

   2. Taylor expanded in b around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. +-commutative 58.8%

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

      4. mul-1-neg 58.8%

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

      5. *-commutative 58.8%

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

      6. *-commutative 58.8%

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

      7. fma-neg 64.7%

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

      8. fma-def 64.7%

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

      9. mul-1-neg 64.7%

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

      10. +-commutative 64.7%

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

      11. sub-neg 64.7%

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

      12. fma-udef 58.8%

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

      13. *-commutative 58.8%

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

      14. *-commutative 58.8%

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

      15. distribute-lft-neg-in 58.8%

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

      16. *-commutative 58.8%

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

   4. Simplified 64.7%

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

      1. distribute-rgt-neg-out 64.7%

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

      2. fma-neg 58.8%

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

      3. *-commutative 58.8%

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

      4. *-commutative 58.8%

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

   6. Applied egg-rr 58.8%

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

   7. Taylor expanded in z around inf 59.6%

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

   if -9.2000000000000002e126 < y < -3.4e8

   1. Initial program 76.4%

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

   2. Taylor expanded in y around inf 42.8%

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

      1. +-commutative 42.8%

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

      2. mul-1-neg 42.8%

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

      3. unsub-neg 42.8%

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

   4. Simplified 42.8%

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

   5. Taylor expanded in x around 0 37.7%

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

      1. mul-1-neg 37.7%

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

      2. distribute-lft-neg-out 37.7%

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

      3. *-commutative 37.7%

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

   7. Simplified 37.7%

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

   if -3.4e8 < y < -4.2e-54

   1. Initial program 90.0%

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

   2. Taylor expanded in b around inf 41.9%

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

      1. *-commutative 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in a around inf 31.6%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. expm1-log1p-u 16.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)\right)} \]

      2. expm1-udef 6.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)} - 1} \]

      3. *-commutative 6.9%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(i \cdot b\right)}\right)} - 1 \]

   8. Applied egg-rr 6.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 16.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. expm1-log1p 31.7%

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

      3. *-commutative 31.7%

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

      4. associate-*l* 31.7%

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

   10. Simplified 31.7%

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

   if -4.2e-54 < y < -1.6999999999999999e-179 or 4.8000000000000003e-90 < y < 7.49999999999999976e-51

   1. Initial program 92.0%

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

   2. Taylor expanded in b around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in a around 0 53.2%

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

      1. neg-mul-1 53.2%

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

      2. *-commutative 53.2%

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

      3. distribute-rgt-neg-in 53.2%

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

   7. Simplified 53.2%

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

   if -1.6999999999999999e-179 < y < -4.2000000000000004e-264

   1. Initial program 65.4%

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

   2. Taylor expanded in b around 0 44.2%

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

      1. +-commutative 44.2%

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

      2. sub-neg 44.2%

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

      3. +-commutative 44.2%

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

      4. mul-1-neg 44.2%

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

      5. *-commutative 44.2%

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

      6. *-commutative 44.2%

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

      7. fma-neg 44.2%

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

      8. fma-def 44.2%

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

      9. mul-1-neg 44.2%

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

      10. +-commutative 44.2%

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

      11. sub-neg 44.2%

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

      12. fma-udef 44.2%

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

      13. *-commutative 44.2%

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

      14. *-commutative 44.2%

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

      15. distribute-lft-neg-in 44.2%

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

      16. *-commutative 44.2%

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

   4. Simplified 44.2%

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

      1. distribute-rgt-neg-out 44.2%

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

      2. fma-neg 44.2%

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

      3. *-commutative 44.2%

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

      4. *-commutative 44.2%

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

   6. Applied egg-rr 44.2%

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

   7. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. neg-mul-1 50.6%

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

   9. Simplified 50.6%

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

   if -4.2000000000000004e-264 < y < 2.25999999999999993e-240

   1. Initial program 77.6%

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

   2. Taylor expanded in c around inf 58.4%

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

   3. Taylor expanded in j around inf 46.8%

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

      1. associate-*r* 40.6%

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

      2. *-commutative 40.6%

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

      3. associate-*l* 49.7%

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

   5. Simplified 49.7%

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

   if 2.25999999999999993e-240 < y < 4.8000000000000003e-90

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in c around 0 47.4%

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

      1. mul-1-neg 47.4%

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

      2. *-commutative 47.4%

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

      3. distribute-rgt-neg-in 47.4%

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

   7. Simplified 47.4%

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

   if 2.5000000000000002e53 < y

   1. Initial program 74.1%

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

   2. Taylor expanded in y around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in x around inf 48.6%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -340000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-179}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.26 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 9: 51.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -0.13:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -1.05e+49)
     t_3
     (if (<= y -0.13)
       t_2
       (if (<= y -1.75e-48)
         t_3
         (if (<= y -9.8e-136)
           t_1
           (if (<= y -1.1e-254)
             t_2
             (if (<= y -3.6e-298)
               (- (* c (* t j)) (* x (* t a)))
               (if (<= y 3.9e-86)
                 (* a (- (* b i) (* x t)))
                 (if (<= y 1.5e-50) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+49) {
		tmp = t_3;
	} else if (y <= -0.13) {
		tmp = t_2;
	} else if (y <= -1.75e-48) {
		tmp = t_3;
	} else if (y <= -9.8e-136) {
		tmp = t_1;
	} else if (y <= -1.1e-254) {
		tmp = t_2;
	} else if (y <= -3.6e-298) {
		tmp = (c * (t * j)) - (x * (t * a));
	} else if (y <= 3.9e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 1.5e-50) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = b * ((a * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-1.05d+49)) then
        tmp = t_3
    else if (y <= (-0.13d0)) then
        tmp = t_2
    else if (y <= (-1.75d-48)) then
        tmp = t_3
    else if (y <= (-9.8d-136)) then
        tmp = t_1
    else if (y <= (-1.1d-254)) then
        tmp = t_2
    else if (y <= (-3.6d-298)) then
        tmp = (c * (t * j)) - (x * (t * a))
    else if (y <= 3.9d-86) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 1.5d-50) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+49) {
		tmp = t_3;
	} else if (y <= -0.13) {
		tmp = t_2;
	} else if (y <= -1.75e-48) {
		tmp = t_3;
	} else if (y <= -9.8e-136) {
		tmp = t_1;
	} else if (y <= -1.1e-254) {
		tmp = t_2;
	} else if (y <= -3.6e-298) {
		tmp = (c * (t * j)) - (x * (t * a));
	} else if (y <= 3.9e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 1.5e-50) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = b * ((a * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.05e+49:
		tmp = t_3
	elif y <= -0.13:
		tmp = t_2
	elif y <= -1.75e-48:
		tmp = t_3
	elif y <= -9.8e-136:
		tmp = t_1
	elif y <= -1.1e-254:
		tmp = t_2
	elif y <= -3.6e-298:
		tmp = (c * (t * j)) - (x * (t * a))
	elif y <= 3.9e-86:
		tmp = a * ((b * i) - (x * t))
	elif y <= 1.5e-50:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.05e+49)
		tmp = t_3;
	elseif (y <= -0.13)
		tmp = t_2;
	elseif (y <= -1.75e-48)
		tmp = t_3;
	elseif (y <= -9.8e-136)
		tmp = t_1;
	elseif (y <= -1.1e-254)
		tmp = t_2;
	elseif (y <= -3.6e-298)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(x * Float64(t * a)));
	elseif (y <= 3.9e-86)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 1.5e-50)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = b * ((a * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.05e+49)
		tmp = t_3;
	elseif (y <= -0.13)
		tmp = t_2;
	elseif (y <= -1.75e-48)
		tmp = t_3;
	elseif (y <= -9.8e-136)
		tmp = t_1;
	elseif (y <= -1.1e-254)
		tmp = t_2;
	elseif (y <= -3.6e-298)
		tmp = (c * (t * j)) - (x * (t * a));
	elseif (y <= 3.9e-86)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 1.5e-50)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+49], t$95$3, If[LessEqual[y, -0.13], t$95$2, If[LessEqual[y, -1.75e-48], t$95$3, If[LessEqual[y, -9.8e-136], t$95$1, If[LessEqual[y, -1.1e-254], t$95$2, If[LessEqual[y, -3.6e-298], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-86], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-50], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05000000000000005e49 or -0.13 < y < -1.74999999999999996e-48 or 1.49999999999999995e-50 < y

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   4. Simplified 67.9%

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

   if -1.05000000000000005e49 < y < -0.13 or -9.7999999999999999e-136 < y < -1.1000000000000001e-254

   1. Initial program 80.8%

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

   2. Taylor expanded in b around inf 70.2%

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

      1. *-commutative 70.2%

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

   4. Simplified 70.2%

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

   if -1.74999999999999996e-48 < y < -9.7999999999999999e-136 or 3.9000000000000002e-86 < y < 1.49999999999999995e-50

   1. Initial program 92.2%

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

   2. Taylor expanded in c around inf 75.6%

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

   if -1.1000000000000001e-254 < y < -3.60000000000000002e-298

   1. Initial program 70.7%

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

   2. Taylor expanded in b around 0 99.8%

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

   3. Taylor expanded in y around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. associate-*r* 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -3.60000000000000002e-298 < y < 3.9000000000000002e-86

   1. Initial program 85.4%

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

   2. Taylor expanded in a around -inf 62.5%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -0.13:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-136}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 10: 28.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -50000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))) (t_2 (* y (* i (- j)))))
   (if (<= y -7.5e+202)
     t_2
     (if (<= y -8e+122)
       (* x (* y z))
       (if (<= y -50000000.0)
         t_2
         (if (<= y -1.3e-50)
           (* i (* a b))
           (if (<= y -5.5e-261)
             t_1
             (if (<= y 1.05e-234)
               (* j (* t c))
               (if (<= y 2.35e-93)
                 (* t (* x (- a)))
                 (if (<= y 8.2e-51)
                   t_1
                   (if (<= y 1.6e+41) t_2 (* y (* x z)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = y * (i * -j);
	double tmp;
	if (y <= -7.5e+202) {
		tmp = t_2;
	} else if (y <= -8e+122) {
		tmp = x * (y * z);
	} else if (y <= -50000000.0) {
		tmp = t_2;
	} else if (y <= -1.3e-50) {
		tmp = i * (a * b);
	} else if (y <= -5.5e-261) {
		tmp = t_1;
	} else if (y <= 1.05e-234) {
		tmp = j * (t * c);
	} else if (y <= 2.35e-93) {
		tmp = t * (x * -a);
	} else if (y <= 8.2e-51) {
		tmp = t_1;
	} else if (y <= 1.6e+41) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * c) * -b
    t_2 = y * (i * -j)
    if (y <= (-7.5d+202)) then
        tmp = t_2
    else if (y <= (-8d+122)) then
        tmp = x * (y * z)
    else if (y <= (-50000000.0d0)) then
        tmp = t_2
    else if (y <= (-1.3d-50)) then
        tmp = i * (a * b)
    else if (y <= (-5.5d-261)) then
        tmp = t_1
    else if (y <= 1.05d-234) then
        tmp = j * (t * c)
    else if (y <= 2.35d-93) then
        tmp = t * (x * -a)
    else if (y <= 8.2d-51) then
        tmp = t_1
    else if (y <= 1.6d+41) then
        tmp = t_2
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = y * (i * -j);
	double tmp;
	if (y <= -7.5e+202) {
		tmp = t_2;
	} else if (y <= -8e+122) {
		tmp = x * (y * z);
	} else if (y <= -50000000.0) {
		tmp = t_2;
	} else if (y <= -1.3e-50) {
		tmp = i * (a * b);
	} else if (y <= -5.5e-261) {
		tmp = t_1;
	} else if (y <= 1.05e-234) {
		tmp = j * (t * c);
	} else if (y <= 2.35e-93) {
		tmp = t * (x * -a);
	} else if (y <= 8.2e-51) {
		tmp = t_1;
	} else if (y <= 1.6e+41) {
		tmp = t_2;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	t_2 = y * (i * -j)
	tmp = 0
	if y <= -7.5e+202:
		tmp = t_2
	elif y <= -8e+122:
		tmp = x * (y * z)
	elif y <= -50000000.0:
		tmp = t_2
	elif y <= -1.3e-50:
		tmp = i * (a * b)
	elif y <= -5.5e-261:
		tmp = t_1
	elif y <= 1.05e-234:
		tmp = j * (t * c)
	elif y <= 2.35e-93:
		tmp = t * (x * -a)
	elif y <= 8.2e-51:
		tmp = t_1
	elif y <= 1.6e+41:
		tmp = t_2
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(-b))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (y <= -7.5e+202)
		tmp = t_2;
	elseif (y <= -8e+122)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -50000000.0)
		tmp = t_2;
	elseif (y <= -1.3e-50)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= -5.5e-261)
		tmp = t_1;
	elseif (y <= 1.05e-234)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 2.35e-93)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 8.2e-51)
		tmp = t_1;
	elseif (y <= 1.6e+41)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	t_2 = y * (i * -j);
	tmp = 0.0;
	if (y <= -7.5e+202)
		tmp = t_2;
	elseif (y <= -8e+122)
		tmp = x * (y * z);
	elseif (y <= -50000000.0)
		tmp = t_2;
	elseif (y <= -1.3e-50)
		tmp = i * (a * b);
	elseif (y <= -5.5e-261)
		tmp = t_1;
	elseif (y <= 1.05e-234)
		tmp = j * (t * c);
	elseif (y <= 2.35e-93)
		tmp = t * (x * -a);
	elseif (y <= 8.2e-51)
		tmp = t_1;
	elseif (y <= 1.6e+41)
		tmp = t_2;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+202], t$95$2, If[LessEqual[y, -8e+122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -50000000.0], t$95$2, If[LessEqual[y, -1.3e-50], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-261], t$95$1, If[LessEqual[y, 1.05e-234], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-93], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-51], t$95$1, If[LessEqual[y, 1.6e+41], t$95$2, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -7.4999999999999999e202 or -8.00000000000000012e122 < y < -5e7 or 8.19999999999999947e-51 < y < 1.60000000000000005e41

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in x around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. distribute-lft-neg-out 51.2%

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

      3. *-commutative 51.2%

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

   7. Simplified 51.2%

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

   if -7.4999999999999999e202 < y < -8.00000000000000012e122

   1. Initial program 52.8%

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

   2. Taylor expanded in b around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. +-commutative 58.8%

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

      4. mul-1-neg 58.8%

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

      5. *-commutative 58.8%

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

      6. *-commutative 58.8%

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

      7. fma-neg 64.7%

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

      8. fma-def 64.7%

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

      9. mul-1-neg 64.7%

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

      10. +-commutative 64.7%

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

      11. sub-neg 64.7%

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

      12. fma-udef 58.8%

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

      13. *-commutative 58.8%

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

      14. *-commutative 58.8%

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

      15. distribute-lft-neg-in 58.8%

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

      16. *-commutative 58.8%

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

   4. Simplified 64.7%

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

      1. distribute-rgt-neg-out 64.7%

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

      2. fma-neg 58.8%

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

      3. *-commutative 58.8%

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

      4. *-commutative 58.8%

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

   6. Applied egg-rr 58.8%

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

   7. Taylor expanded in z around inf 59.6%

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

   if -5e7 < y < -1.3000000000000001e-50

   1. Initial program 90.0%

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

   2. Taylor expanded in b around inf 41.9%

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

      1. *-commutative 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in a around inf 31.6%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. expm1-log1p-u 16.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)\right)} \]

      2. expm1-udef 6.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)} - 1} \]

      3. *-commutative 6.9%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(i \cdot b\right)}\right)} - 1 \]

   8. Applied egg-rr 6.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 16.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. expm1-log1p 31.7%

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

      3. *-commutative 31.7%

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

      4. associate-*l* 31.7%

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

   10. Simplified 31.7%

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

   if -1.3000000000000001e-50 < y < -5.50000000000000042e-261 or 2.35e-93 < y < 8.19999999999999947e-51

   1. Initial program 84.1%

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

   2. Taylor expanded in b around inf 65.7%

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

      1. *-commutative 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in a around 0 44.7%

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

      1. neg-mul-1 44.7%

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

      2. *-commutative 44.7%

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

      3. distribute-rgt-neg-in 44.7%

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

   7. Simplified 44.7%

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

   if -5.50000000000000042e-261 < y < 1.04999999999999996e-234

   1. Initial program 78.9%

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

   2. Taylor expanded in c around inf 55.0%

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

   3. Taylor expanded in j around inf 44.1%

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

      1. associate-*r* 38.3%

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

      2. *-commutative 38.3%

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

      3. associate-*l* 46.9%

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

   5. Simplified 46.9%

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

   if 1.04999999999999996e-234 < y < 2.35e-93

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in c around 0 47.4%

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

      1. mul-1-neg 47.4%

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

      2. *-commutative 47.4%

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

      3. distribute-rgt-neg-in 47.4%

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

   7. Simplified 47.4%

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

   if 1.60000000000000005e41 < y

   1. Initial program 74.1%

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

   2. Taylor expanded in y around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in x around inf 48.6%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -50000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 39.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+203}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= y -4.8e+203)
     (* i (* y (- j)))
     (if (<= y -2.8e+122)
       (* x (* y z))
       (if (<= y -1.6e-261)
         t_1
         (if (<= y 6e-284)
           (* j (* t c))
           (if (<= y 2.35e-169)
             t_1
             (if (<= y 1.3e-94)
               (* t (* x (- a)))
               (if (<= y 4.5e+56) t_1 (* y (* x z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -4.8e+203) {
		tmp = i * (y * -j);
	} else if (y <= -2.8e+122) {
		tmp = x * (y * z);
	} else if (y <= -1.6e-261) {
		tmp = t_1;
	} else if (y <= 6e-284) {
		tmp = j * (t * c);
	} else if (y <= 2.35e-169) {
		tmp = t_1;
	} else if (y <= 1.3e-94) {
		tmp = t * (x * -a);
	} else if (y <= 4.5e+56) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (y <= (-4.8d+203)) then
        tmp = i * (y * -j)
    else if (y <= (-2.8d+122)) then
        tmp = x * (y * z)
    else if (y <= (-1.6d-261)) then
        tmp = t_1
    else if (y <= 6d-284) then
        tmp = j * (t * c)
    else if (y <= 2.35d-169) then
        tmp = t_1
    else if (y <= 1.3d-94) then
        tmp = t * (x * -a)
    else if (y <= 4.5d+56) then
        tmp = t_1
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -4.8e+203) {
		tmp = i * (y * -j);
	} else if (y <= -2.8e+122) {
		tmp = x * (y * z);
	} else if (y <= -1.6e-261) {
		tmp = t_1;
	} else if (y <= 6e-284) {
		tmp = j * (t * c);
	} else if (y <= 2.35e-169) {
		tmp = t_1;
	} else if (y <= 1.3e-94) {
		tmp = t * (x * -a);
	} else if (y <= 4.5e+56) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -4.8e+203:
		tmp = i * (y * -j)
	elif y <= -2.8e+122:
		tmp = x * (y * z)
	elif y <= -1.6e-261:
		tmp = t_1
	elif y <= 6e-284:
		tmp = j * (t * c)
	elif y <= 2.35e-169:
		tmp = t_1
	elif y <= 1.3e-94:
		tmp = t * (x * -a)
	elif y <= 4.5e+56:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -4.8e+203)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -2.8e+122)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1.6e-261)
		tmp = t_1;
	elseif (y <= 6e-284)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 2.35e-169)
		tmp = t_1;
	elseif (y <= 1.3e-94)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 4.5e+56)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (y <= -4.8e+203)
		tmp = i * (y * -j);
	elseif (y <= -2.8e+122)
		tmp = x * (y * z);
	elseif (y <= -1.6e-261)
		tmp = t_1;
	elseif (y <= 6e-284)
		tmp = j * (t * c);
	elseif (y <= 2.35e-169)
		tmp = t_1;
	elseif (y <= 1.3e-94)
		tmp = t * (x * -a);
	elseif (y <= 4.5e+56)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+203], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e+122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-261], t$95$1, If[LessEqual[y, 6e-284], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-169], t$95$1, If[LessEqual[y, 1.3e-94], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+56], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.8000000000000002e203

   1. Initial program 61.7%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

   5. Taylor expanded in x around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. neg-mul-1 70.9%

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

      3. *-commutative 70.9%

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

   7. Simplified 70.9%

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

   if -4.8000000000000002e203 < y < -2.8e122

   1. Initial program 52.8%

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

   2. Taylor expanded in b around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. sub-neg 58.8%

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

      3. +-commutative 58.8%

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

      4. mul-1-neg 58.8%

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

      5. *-commutative 58.8%

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

      6. *-commutative 58.8%

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

      7. fma-neg 64.7%

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

      8. fma-def 64.7%

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

      9. mul-1-neg 64.7%

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

      10. +-commutative 64.7%

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

      11. sub-neg 64.7%

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

      12. fma-udef 58.8%

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

      13. *-commutative 58.8%

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

      14. *-commutative 58.8%

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

      15. distribute-lft-neg-in 58.8%

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

      16. *-commutative 58.8%

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

   4. Simplified 64.7%

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

      1. distribute-rgt-neg-out 64.7%

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

      2. fma-neg 58.8%

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

      3. *-commutative 58.8%

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

      4. *-commutative 58.8%

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

   6. Applied egg-rr 58.8%

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

   7. Taylor expanded in z around inf 59.6%

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

   if -2.8e122 < y < -1.60000000000000002e-261 or 5.9999999999999999e-284 < y < 2.34999999999999995e-169 or 1.29999999999999997e-94 < y < 4.5000000000000003e56

   1. Initial program 87.2%

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

   2. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   4. Simplified 51.2%

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

   if -1.60000000000000002e-261 < y < 5.9999999999999999e-284

   1. Initial program 69.8%

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

   2. Taylor expanded in c around inf 52.6%

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

   3. Taylor expanded in j around inf 45.3%

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

      1. associate-*r* 37.0%

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

      2. *-commutative 37.0%

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

      3. associate-*l* 49.3%

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

   5. Simplified 49.3%

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

   if 2.34999999999999995e-169 < y < 1.29999999999999997e-94

   1. Initial program 89.8%

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

   2. Taylor expanded in t around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in c around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

   7. Simplified 61.9%

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

   if 4.5000000000000003e56 < y

   1. Initial program 72.8%

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

   2. Taylor expanded in y around inf 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in x around inf 50.9%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+203}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 12: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -3.2e+60)
     t_3
     (if (<= j -4e-18)
       t_1
       (if (<= j -2.2e-43)
         (* t (- (* c j) (* x a)))
         (if (<= j -1.25e-189)
           t_2
           (if (<= j 4.8e-269)
             t_1
             (if (<= j 5.2e-159) t_2 (if (<= j 2.25e+49) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.2e+60) {
		tmp = t_3;
	} else if (j <= -4e-18) {
		tmp = t_1;
	} else if (j <= -2.2e-43) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= -1.25e-189) {
		tmp = t_2;
	} else if (j <= 4.8e-269) {
		tmp = t_1;
	} else if (j <= 5.2e-159) {
		tmp = t_2;
	} else if (j <= 2.25e+49) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-3.2d+60)) then
        tmp = t_3
    else if (j <= (-4d-18)) then
        tmp = t_1
    else if (j <= (-2.2d-43)) then
        tmp = t * ((c * j) - (x * a))
    else if (j <= (-1.25d-189)) then
        tmp = t_2
    else if (j <= 4.8d-269) then
        tmp = t_1
    else if (j <= 5.2d-159) then
        tmp = t_2
    else if (j <= 2.25d+49) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.2e+60) {
		tmp = t_3;
	} else if (j <= -4e-18) {
		tmp = t_1;
	} else if (j <= -2.2e-43) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= -1.25e-189) {
		tmp = t_2;
	} else if (j <= 4.8e-269) {
		tmp = t_1;
	} else if (j <= 5.2e-159) {
		tmp = t_2;
	} else if (j <= 2.25e+49) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.2e+60:
		tmp = t_3
	elif j <= -4e-18:
		tmp = t_1
	elif j <= -2.2e-43:
		tmp = t * ((c * j) - (x * a))
	elif j <= -1.25e-189:
		tmp = t_2
	elif j <= 4.8e-269:
		tmp = t_1
	elif j <= 5.2e-159:
		tmp = t_2
	elif j <= 2.25e+49:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.2e+60)
		tmp = t_3;
	elseif (j <= -4e-18)
		tmp = t_1;
	elseif (j <= -2.2e-43)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (j <= -1.25e-189)
		tmp = t_2;
	elseif (j <= 4.8e-269)
		tmp = t_1;
	elseif (j <= 5.2e-159)
		tmp = t_2;
	elseif (j <= 2.25e+49)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.2e+60)
		tmp = t_3;
	elseif (j <= -4e-18)
		tmp = t_1;
	elseif (j <= -2.2e-43)
		tmp = t * ((c * j) - (x * a));
	elseif (j <= -1.25e-189)
		tmp = t_2;
	elseif (j <= 4.8e-269)
		tmp = t_1;
	elseif (j <= 5.2e-159)
		tmp = t_2;
	elseif (j <= 2.25e+49)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+60], t$95$3, If[LessEqual[j, -4e-18], t$95$1, If[LessEqual[j, -2.2e-43], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.25e-189], t$95$2, If[LessEqual[j, 4.8e-269], t$95$1, If[LessEqual[j, 5.2e-159], t$95$2, If[LessEqual[j, 2.25e+49], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.19999999999999991e60 or 2.24999999999999991e49 < j

   1. Initial program 79.3%

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

   2. Taylor expanded in j around inf 65.2%

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

   if -3.19999999999999991e60 < j < -4.0000000000000003e-18 or -1.2499999999999999e-189 < j < 4.8000000000000002e-269 or 5.1999999999999997e-159 < j < 2.24999999999999991e49

   1. Initial program 77.4%

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

   2. Taylor expanded in b around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. sub-neg 67.9%

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

      3. +-commutative 67.9%

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

      4. mul-1-neg 67.9%

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

      5. *-commutative 67.9%

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

      6. *-commutative 67.9%

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

      7. fma-neg 69.0%

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

      8. fma-def 69.0%

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

      9. mul-1-neg 69.0%

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

      10. +-commutative 69.0%

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

      11. sub-neg 69.0%

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

      12. fma-udef 67.9%

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

      13. *-commutative 67.9%

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

      14. *-commutative 67.9%

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

      15. distribute-lft-neg-in 67.9%

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

      16. *-commutative 67.9%

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

   4. Simplified 69.0%

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

      1. distribute-rgt-neg-out 69.0%

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

      2. fma-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. *-commutative 67.9%

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

   6. Applied egg-rr 67.9%

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

   7. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

   9. Simplified 61.1%

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

   if -4.0000000000000003e-18 < j < -2.19999999999999997e-43

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. *-commutative 69.1%

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

   4. Simplified 69.1%

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

   if -2.19999999999999997e-43 < j < -1.2499999999999999e-189 or 4.8000000000000002e-269 < j < 5.1999999999999997e-159

   1. Initial program 78.1%

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

   2. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   4. Simplified 63.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-189}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 13: 51.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -0.165:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -1.22e+49)
     t_3
     (if (<= y -0.165)
       t_2
       (if (<= y -8.6e-50)
         t_3
         (if (<= y -1e-135)
           t_1
           (if (<= y -1.8e-253)
             t_2
             (if (<= y 1.9e-89)
               (* t (- (* c j) (* x a)))
               (if (<= y 9.4e-51) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.22e+49) {
		tmp = t_3;
	} else if (y <= -0.165) {
		tmp = t_2;
	} else if (y <= -8.6e-50) {
		tmp = t_3;
	} else if (y <= -1e-135) {
		tmp = t_1;
	} else if (y <= -1.8e-253) {
		tmp = t_2;
	} else if (y <= 1.9e-89) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 9.4e-51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = b * ((a * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-1.22d+49)) then
        tmp = t_3
    else if (y <= (-0.165d0)) then
        tmp = t_2
    else if (y <= (-8.6d-50)) then
        tmp = t_3
    else if (y <= (-1d-135)) then
        tmp = t_1
    else if (y <= (-1.8d-253)) then
        tmp = t_2
    else if (y <= 1.9d-89) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 9.4d-51) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.22e+49) {
		tmp = t_3;
	} else if (y <= -0.165) {
		tmp = t_2;
	} else if (y <= -8.6e-50) {
		tmp = t_3;
	} else if (y <= -1e-135) {
		tmp = t_1;
	} else if (y <= -1.8e-253) {
		tmp = t_2;
	} else if (y <= 1.9e-89) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 9.4e-51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = b * ((a * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.22e+49:
		tmp = t_3
	elif y <= -0.165:
		tmp = t_2
	elif y <= -8.6e-50:
		tmp = t_3
	elif y <= -1e-135:
		tmp = t_1
	elif y <= -1.8e-253:
		tmp = t_2
	elif y <= 1.9e-89:
		tmp = t * ((c * j) - (x * a))
	elif y <= 9.4e-51:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.22e+49)
		tmp = t_3;
	elseif (y <= -0.165)
		tmp = t_2;
	elseif (y <= -8.6e-50)
		tmp = t_3;
	elseif (y <= -1e-135)
		tmp = t_1;
	elseif (y <= -1.8e-253)
		tmp = t_2;
	elseif (y <= 1.9e-89)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 9.4e-51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = b * ((a * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.22e+49)
		tmp = t_3;
	elseif (y <= -0.165)
		tmp = t_2;
	elseif (y <= -8.6e-50)
		tmp = t_3;
	elseif (y <= -1e-135)
		tmp = t_1;
	elseif (y <= -1.8e-253)
		tmp = t_2;
	elseif (y <= 1.9e-89)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 9.4e-51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+49], t$95$3, If[LessEqual[y, -0.165], t$95$2, If[LessEqual[y, -8.6e-50], t$95$3, If[LessEqual[y, -1e-135], t$95$1, If[LessEqual[y, -1.8e-253], t$95$2, If[LessEqual[y, 1.9e-89], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e-51], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.21999999999999988e49 or -0.165000000000000008 < y < -8.59999999999999995e-50 or 9.3999999999999995e-51 < y

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

   4. Simplified 67.9%

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

   if -1.21999999999999988e49 < y < -0.165000000000000008 or -1e-135 < y < -1.8e-253

   1. Initial program 80.8%

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

   2. Taylor expanded in b around inf 70.2%

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

      1. *-commutative 70.2%

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

   4. Simplified 70.2%

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

   if -8.59999999999999995e-50 < y < -1e-135 or 1.9000000000000001e-89 < y < 9.3999999999999995e-51

   1. Initial program 92.2%

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

   2. Taylor expanded in c around inf 75.6%

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

   if -1.8e-253 < y < 1.9000000000000001e-89

   1. Initial program 82.9%

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

   2. Taylor expanded in t around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

   4. Simplified 55.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -0.165:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-253}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 14: 56.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-307}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-50}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2e+94)
     t_2
     (if (<= y 2.15e-307)
       (- t_1 (* c (* z b)))
       (if (<= y 5.2e-179)
         (* a (- (* b i) (* x t)))
         (if (<= y 1.55e-50) (- t_1 (* b (* z c))) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2e+94) {
		tmp = t_2;
	} else if (y <= 2.15e-307) {
		tmp = t_1 - (c * (z * b));
	} else if (y <= 5.2e-179) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 1.55e-50) {
		tmp = t_1 - (b * (z * c));
	} 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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2d+94)) then
        tmp = t_2
    else if (y <= 2.15d-307) then
        tmp = t_1 - (c * (z * b))
    else if (y <= 5.2d-179) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 1.55d-50) then
        tmp = t_1 - (b * (z * c))
    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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2e+94) {
		tmp = t_2;
	} else if (y <= 2.15e-307) {
		tmp = t_1 - (c * (z * b));
	} else if (y <= 5.2e-179) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 1.55e-50) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2e+94:
		tmp = t_2
	elif y <= 2.15e-307:
		tmp = t_1 - (c * (z * b))
	elif y <= 5.2e-179:
		tmp = a * ((b * i) - (x * t))
	elif y <= 1.55e-50:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2e+94)
		tmp = t_2;
	elseif (y <= 2.15e-307)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (y <= 5.2e-179)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 1.55e-50)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2e+94)
		tmp = t_2;
	elseif (y <= 2.15e-307)
		tmp = t_1 - (c * (z * b));
	elseif (y <= 5.2e-179)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 1.55e-50)
		tmp = t_1 - (b * (z * c));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+94], t$95$2, If[LessEqual[y, 2.15e-307], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-179], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-50], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2e94 or 1.5500000000000001e-50 < y

   1. Initial program 72.4%

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

   2. Taylor expanded in y around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

   4. Simplified 71.6%

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

   if -2e94 < y < 2.15000000000000005e-307

   1. Initial program 78.9%

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

   2. Taylor expanded in i around -inf 82.7%

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

      1. expm1-log1p-u 62.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. expm1-udef 61.0%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot z\right)\right)} - 1\right)} \]

   4. Applied egg-rr 61.0%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot z\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 62.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right) + \left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. expm1-log1p 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*l* 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around -inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. *-commutative 60.8%

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

      3. distribute-rgt-neg-in 60.8%

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

      4. +-commutative 60.8%

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

      5. mul-1-neg 60.8%

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

      6. unsub-neg 60.8%

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

   9. Simplified 60.8%

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

   if 2.15000000000000005e-307 < y < 5.20000000000000011e-179

   1. Initial program 86.8%

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

   2. Taylor expanded in a around -inf 67.0%

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

   if 5.20000000000000011e-179 < y < 1.5500000000000001e-50

   1. Initial program 95.9%

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

   2. Taylor expanded in i around -inf 95.6%

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

   3. Taylor expanded in t around -inf 71.8%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. +-commutative 64.0%

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

      5. mul-1-neg 64.0%

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

      6. unsub-neg 64.0%

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

   5. Simplified 71.8%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 15: 28.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-260}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* j (* t c))) (t_3 (* y (* x z))))
   (if (<= y -3.15e+122)
     (* x (* y z))
     (if (<= y -3.4e-30)
       t_1
       (if (<= y -1.65e-50)
         t_3
         (if (<= y -8.5e-260)
           (* (* z c) (- b))
           (if (<= y 6.2e-239)
             t_2
             (if (<= y 2.9e-74)
               (* t (* x (- a)))
               (if (<= y 1.4e-56) t_2 (if (<= y 2.3e-22) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = j * (t * c);
	double t_3 = y * (x * z);
	double tmp;
	if (y <= -3.15e+122) {
		tmp = x * (y * z);
	} else if (y <= -3.4e-30) {
		tmp = t_1;
	} else if (y <= -1.65e-50) {
		tmp = t_3;
	} else if (y <= -8.5e-260) {
		tmp = (z * c) * -b;
	} else if (y <= 6.2e-239) {
		tmp = t_2;
	} else if (y <= 2.9e-74) {
		tmp = t * (x * -a);
	} else if (y <= 1.4e-56) {
		tmp = t_2;
	} else if (y <= 2.3e-22) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (b * i)
    t_2 = j * (t * c)
    t_3 = y * (x * z)
    if (y <= (-3.15d+122)) then
        tmp = x * (y * z)
    else if (y <= (-3.4d-30)) then
        tmp = t_1
    else if (y <= (-1.65d-50)) then
        tmp = t_3
    else if (y <= (-8.5d-260)) then
        tmp = (z * c) * -b
    else if (y <= 6.2d-239) then
        tmp = t_2
    else if (y <= 2.9d-74) then
        tmp = t * (x * -a)
    else if (y <= 1.4d-56) then
        tmp = t_2
    else if (y <= 2.3d-22) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = j * (t * c);
	double t_3 = y * (x * z);
	double tmp;
	if (y <= -3.15e+122) {
		tmp = x * (y * z);
	} else if (y <= -3.4e-30) {
		tmp = t_1;
	} else if (y <= -1.65e-50) {
		tmp = t_3;
	} else if (y <= -8.5e-260) {
		tmp = (z * c) * -b;
	} else if (y <= 6.2e-239) {
		tmp = t_2;
	} else if (y <= 2.9e-74) {
		tmp = t * (x * -a);
	} else if (y <= 1.4e-56) {
		tmp = t_2;
	} else if (y <= 2.3e-22) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = j * (t * c)
	t_3 = y * (x * z)
	tmp = 0
	if y <= -3.15e+122:
		tmp = x * (y * z)
	elif y <= -3.4e-30:
		tmp = t_1
	elif y <= -1.65e-50:
		tmp = t_3
	elif y <= -8.5e-260:
		tmp = (z * c) * -b
	elif y <= 6.2e-239:
		tmp = t_2
	elif y <= 2.9e-74:
		tmp = t * (x * -a)
	elif y <= 1.4e-56:
		tmp = t_2
	elif y <= 2.3e-22:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(j * Float64(t * c))
	t_3 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (y <= -3.15e+122)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3.4e-30)
		tmp = t_1;
	elseif (y <= -1.65e-50)
		tmp = t_3;
	elseif (y <= -8.5e-260)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= 6.2e-239)
		tmp = t_2;
	elseif (y <= 2.9e-74)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 1.4e-56)
		tmp = t_2;
	elseif (y <= 2.3e-22)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	t_2 = j * (t * c);
	t_3 = y * (x * z);
	tmp = 0.0;
	if (y <= -3.15e+122)
		tmp = x * (y * z);
	elseif (y <= -3.4e-30)
		tmp = t_1;
	elseif (y <= -1.65e-50)
		tmp = t_3;
	elseif (y <= -8.5e-260)
		tmp = (z * c) * -b;
	elseif (y <= 6.2e-239)
		tmp = t_2;
	elseif (y <= 2.9e-74)
		tmp = t * (x * -a);
	elseif (y <= 1.4e-56)
		tmp = t_2;
	elseif (y <= 2.3e-22)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e+122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-30], t$95$1, If[LessEqual[y, -1.65e-50], t$95$3, If[LessEqual[y, -8.5e-260], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, 6.2e-239], t$95$2, If[LessEqual[y, 2.9e-74], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-56], t$95$2, If[LessEqual[y, 2.3e-22], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.1500000000000001e122

   1. Initial program 58.2%

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

   2. Taylor expanded in b around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. sub-neg 63.8%

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

      3. +-commutative 63.8%

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

      4. mul-1-neg 63.8%

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

      5. *-commutative 63.8%

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

      6. *-commutative 63.8%

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

      7. fma-neg 66.1%

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

      8. fma-def 70.8%

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

      9. mul-1-neg 70.8%

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

      10. +-commutative 70.8%

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

      11. sub-neg 70.8%

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

      12. fma-udef 68.5%

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

      13. *-commutative 68.5%

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

      14. *-commutative 68.5%

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

      15. distribute-lft-neg-in 68.5%

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

      16. *-commutative 68.5%

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

   4. Simplified 70.8%

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

      1. distribute-rgt-neg-out 70.8%

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

      2. fma-neg 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

   6. Applied egg-rr 68.5%

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

   7. Taylor expanded in z around inf 45.2%

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

   if -3.1500000000000001e122 < y < -3.4000000000000003e-30 or 1.39999999999999997e-56 < y < 2.2999999999999998e-22

   1. Initial program 86.0%

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

   2. Taylor expanded in b around inf 43.4%

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

      1. *-commutative 43.4%

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

   4. Simplified 43.4%

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

   5. Taylor expanded in a around inf 34.1%

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

   6. Taylor expanded in b around 0 38.4%

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

   if -3.4000000000000003e-30 < y < -1.6499999999999999e-50 or 2.2999999999999998e-22 < y

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in x around inf 41.4%

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

   if -1.6499999999999999e-50 < y < -8.5000000000000003e-260

   1. Initial program 78.9%

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

   2. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   4. Simplified 65.2%

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

   5. Taylor expanded in a around 0 43.8%

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

      1. neg-mul-1 43.8%

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

      2. *-commutative 43.8%

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

      3. distribute-rgt-neg-in 43.8%

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

   7. Simplified 43.8%

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

   if -8.5000000000000003e-260 < y < 6.1999999999999997e-239 or 2.9e-74 < y < 1.39999999999999997e-56

   1. Initial program 82.6%

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

   2. Taylor expanded in c around inf 61.6%

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

   3. Taylor expanded in j around inf 49.2%

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

      1. associate-*r* 42.2%

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

      2. *-commutative 42.2%

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

      3. associate-*l* 51.5%

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

   5. Simplified 51.5%

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

   if 6.1999999999999997e-239 < y < 2.9e-74

   1. Initial program 92.1%

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

   2. Taylor expanded in t around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. *-commutative 55.5%

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

   4. Simplified 55.5%

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

   5. Taylor expanded in c around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. *-commutative 44.1%

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

      3. distribute-rgt-neg-in 44.1%

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

   7. Simplified 44.1%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-260}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-239}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 16: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -0.042:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.55e+55)
     t_2
     (if (<= b -0.042)
       t_1
       (if (<= b -4.2e-54)
         t_2
         (if (<= b -5.8e-210)
           t_1
           (if (<= b 1.45e-254)
             (* t (- (* c j) (* x a)))
             (if (<= b 1.06e-35) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e+55) {
		tmp = t_2;
	} else if (b <= -0.042) {
		tmp = t_1;
	} else if (b <= -4.2e-54) {
		tmp = t_2;
	} else if (b <= -5.8e-210) {
		tmp = t_1;
	} else if (b <= 1.45e-254) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1.06e-35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.55d+55)) then
        tmp = t_2
    else if (b <= (-0.042d0)) then
        tmp = t_1
    else if (b <= (-4.2d-54)) then
        tmp = t_2
    else if (b <= (-5.8d-210)) then
        tmp = t_1
    else if (b <= 1.45d-254) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 1.06d-35) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e+55) {
		tmp = t_2;
	} else if (b <= -0.042) {
		tmp = t_1;
	} else if (b <= -4.2e-54) {
		tmp = t_2;
	} else if (b <= -5.8e-210) {
		tmp = t_1;
	} else if (b <= 1.45e-254) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1.06e-35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.55e+55:
		tmp = t_2
	elif b <= -0.042:
		tmp = t_1
	elif b <= -4.2e-54:
		tmp = t_2
	elif b <= -5.8e-210:
		tmp = t_1
	elif b <= 1.45e-254:
		tmp = t * ((c * j) - (x * a))
	elif b <= 1.06e-35:
		tmp = 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(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.55e+55)
		tmp = t_2;
	elseif (b <= -0.042)
		tmp = t_1;
	elseif (b <= -4.2e-54)
		tmp = t_2;
	elseif (b <= -5.8e-210)
		tmp = t_1;
	elseif (b <= 1.45e-254)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 1.06e-35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.55e+55)
		tmp = t_2;
	elseif (b <= -0.042)
		tmp = t_1;
	elseif (b <= -4.2e-54)
		tmp = t_2;
	elseif (b <= -5.8e-210)
		tmp = t_1;
	elseif (b <= 1.45e-254)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 1.06e-35)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+55], t$95$2, If[LessEqual[b, -0.042], t$95$1, If[LessEqual[b, -4.2e-54], t$95$2, If[LessEqual[b, -5.8e-210], t$95$1, If[LessEqual[b, 1.45e-254], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-35], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.54999999999999997e55 or -0.0420000000000000026 < b < -4.2e-54 or 1.06e-35 < b

   1. Initial program 76.1%

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

   2. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

   4. Simplified 59.1%

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

   if -1.54999999999999997e55 < b < -0.0420000000000000026 or -4.2e-54 < b < -5.80000000000000012e-210 or 1.45e-254 < b < 1.06e-35

   1. Initial program 82.0%

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

   2. Taylor expanded in j around inf 56.5%

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

   if -5.80000000000000012e-210 < b < 1.45e-254

   1. Initial program 77.3%

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

   2. Taylor expanded in t around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

   4. Simplified 57.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -0.042:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 17: 60.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+67} \lor \neg \left(i \leq 7.5 \cdot 10^{+27}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -9.2e+67) (not (<= i 7.5e+27)))
   (* i (- (* a b) (* y j)))
   (+ (* x (- (* y z) (* t a))) (* t (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -9.2e+67) || !(i <= 7.5e+27)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (t * (c * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-9.2d+67)) .or. (.not. (i <= 7.5d+27))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) + (t * (c * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -9.2e+67) || !(i <= 7.5e+27)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (t * (c * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -9.2e+67) or not (i <= 7.5e+27):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) + (t * (c * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -9.2e+67) || !(i <= 7.5e+27))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(t * Float64(c * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -9.2e+67) || ~((i <= 7.5e+27)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) + (t * (c * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -9.2e+67], N[Not[LessEqual[i, 7.5e+27]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -9.1999999999999994e67 or 7.5000000000000002e27 < i

   1. Initial program 71.7%

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

   2. Taylor expanded in i around inf 63.3%

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

      1. distribute-lft-out-- 63.3%

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

      2. *-commutative 63.3%

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

   4. Simplified 63.3%

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

   if -9.1999999999999994e67 < i < 7.5000000000000002e27

   1. Initial program 84.6%

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

   2. Taylor expanded in b around 0 69.5%

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

   3. Taylor expanded in c around inf 61.5%

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

      1. associate-*r* 63.6%

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

      2. *-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+67} \lor \neg \left(i \leq 7.5 \cdot 10^{+27}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 18: 29.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* j (* t c))) (t_3 (* x (* y z))))
   (if (<= y -2e+122)
     t_3
     (if (<= y -1.95e-261)
       t_1
       (if (<= y 9.6e-284)
         t_2
         (if (<= y 5e-74)
           t_1
           (if (<= y 3.8e-56) t_2 (if (<= y 2.6e-22) (* a (* b i)) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double t_3 = x * (y * z);
	double tmp;
	if (y <= -2e+122) {
		tmp = t_3;
	} else if (y <= -1.95e-261) {
		tmp = t_1;
	} else if (y <= 9.6e-284) {
		tmp = t_2;
	} else if (y <= 5e-74) {
		tmp = t_1;
	} else if (y <= 3.8e-56) {
		tmp = t_2;
	} else if (y <= 2.6e-22) {
		tmp = a * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = j * (t * c)
    t_3 = x * (y * z)
    if (y <= (-2d+122)) then
        tmp = t_3
    else if (y <= (-1.95d-261)) then
        tmp = t_1
    else if (y <= 9.6d-284) then
        tmp = t_2
    else if (y <= 5d-74) then
        tmp = t_1
    else if (y <= 3.8d-56) then
        tmp = t_2
    else if (y <= 2.6d-22) then
        tmp = a * (b * i)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double t_3 = x * (y * z);
	double tmp;
	if (y <= -2e+122) {
		tmp = t_3;
	} else if (y <= -1.95e-261) {
		tmp = t_1;
	} else if (y <= 9.6e-284) {
		tmp = t_2;
	} else if (y <= 5e-74) {
		tmp = t_1;
	} else if (y <= 3.8e-56) {
		tmp = t_2;
	} else if (y <= 2.6e-22) {
		tmp = a * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = j * (t * c)
	t_3 = x * (y * z)
	tmp = 0
	if y <= -2e+122:
		tmp = t_3
	elif y <= -1.95e-261:
		tmp = t_1
	elif y <= 9.6e-284:
		tmp = t_2
	elif y <= 5e-74:
		tmp = t_1
	elif y <= 3.8e-56:
		tmp = t_2
	elif y <= 2.6e-22:
		tmp = a * (b * i)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(j * Float64(t * c))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -2e+122)
		tmp = t_3;
	elseif (y <= -1.95e-261)
		tmp = t_1;
	elseif (y <= 9.6e-284)
		tmp = t_2;
	elseif (y <= 5e-74)
		tmp = t_1;
	elseif (y <= 3.8e-56)
		tmp = t_2;
	elseif (y <= 2.6e-22)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = j * (t * c);
	t_3 = x * (y * z);
	tmp = 0.0;
	if (y <= -2e+122)
		tmp = t_3;
	elseif (y <= -1.95e-261)
		tmp = t_1;
	elseif (y <= 9.6e-284)
		tmp = t_2;
	elseif (y <= 5e-74)
		tmp = t_1;
	elseif (y <= 3.8e-56)
		tmp = t_2;
	elseif (y <= 2.6e-22)
		tmp = a * (b * i);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+122], t$95$3, If[LessEqual[y, -1.95e-261], t$95$1, If[LessEqual[y, 9.6e-284], t$95$2, If[LessEqual[y, 5e-74], t$95$1, If[LessEqual[y, 3.8e-56], t$95$2, If[LessEqual[y, 2.6e-22], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000003e122 or 2.6e-22 < y

   1. Initial program 70.5%

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

   2. Taylor expanded in b around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. sub-neg 72.1%

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

      3. +-commutative 72.1%

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

      4. mul-1-neg 72.1%

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

      5. *-commutative 72.1%

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

      6. *-commutative 72.1%

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

      7. fma-neg 73.0%

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

      8. fma-def 75.9%

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

      9. mul-1-neg 75.9%

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

      10. +-commutative 75.9%

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

      11. sub-neg 75.9%

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

      12. fma-udef 75.0%

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

      13. *-commutative 75.0%

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

      14. *-commutative 75.0%

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

      15. distribute-lft-neg-in 75.0%

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

      16. *-commutative 75.0%

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

   4. Simplified 75.9%

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

      1. distribute-rgt-neg-out 75.9%

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

      2. fma-neg 75.0%

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

      3. *-commutative 75.0%

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

      4. *-commutative 75.0%

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

   6. Applied egg-rr 75.0%

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

   7. Taylor expanded in z around inf 42.9%

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

   if -2.00000000000000003e122 < y < -1.95000000000000009e-261 or 9.60000000000000011e-284 < y < 4.99999999999999998e-74

   1. Initial program 85.5%

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

   2. Taylor expanded in b around inf 51.9%

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

      1. *-commutative 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in a around inf 31.6%

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

   if -1.95000000000000009e-261 < y < 9.60000000000000011e-284 or 4.99999999999999998e-74 < y < 3.8000000000000002e-56

   1. Initial program 76.9%

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

   2. Taylor expanded in c around inf 62.1%

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

   3. Taylor expanded in j around inf 51.9%

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

      1. associate-*r* 42.5%

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

      2. *-commutative 42.5%

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

      3. associate-*l* 55.0%

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

   5. Simplified 55.0%

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

   if 3.8000000000000002e-56 < y < 2.6e-22

   1. Initial program 90.8%

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

   2. Taylor expanded in b around inf 55.7%

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

      1. *-commutative 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in a around inf 38.7%

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

   6. Taylor expanded in b around 0 55.2%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 19: 29.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* j (* t c))))
   (if (<= y -6.2e+122)
     (* x (* y z))
     (if (<= y -9.6e-256)
       t_1
       (if (<= y 7.2e-284)
         t_2
         (if (<= y 3e-73)
           t_1
           (if (<= y 3.4e-57)
             t_2
             (if (<= y 5.9e-22) (* a (* b i)) (* y (* x z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double tmp;
	if (y <= -6.2e+122) {
		tmp = x * (y * z);
	} else if (y <= -9.6e-256) {
		tmp = t_1;
	} else if (y <= 7.2e-284) {
		tmp = t_2;
	} else if (y <= 3e-73) {
		tmp = t_1;
	} else if (y <= 3.4e-57) {
		tmp = t_2;
	} else if (y <= 5.9e-22) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = j * (t * c)
    if (y <= (-6.2d+122)) then
        tmp = x * (y * z)
    else if (y <= (-9.6d-256)) then
        tmp = t_1
    else if (y <= 7.2d-284) then
        tmp = t_2
    else if (y <= 3d-73) then
        tmp = t_1
    else if (y <= 3.4d-57) then
        tmp = t_2
    else if (y <= 5.9d-22) then
        tmp = a * (b * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double tmp;
	if (y <= -6.2e+122) {
		tmp = x * (y * z);
	} else if (y <= -9.6e-256) {
		tmp = t_1;
	} else if (y <= 7.2e-284) {
		tmp = t_2;
	} else if (y <= 3e-73) {
		tmp = t_1;
	} else if (y <= 3.4e-57) {
		tmp = t_2;
	} else if (y <= 5.9e-22) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = j * (t * c)
	tmp = 0
	if y <= -6.2e+122:
		tmp = x * (y * z)
	elif y <= -9.6e-256:
		tmp = t_1
	elif y <= 7.2e-284:
		tmp = t_2
	elif y <= 3e-73:
		tmp = t_1
	elif y <= 3.4e-57:
		tmp = t_2
	elif y <= 5.9e-22:
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (y <= -6.2e+122)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -9.6e-256)
		tmp = t_1;
	elseif (y <= 7.2e-284)
		tmp = t_2;
	elseif (y <= 3e-73)
		tmp = t_1;
	elseif (y <= 3.4e-57)
		tmp = t_2;
	elseif (y <= 5.9e-22)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (y <= -6.2e+122)
		tmp = x * (y * z);
	elseif (y <= -9.6e-256)
		tmp = t_1;
	elseif (y <= 7.2e-284)
		tmp = t_2;
	elseif (y <= 3e-73)
		tmp = t_1;
	elseif (y <= 3.4e-57)
		tmp = t_2;
	elseif (y <= 5.9e-22)
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.6e-256], t$95$1, If[LessEqual[y, 7.2e-284], t$95$2, If[LessEqual[y, 3e-73], t$95$1, If[LessEqual[y, 3.4e-57], t$95$2, If[LessEqual[y, 5.9e-22], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.19999999999999998e122

   1. Initial program 58.2%

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

   2. Taylor expanded in b around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. sub-neg 63.8%

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

      3. +-commutative 63.8%

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

      4. mul-1-neg 63.8%

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

      5. *-commutative 63.8%

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

      6. *-commutative 63.8%

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

      7. fma-neg 66.1%

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

      8. fma-def 70.8%

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

      9. mul-1-neg 70.8%

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

      10. +-commutative 70.8%

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

      11. sub-neg 70.8%

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

      12. fma-udef 68.5%

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

      13. *-commutative 68.5%

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

      14. *-commutative 68.5%

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

      15. distribute-lft-neg-in 68.5%

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

      16. *-commutative 68.5%

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

   4. Simplified 70.8%

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

      1. distribute-rgt-neg-out 70.8%

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

      2. fma-neg 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

   6. Applied egg-rr 68.5%

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

   7. Taylor expanded in z around inf 45.2%

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

   if -6.19999999999999998e122 < y < -9.5999999999999998e-256 or 7.2000000000000004e-284 < y < 3e-73

   1. Initial program 85.5%

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

   2. Taylor expanded in b around inf 51.9%

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

      1. *-commutative 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in a around inf 31.6%

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

   if -9.5999999999999998e-256 < y < 7.2000000000000004e-284 or 3e-73 < y < 3.40000000000000016e-57

   1. Initial program 76.9%

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

   2. Taylor expanded in c around inf 62.1%

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

   3. Taylor expanded in j around inf 51.9%

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

      1. associate-*r* 42.5%

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

      2. *-commutative 42.5%

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

      3. associate-*l* 55.0%

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

   5. Simplified 55.0%

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

   if 3.40000000000000016e-57 < y < 5.90000000000000008e-22

   1. Initial program 90.8%

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

   2. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 55.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 38.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   6. Taylor expanded in b around 0 55.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 5.90000000000000008e-22 < y

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around inf 71.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 71.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 71.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 71.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   4. Simplified 71.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   5. Taylor expanded in x around inf 41.4%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 20: 51.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+55} \lor \neg \left(b \leq -0.024\right) \land \left(b \leq -3.7 \cdot 10^{-53} \lor \neg \left(b \leq 1.14 \cdot 10^{-35}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.7e+55)
         (and (not (<= b -0.024)) (or (<= b -3.7e-53) (not (<= b 1.14e-35)))))
   (* b (- (* a i) (* z c)))
   (* j (- (* t c) (* y 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 ((b <= -1.7e+55) || (!(b <= -0.024) && ((b <= -3.7e-53) || !(b <= 1.14e-35)))) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * 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 ((b <= (-1.7d+55)) .or. (.not. (b <= (-0.024d0))) .and. (b <= (-3.7d-53)) .or. (.not. (b <= 1.14d-35))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = j * ((t * c) - (y * 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 ((b <= -1.7e+55) || (!(b <= -0.024) && ((b <= -3.7e-53) || !(b <= 1.14e-35)))) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.7e+55) or (not (b <= -0.024) and ((b <= -3.7e-53) or not (b <= 1.14e-35))):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.7e+55) || (!(b <= -0.024) && ((b <= -3.7e-53) || !(b <= 1.14e-35))))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.7e+55) || (~((b <= -0.024)) && ((b <= -3.7e-53) || ~((b <= 1.14e-35)))))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.7e+55], And[N[Not[LessEqual[b, -0.024]], $MachinePrecision], Or[LessEqual[b, -3.7e-53], N[Not[LessEqual[b, 1.14e-35]], $MachinePrecision]]]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6999999999999999e55 or -0.024 < b < -3.69999999999999982e-53 or 1.14e-35 < b

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 59.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 59.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 59.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -1.6999999999999999e55 < b < -0.024 or -3.69999999999999982e-53 < b < 1.14e-35

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 52.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+55} \lor \neg \left(b \leq -0.024\right) \land \left(b \leq -3.7 \cdot 10^{-53} \lor \neg \left(b \leq 1.14 \cdot 10^{-35}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 21: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= c -1.5e-72)
     (* t (* c j))
     (if (<= c 2e-224)
       (* i (* a b))
       (if (<= c 1.9e-83)
         t_1
         (if (<= c 2.4e-14)
           (* b (* a i))
           (if (<= c 2.8e+127) t_1 (* j (* t c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (c <= -1.5e-72) {
		tmp = t * (c * j);
	} else if (c <= 2e-224) {
		tmp = i * (a * b);
	} else if (c <= 1.9e-83) {
		tmp = t_1;
	} else if (c <= 2.4e-14) {
		tmp = b * (a * i);
	} else if (c <= 2.8e+127) {
		tmp = t_1;
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (c <= (-1.5d-72)) then
        tmp = t * (c * j)
    else if (c <= 2d-224) then
        tmp = i * (a * b)
    else if (c <= 1.9d-83) then
        tmp = t_1
    else if (c <= 2.4d-14) then
        tmp = b * (a * i)
    else if (c <= 2.8d+127) then
        tmp = t_1
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (c <= -1.5e-72) {
		tmp = t * (c * j);
	} else if (c <= 2e-224) {
		tmp = i * (a * b);
	} else if (c <= 1.9e-83) {
		tmp = t_1;
	} else if (c <= 2.4e-14) {
		tmp = b * (a * i);
	} else if (c <= 2.8e+127) {
		tmp = t_1;
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if c <= -1.5e-72:
		tmp = t * (c * j)
	elif c <= 2e-224:
		tmp = i * (a * b)
	elif c <= 1.9e-83:
		tmp = t_1
	elif c <= 2.4e-14:
		tmp = b * (a * i)
	elif c <= 2.8e+127:
		tmp = t_1
	else:
		tmp = j * (t * c)
	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 (c <= -1.5e-72)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 2e-224)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 1.9e-83)
		tmp = t_1;
	elseif (c <= 2.4e-14)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 2.8e+127)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(t * c));
	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 (c <= -1.5e-72)
		tmp = t * (c * j);
	elseif (c <= 2e-224)
		tmp = i * (a * b);
	elseif (c <= 1.9e-83)
		tmp = t_1;
	elseif (c <= 2.4e-14)
		tmp = b * (a * i);
	elseif (c <= 2.8e+127)
		tmp = t_1;
	else
		tmp = j * (t * c);
	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[c, -1.5e-72], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-224], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e-83], t$95$1, If[LessEqual[c, 2.4e-14], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e+127], t$95$1, N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.5e-72

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 49.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 32.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

   5. Simplified 35.6%

      \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

   if -1.5e-72 < c < 2e-224

   1. Initial program 84.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 44.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 44.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 39.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   6. Taylor expanded in b around 0 38.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 15.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)\right)} \]

      2. expm1-udef 11.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)} - 1} \]

      3. *-commutative 11.6%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(i \cdot b\right)}\right)} - 1 \]

   8. Applied egg-rr 11.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 15.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. expm1-log1p 38.1%

         \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

      3. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} \]

      4. associate-*l* 39.7%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   10. Simplified 39.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   if 2e-224 < c < 1.89999999999999988e-83 or 2.4e-14 < c < 2.8000000000000002e127

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0 72.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg 72.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. +-commutative 72.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(-a \cdot t\right) + y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. mul-1-neg 72.9%

         \[\leadsto x \cdot \left(\color{blue}{-1 \cdot \left(a \cdot t\right)} + y \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 72.9%

         \[\leadsto x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 72.9%

         \[\leadsto x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

      7. fma-neg 72.9%

         \[\leadsto x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, -y \cdot i\right)} \]

      8. fma-def 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, -1 \cdot \left(a \cdot t\right) + y \cdot z, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right)} \]

      9. mul-1-neg 72.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-a \cdot t\right)} + y \cdot z, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right) \]

      10. +-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z + \left(-a \cdot t\right)}, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right) \]

      11. sub-neg 72.9%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right) \]

      12. fma-udef 72.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \color{blue}{\left(t \cdot c + \left(-y \cdot i\right)\right)}\right) \]

      13. *-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(\color{blue}{c \cdot t} + \left(-y \cdot i\right)\right)\right) \]

      14. *-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(c \cdot t + \left(-\color{blue}{i \cdot y}\right)\right)\right) \]

      15. distribute-lft-neg-in 72.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(c \cdot t + \color{blue}{\left(-i\right) \cdot y}\right)\right) \]

      16. *-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right)\right) \]

   4. Simplified 72.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-neg-out 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      2. fma-neg 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \color{blue}{\left(t \cdot c - i \cdot y\right)}\right) \]

      3. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(\color{blue}{c \cdot t} - i \cdot y\right)\right) \]

      4. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(c \cdot t - \color{blue}{y \cdot i}\right)\right) \]

   6. Applied egg-rr 72.9%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \color{blue}{\left(c \cdot t - y \cdot i\right)}\right) \]

   7. Taylor expanded in z around inf 36.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.89999999999999988e-83 < c < 2.4e-14

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 58.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 58.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 44.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 2.8000000000000002e127 < c

   1. Initial program 67.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 76.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 41.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 38.1%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

      3. associate-*l* 46.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   5. Simplified 46.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 22: 41.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+81}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.35e-161)
   (* b (- (* a i) (* z c)))
   (if (<= a 9.5e-37)
     (* c (- (* t j) (* z b)))
     (if (<= a 4.1e+71)
       (* x (* y z))
       (if (<= a 5.2e+81) (* (* z b) (- c)) (* x (* t (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.35e-161) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 9.5e-37) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 4.1e+71) {
		tmp = x * (y * z);
	} else if (a <= 5.2e+81) {
		tmp = (z * b) * -c;
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.35d-161)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 9.5d-37) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 4.1d+71) then
        tmp = x * (y * z)
    else if (a <= 5.2d+81) then
        tmp = (z * b) * -c
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.35e-161) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 9.5e-37) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 4.1e+71) {
		tmp = x * (y * z);
	} else if (a <= 5.2e+81) {
		tmp = (z * b) * -c;
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.35e-161:
		tmp = b * ((a * i) - (z * c))
	elif a <= 9.5e-37:
		tmp = c * ((t * j) - (z * b))
	elif a <= 4.1e+71:
		tmp = x * (y * z)
	elif a <= 5.2e+81:
		tmp = (z * b) * -c
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.35e-161)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 9.5e-37)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 4.1e+71)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 5.2e+81)
		tmp = Float64(Float64(z * b) * Float64(-c));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.35e-161)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 9.5e-37)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 4.1e+71)
		tmp = x * (y * z);
	elseif (a <= 5.2e+81)
		tmp = (z * b) * -c;
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.35e-161], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-37], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+71], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+81], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35e-161

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 48.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 48.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -1.35e-161 < a < 9.49999999999999927e-37

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 51.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if 9.49999999999999927e-37 < a < 4.1000000000000002e71

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0 70.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   3. Step-by-step derivation

      1. +-commutative 70.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg 70.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. +-commutative 70.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(-a \cdot t\right) + y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. mul-1-neg 70.3%

         \[\leadsto x \cdot \left(\color{blue}{-1 \cdot \left(a \cdot t\right)} + y \cdot z\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 70.3%

         \[\leadsto x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 70.3%

         \[\leadsto x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

      7. fma-neg 70.3%

         \[\leadsto x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, -y \cdot i\right)} \]

      8. fma-def 70.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, -1 \cdot \left(a \cdot t\right) + y \cdot z, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right)} \]

      9. mul-1-neg 70.3%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-a \cdot t\right)} + y \cdot z, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right) \]

      10. +-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z + \left(-a \cdot t\right)}, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right) \]

      11. sub-neg 70.3%

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{y \cdot z - a \cdot t}, j \cdot \mathsf{fma}\left(t, c, -y \cdot i\right)\right) \]

      12. fma-udef 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \color{blue}{\left(t \cdot c + \left(-y \cdot i\right)\right)}\right) \]

      13. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(\color{blue}{c \cdot t} + \left(-y \cdot i\right)\right)\right) \]

      14. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(c \cdot t + \left(-\color{blue}{i \cdot y}\right)\right)\right) \]

      15. distribute-lft-neg-in 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(c \cdot t + \color{blue}{\left(-i\right) \cdot y}\right)\right) \]

      16. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right)\right) \]

   4. Simplified 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-neg-out 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      2. fma-neg 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \color{blue}{\left(t \cdot c - i \cdot y\right)}\right) \]

      3. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(\color{blue}{c \cdot t} - i \cdot y\right)\right) \]

      4. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \left(c \cdot t - \color{blue}{y \cdot i}\right)\right) \]

   6. Applied egg-rr 70.3%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - a \cdot t, j \cdot \color{blue}{\left(c \cdot t - y \cdot i\right)}\right) \]

   7. Taylor expanded in z around inf 40.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 4.1000000000000002e71 < a < 5.19999999999999984e81

   1. Initial program 60.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 41.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 41.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 41.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around 0 61.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. *-commutative 61.2%

         \[\leadsto \left(-1 \cdot b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

      3. associate-*r* 61.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot b\right) \cdot z\right) \cdot c} \]

      4. mul-1-neg 61.2%

         \[\leadsto \left(\color{blue}{\left(-b\right)} \cdot z\right) \cdot c \]

   7. Simplified 61.2%

      \[\leadsto \color{blue}{\left(\left(-b\right) \cdot z\right) \cdot c} \]

   if 5.19999999999999984e81 < a

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0 63.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   3. Taylor expanded in y around 0 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)} \]

   4. Taylor expanded in a around inf 54.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 54.9%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 54.9%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-rgt-neg-in 54.9%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-x\right)} \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+81}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 23: 30.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-92} \lor \neg \left(b \leq 1.14 \cdot 10^{-35}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.75e-92) (not (<= b 1.14e-35))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.75e-92) || !(b <= 1.14e-35)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.75d-92)) .or. (.not. (b <= 1.14d-35))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.75e-92) || !(b <= 1.14e-35)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.75e-92) or not (b <= 1.14e-35):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.75e-92) || !(b <= 1.14e-35))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.75e-92) || ~((b <= 1.14e-35)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.75e-92], N[Not[LessEqual[b, 1.14e-35]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.75e-92 or 1.14e-35 < b

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 53.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 33.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   6. Taylor expanded in b around 0 35.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.75e-92 < b < 1.14e-35

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 35.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 27.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-92} \lor \neg \left(b \leq 1.14 \cdot 10^{-35}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 24: 30.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.75e-95)
   (* a (* b i))
   (if (<= b 1.1e-35) (* c (* t j)) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.75e-95) {
		tmp = a * (b * i);
	} else if (b <= 1.1e-35) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.75d-95)) then
        tmp = a * (b * i)
    else if (b <= 1.1d-35) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.75e-95) {
		tmp = a * (b * i);
	} else if (b <= 1.1e-35) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.75e-95:
		tmp = a * (b * i)
	elif b <= 1.1e-35:
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.75e-95)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 1.1e-35)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.75e-95)
		tmp = a * (b * i);
	elseif (b <= 1.1e-35)
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.75e-95], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-35], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.75000000000000001e-95

   1. Initial program 81.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 54.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 54.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 38.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   6. Taylor expanded in b around 0 43.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -2.75000000000000001e-95 < b < 1.09999999999999997e-35

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 35.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 27.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 1.09999999999999997e-35 < b

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 51.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 26.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   6. Taylor expanded in b around 0 26.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 13.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)\right)} \]

      2. expm1-udef 11.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot i\right)\right)} - 1} \]

      3. *-commutative 11.2%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(i \cdot b\right)}\right)} - 1 \]

   8. Applied egg-rr 11.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 13.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. expm1-log1p 26.8%

         \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

      3. *-commutative 26.8%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} \]

      4. associate-*l* 28.0%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   10. Simplified 28.0%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 25: 30.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.3 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 10^{+90}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -8.3e-72)
   (* c (* t j))
   (if (<= c 1e+90) (* b (* a i)) (* j (* t c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.3e-72) {
		tmp = c * (t * j);
	} else if (c <= 1e+90) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-8.3d-72)) then
        tmp = c * (t * j)
    else if (c <= 1d+90) then
        tmp = b * (a * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.3e-72) {
		tmp = c * (t * j);
	} else if (c <= 1e+90) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -8.3e-72:
		tmp = c * (t * j)
	elif c <= 1e+90:
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -8.3e-72)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= 1e+90)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -8.3e-72)
		tmp = c * (t * j);
	elseif (c <= 1e+90)
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -8.3e-72], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e+90], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.2999999999999997e-72

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 49.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 32.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -8.2999999999999997e-72 < c < 9.99999999999999966e89

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 37.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 37.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in a around inf 29.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 9.99999999999999966e89 < c

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 66.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   3. Taylor expanded in j around inf 36.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 36.8%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

      3. associate-*l* 41.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.3 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 10^{+90}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 26: 23.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in b around inf 37.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Step-by-step derivation

   1. *-commutative 37.3%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

4. Simplified 37.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

5. Taylor expanded in a around inf 22.4%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

6. Taylor expanded in b around 0 22.8%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

7. Final simplification 22.8%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))