Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.3% → 82.9%

Time: 21.1s

Alternatives: 21

Speedup: 0.5×

• 57.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 74.3% accurate, 1.0× speedup

Math

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

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: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

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

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

Java

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((b * i) - (x * t))
	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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((b * i) - (x * t));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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 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. Add Preprocessing

   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. Add Preprocessing

   3. Taylor expanded in y around inf 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

      3. associate-/l* 7.5%

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

   5. Simplified 7.5%

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

   6. Taylor expanded in a around -inf 51.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.6%

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

Alternative 2: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* a (* b i))))
        (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.4e+144)
     t_2
     (if (<= i -5.2e-83)
       t_1
       (if (<= i 8.5e-184)
         (* x (- (* y z) (* t a)))
         (if (<= i 1.2e-58)
           (* t (- (* c j) (* x a)))
           (if (<= i 2.6e+138) 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))) + (a * (b * i));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.4e+144) {
		tmp = t_2;
	} else if (i <= -5.2e-83) {
		tmp = t_1;
	} else if (i <= 8.5e-184) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.2e-58) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.6e+138) {
		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))) + (a * (b * i))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.4d+144)) then
        tmp = t_2
    else if (i <= (-5.2d-83)) then
        tmp = t_1
    else if (i <= 8.5d-184) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 1.2d-58) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 2.6d+138) 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))) + (a * (b * i));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.4e+144) {
		tmp = t_2;
	} else if (i <= -5.2e-83) {
		tmp = t_1;
	} else if (i <= 8.5e-184) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.2e-58) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.6e+138) {
		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))) + (a * (b * i))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.4e+144:
		tmp = t_2
	elif i <= -5.2e-83:
		tmp = t_1
	elif i <= 8.5e-184:
		tmp = x * ((y * z) - (t * a))
	elif i <= 1.2e-58:
		tmp = t * ((c * j) - (x * a))
	elif i <= 2.6e+138:
		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(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.4e+144)
		tmp = t_2;
	elseif (i <= -5.2e-83)
		tmp = t_1;
	elseif (i <= 8.5e-184)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 1.2e-58)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 2.6e+138)
		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))) + (a * (b * i));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.4e+144)
		tmp = t_2;
	elseif (i <= -5.2e-83)
		tmp = t_1;
	elseif (i <= 8.5e-184)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 1.2e-58)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 2.6e+138)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+144], t$95$2, If[LessEqual[i, -5.2e-83], t$95$1, If[LessEqual[i, 8.5e-184], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e-58], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+138], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.40000000000000003e144 or 2.6000000000000001e138 < i

   1. Initial program 52.5%

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

      1. +-commutative 52.5%

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

      2. fma-define 53.8%

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

      3. *-commutative 53.8%

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

      4. *-commutative 53.8%

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

      5. cancel-sign-sub-inv 53.8%

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

      6. cancel-sign-sub 53.8%

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

      7. fma-neg 55.2%

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

      8. distribute-rgt-neg-out 55.2%

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

      9. remove-double-neg 55.2%

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

      10. *-commutative 55.2%

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

      11. *-commutative 55.2%

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

   3. Simplified 55.2%

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

   5. Taylor expanded in i around inf 77.8%

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

      1. distribute-lft-out-- 77.8%

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

      2. *-commutative 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in i around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. *-commutative 77.8%

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

      3. distribute-rgt-neg-out 77.8%

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

      4. neg-mul-1 77.8%

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

      5. *-commutative 77.8%

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

      6. distribute-lft-out-- 77.8%

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

      7. sub-neg 77.8%

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

      8. neg-mul-1 77.8%

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

      9. remove-double-neg 77.8%

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

      10. +-commutative 77.8%

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

      11. mul-1-neg 77.8%

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

      12. *-commutative 77.8%

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

      13. unsub-neg 77.8%

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

   10. Simplified 77.8%

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

   if -1.40000000000000003e144 < i < -5.20000000000000018e-83 or 1.2e-58 < i < 2.6000000000000001e138

   1. Initial program 84.0%

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

      1. cancel-sign-sub-inv 84.0%

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

      2. cancel-sign-sub 84.0%

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

      3. *-commutative 84.0%

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

      4. fma-neg 85.2%

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

      5. distribute-rgt-neg-in 85.2%

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

      6. remove-double-neg 85.2%

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

      7. *-commutative 85.2%

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

      8. *-commutative 85.2%

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

      9. sub-neg 85.2%

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

      10. sub-neg 85.2%

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

      11. *-commutative 85.2%

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

      12. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around inf 68.7%

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

   if -5.20000000000000018e-83 < i < 8.50000000000000036e-184

   1. Initial program 80.3%

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

   3. Taylor expanded in j around 0 73.0%

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

   4. Taylor expanded in x around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   if 8.50000000000000036e-184 < i < 1.2e-58

   1. Initial program 74.0%

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

      1. +-commutative 74.0%

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

      2. fma-define 82.7%

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

      3. *-commutative 82.7%

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

      4. *-commutative 82.7%

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

      5. cancel-sign-sub-inv 82.7%

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

      6. cancel-sign-sub 82.7%

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

      7. fma-neg 82.7%

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

      8. distribute-rgt-neg-out 82.7%

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

      9. remove-double-neg 82.7%

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

      10. *-commutative 82.7%

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

      11. *-commutative 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in t around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

      4. *-commutative 70.3%

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

   7. Simplified 70.3%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+144}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))))
   (if (<= y -1.5e+220)
     (* y (- (* x z) (* i j)))
     (if (<= y -8.2e+63)
       t_1
       (if (<= y 6.3e+44)
         (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))
         (if (<= y 1.05e+217) t_1 (* i (- (* a b) (* y 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))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (y <= -1.5e+220) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -8.2e+63) {
		tmp = t_1;
	} else if (y <= 6.3e+44) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else if (y <= 1.05e+217) {
		tmp = t_1;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    if (y <= (-1.5d+220)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-8.2d+63)) then
        tmp = t_1
    else if (y <= 6.3d+44) then
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    else if (y <= 1.05d+217) then
        tmp = t_1
    else
        tmp = i * ((a * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (y <= -1.5e+220) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -8.2e+63) {
		tmp = t_1;
	} else if (y <= 6.3e+44) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else if (y <= 1.05e+217) {
		tmp = t_1;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	tmp = 0
	if y <= -1.5e+220:
		tmp = y * ((x * z) - (i * j))
	elif y <= -8.2e+63:
		tmp = t_1
	elif y <= 6.3e+44:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	elif y <= 1.05e+217:
		tmp = t_1
	else:
		tmp = i * ((a * b) - (y * 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(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (y <= -1.5e+220)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -8.2e+63)
		tmp = t_1;
	elseif (y <= 6.3e+44)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (y <= 1.05e+217)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * 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))) + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (y <= -1.5e+220)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -8.2e+63)
		tmp = t_1;
	elseif (y <= 6.3e+44)
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	elseif (y <= 1.05e+217)
		tmp = t_1;
	else
		tmp = i * ((a * b) - (y * 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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+220], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e+63], t$95$1, If[LessEqual[y, 6.3e+44], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+217], t$95$1, N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.50000000000000012e220

   1. Initial program 37.3%

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

      1. +-commutative 37.3%

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

      2. fma-define 37.3%

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

      3. *-commutative 37.3%

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

      4. *-commutative 37.3%

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

      5. cancel-sign-sub-inv 37.3%

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

      6. cancel-sign-sub 37.3%

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

      7. fma-neg 44.5%

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

      8. distribute-rgt-neg-out 44.5%

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

      9. remove-double-neg 44.5%

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

      10. *-commutative 44.5%

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

      11. *-commutative 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in y around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

   7. Simplified 65.9%

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

   if -1.50000000000000012e220 < y < -8.19999999999999985e63 or 6.3e44 < y < 1.05e217

   1. Initial program 66.4%

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

      1. cancel-sign-sub-inv 66.4%

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

      2. cancel-sign-sub 66.4%

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

      3. *-commutative 66.4%

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

      4. fma-neg 66.4%

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

      5. distribute-rgt-neg-in 66.4%

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

      6. remove-double-neg 66.4%

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

      7. *-commutative 66.4%

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

      8. *-commutative 66.4%

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

      9. sub-neg 66.4%

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

      10. sub-neg 66.4%

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

      11. *-commutative 66.4%

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

      12. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in z around inf 73.2%

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

   if -8.19999999999999985e63 < y < 6.3e44

   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. Step-by-step derivation

      1. +-commutative 80.7%

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

      2. fma-define 82.1%

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

      3. *-commutative 82.1%

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

      4. *-commutative 82.1%

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

      5. cancel-sign-sub-inv 82.1%

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

      6. cancel-sign-sub 82.1%

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

      7. fma-neg 82.8%

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

      8. distribute-rgt-neg-out 82.8%

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

      9. remove-double-neg 82.8%

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

      10. *-commutative 82.8%

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

      11. *-commutative 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 74.4%

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

      4. *-commutative 74.4%

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

      5. associate-*r* 74.4%

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

      6. *-commutative 74.4%

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

      7. *-commutative 74.4%

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

      8. associate-*r* 74.4%

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

      9. *-commutative 74.4%

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

      10. associate-*r* 76.4%

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

      11. distribute-lft-in 77.1%

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

      12. +-commutative 77.1%

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

      13. mul-1-neg 77.1%

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

      14. unsub-neg 77.1%

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

      15. *-commutative 77.1%

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

      16. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   if 1.05e217 < y

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. fma-define 67.1%

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

      3. *-commutative 67.1%

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

      4. *-commutative 67.1%

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

      5. cancel-sign-sub-inv 67.1%

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

      6. cancel-sign-sub 67.1%

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

      7. fma-neg 67.1%

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

      8. distribute-rgt-neg-out 67.1%

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

      9. remove-double-neg 67.1%

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

      10. *-commutative 67.1%

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

      11. *-commutative 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in i around inf 78.4%

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

      1. distribute-lft-out-- 78.4%

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

      2. *-commutative 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in i around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. *-commutative 78.4%

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

      3. distribute-rgt-neg-out 78.4%

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

      4. neg-mul-1 78.4%

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

      5. *-commutative 78.4%

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

      6. distribute-lft-out-- 78.4%

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

      7. sub-neg 78.4%

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

      8. neg-mul-1 78.4%

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

      9. remove-double-neg 78.4%

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

      10. +-commutative 78.4%

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

      11. mul-1-neg 78.4%

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

      12. *-commutative 78.4%

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

      13. unsub-neg 78.4%

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

   10. Simplified 78.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+217}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;t\_2 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \left(x \cdot y + t \cdot \frac{c \cdot j - x \cdot a}{z}\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+143}:\\ \;\;\;\;t\_2 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (* c j)) (* b (- (* a i) (* z c)))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= b -3.2e+62)
     t_1
     (if (<= b -2.1e-55)
       (+ t_2 (* a (* b i)))
       (if (<= b -4.7e-241)
         (* z (+ (* x y) (* t (/ (- (* c j) (* x a)) z))))
         (if (<= b 2.1e+143) (+ t_2 (* z (- (* x y) (* b c)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -3.2e+62) {
		tmp = t_1;
	} else if (b <= -2.1e-55) {
		tmp = t_2 + (a * (b * i));
	} else if (b <= -4.7e-241) {
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)));
	} else if (b <= 2.1e+143) {
		tmp = t_2 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)))
    t_2 = j * ((t * c) - (y * i))
    if (b <= (-3.2d+62)) then
        tmp = t_1
    else if (b <= (-2.1d-55)) then
        tmp = t_2 + (a * (b * i))
    else if (b <= (-4.7d-241)) then
        tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)))
    else if (b <= 2.1d+143) then
        tmp = t_2 + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -3.2e+62) {
		tmp = t_1;
	} else if (b <= -2.1e-55) {
		tmp = t_2 + (a * (b * i));
	} else if (b <= -4.7e-241) {
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)));
	} else if (b <= 2.1e+143) {
		tmp = t_2 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -3.2e+62:
		tmp = t_1
	elif b <= -2.1e-55:
		tmp = t_2 + (a * (b * i))
	elif b <= -4.7e-241:
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)))
	elif b <= 2.1e+143:
		tmp = t_2 + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -3.2e+62)
		tmp = t_1;
	elseif (b <= -2.1e-55)
		tmp = Float64(t_2 + Float64(a * Float64(b * i)));
	elseif (b <= -4.7e-241)
		tmp = Float64(z * Float64(Float64(x * y) + Float64(t * Float64(Float64(Float64(c * j) - Float64(x * a)) / z))));
	elseif (b <= 2.1e+143)
		tmp = Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -3.2e+62)
		tmp = t_1;
	elseif (b <= -2.1e-55)
		tmp = t_2 + (a * (b * i));
	elseif (b <= -4.7e-241)
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)));
	elseif (b <= 2.1e+143)
		tmp = t_2 + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+62], t$95$1, If[LessEqual[b, -2.1e-55], N[(t$95$2 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.7e-241], N[(z * N[(N[(x * y), $MachinePrecision] + N[(t * N[(N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+143], N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.19999999999999984e62 or 2.09999999999999988e143 < b

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-define 72.0%

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

      3. *-commutative 72.0%

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

      4. *-commutative 72.0%

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

      5. cancel-sign-sub-inv 72.0%

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

      6. cancel-sign-sub 72.0%

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

      7. fma-neg 73.1%

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

      8. distribute-rgt-neg-out 73.1%

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

      9. remove-double-neg 73.1%

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

      10. *-commutative 73.1%

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

      11. *-commutative 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*r* 69.8%

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

      4. *-commutative 69.8%

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

      5. associate-*r* 69.8%

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

      6. *-commutative 69.8%

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

      7. *-commutative 69.8%

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

      8. associate-*r* 67.5%

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

      9. *-commutative 67.5%

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

      10. associate-*r* 70.9%

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

      11. distribute-lft-in 70.9%

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

      12. +-commutative 70.9%

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

      13. mul-1-neg 70.9%

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

      14. unsub-neg 70.9%

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

      15. *-commutative 70.9%

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

      16. *-commutative 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in c around inf 70.8%

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

   if -3.19999999999999984e62 < b < -2.1000000000000002e-55

   1. Initial program 71.5%

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

      1. cancel-sign-sub-inv 71.5%

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

      2. cancel-sign-sub 71.5%

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

      3. *-commutative 71.5%

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

      4. fma-neg 74.8%

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

      5. distribute-rgt-neg-in 74.8%

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

      6. remove-double-neg 74.8%

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

      7. *-commutative 74.8%

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

      8. *-commutative 74.8%

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

      9. sub-neg 74.8%

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

      10. sub-neg 74.8%

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

      11. *-commutative 74.8%

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

      12. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in i around inf 74.8%

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

   if -2.1000000000000002e-55 < b < -4.6999999999999999e-241

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. fma-define 85.0%

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

      3. *-commutative 85.0%

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

      4. *-commutative 85.0%

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

      5. cancel-sign-sub-inv 85.0%

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

      6. cancel-sign-sub 85.0%

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

      7. fma-neg 85.0%

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

      8. distribute-rgt-neg-out 85.0%

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

      9. remove-double-neg 85.0%

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

      10. *-commutative 85.0%

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

      11. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around -inf 74.8%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in x around inf 76.8%

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

   9. Taylor expanded in z around inf 81.1%

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

       1. +-commutative 81.1%

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

       2. mul-1-neg 81.1%

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

       3. unsub-neg 81.1%

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

       4. *-commutative 81.1%

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

       5. associate-/l* 79.0%

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

       6. *-commutative 79.0%

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

       7. *-commutative 79.0%

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

   11. Simplified 79.0%

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

   if -4.6999999999999999e-241 < b < 2.09999999999999988e143

   1. Initial program 70.3%

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

      1. cancel-sign-sub-inv 70.3%

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

      2. cancel-sign-sub 70.3%

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

      3. *-commutative 70.3%

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

      4. fma-neg 70.3%

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

      5. distribute-rgt-neg-in 70.3%

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

      6. remove-double-neg 70.3%

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

      7. *-commutative 70.3%

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

      8. *-commutative 70.3%

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

      9. sub-neg 70.3%

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

      10. sub-neg 70.3%

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

      11. *-commutative 70.3%

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

      12. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 71.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \left(x \cdot y + t \cdot \frac{c \cdot j - x \cdot a}{z}\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{+189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t\_1\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-203}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\right) + i \cdot \frac{c \cdot \left(t \cdot j\right)}{i}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.22e+189)
     (+ (* t (* c j)) t_1)
     (if (<= b -7.8e-203)
       (+ (+ (* x (- (* y z) (* t a))) t_1) (* i (/ (* c (* t j)) i)))
       (if (<= b 2e-30)
         (+ (* a (- (* b i) (* x t))) (* j (- (* t c) (* y i))))
         (+ (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.22e+189) {
		tmp = (t * (c * j)) + t_1;
	} else if (b <= -7.8e-203) {
		tmp = ((x * ((y * z) - (t * a))) + t_1) + (i * ((c * (t * j)) / i));
	} else if (b <= 2e-30) {
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.22d+189)) then
        tmp = (t * (c * j)) + t_1
    else if (b <= (-7.8d-203)) then
        tmp = ((x * ((y * z) - (t * a))) + t_1) + (i * ((c * (t * j)) / i))
    else if (b <= 2d-30) then
        tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)))
    else
        tmp = (t * ((c * j) - (x * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.22e+189) {
		tmp = (t * (c * j)) + t_1;
	} else if (b <= -7.8e-203) {
		tmp = ((x * ((y * z) - (t * a))) + t_1) + (i * ((c * (t * j)) / i));
	} else if (b <= 2e-30) {
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.22e+189:
		tmp = (t * (c * j)) + t_1
	elif b <= -7.8e-203:
		tmp = ((x * ((y * z) - (t * a))) + t_1) + (i * ((c * (t * j)) / i))
	elif b <= 2e-30:
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)))
	else:
		tmp = (t * ((c * j) - (x * a))) + t_1
	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 (b <= -1.22e+189)
		tmp = Float64(Float64(t * Float64(c * j)) + t_1);
	elseif (b <= -7.8e-203)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(i * Float64(Float64(c * Float64(t * j)) / i)));
	elseif (b <= 2e-30)
		tmp = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	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 (b <= -1.22e+189)
		tmp = (t * (c * j)) + t_1;
	elseif (b <= -7.8e-203)
		tmp = ((x * ((y * z) - (t * a))) + t_1) + (i * ((c * (t * j)) / i));
	elseif (b <= 2e-30)
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)));
	else
		tmp = (t * ((c * j) - (x * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.22e+189], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -7.8e-203], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(i * N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-30], N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.2200000000000001e189

   1. Initial program 59.9%

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

      1. +-commutative 59.9%

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

      2. fma-define 59.9%

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

      3. *-commutative 59.9%

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

      4. *-commutative 59.9%

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

      5. cancel-sign-sub-inv 59.9%

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

      6. cancel-sign-sub 59.9%

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

      7. fma-neg 63.3%

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

      8. distribute-rgt-neg-out 63.3%

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

      9. remove-double-neg 63.3%

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

      10. *-commutative 63.3%

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

      11. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in y around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 58.5%

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

      4. *-commutative 58.5%

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

      5. associate-*r* 58.5%

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

      6. *-commutative 58.5%

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

      7. *-commutative 58.5%

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

      8. associate-*r* 55.2%

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

      9. *-commutative 55.2%

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

      10. associate-*r* 58.5%

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

      11. distribute-lft-in 58.5%

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

      12. +-commutative 58.5%

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

      13. mul-1-neg 58.5%

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

      14. unsub-neg 58.5%

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

      15. *-commutative 58.5%

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

      16. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in c around inf 71.9%

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

   if -1.2200000000000001e189 < b < -7.7999999999999998e-203

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf 78.3%

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

      1. +-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. associate-/l* 78.4%

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

      5. *-commutative 78.4%

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

      6. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in c around inf 76.3%

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

   if -7.7999999999999998e-203 < b < 2e-30

   1. Initial program 77.1%

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

      1. cancel-sign-sub-inv 77.1%

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

      2. cancel-sign-sub 77.1%

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

      3. *-commutative 77.1%

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

      4. fma-neg 77.1%

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

      5. distribute-rgt-neg-in 77.1%

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

      6. remove-double-neg 77.1%

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

      7. *-commutative 77.1%

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

      8. *-commutative 77.1%

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

      9. sub-neg 77.1%

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

      10. sub-neg 77.1%

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

      11. *-commutative 77.1%

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

      12. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in a around -inf 78.0%

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

   if 2e-30 < b

   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. Step-by-step derivation

      1. +-commutative 63.4%

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

      2. fma-define 65.2%

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

      3. *-commutative 65.2%

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

      4. *-commutative 65.2%

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

      5. cancel-sign-sub-inv 65.2%

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

      6. cancel-sign-sub 65.2%

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

      7. fma-neg 65.1%

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

      8. distribute-rgt-neg-out 65.1%

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

      9. remove-double-neg 65.1%

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

      10. *-commutative 65.1%

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

      11. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in y around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

      5. associate-*r* 75.9%

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

      6. *-commutative 75.9%

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

      7. *-commutative 75.9%

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

      8. associate-*r* 74.2%

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

      9. *-commutative 74.2%

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

      10. associate-*r* 79.4%

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

      11. distribute-lft-in 79.4%

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

      12. +-commutative 79.4%

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

      13. mul-1-neg 79.4%

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

      14. unsub-neg 79.4%

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

      15. *-commutative 79.4%

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

      16. *-commutative 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+189}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-203}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + i \cdot \frac{c \cdot \left(t \cdot j\right)}{i}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-65}:\\ \;\;\;\;t\_2 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(x \cdot y + t \cdot \frac{c \cdot j - x \cdot a}{z}\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;t\_2 - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (* c j)) (* b (- (* a i) (* z c)))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= b -5.6e+63)
     t_1
     (if (<= b -2.9e-65)
       (+ t_2 (* a (* b i)))
       (if (<= b -3.3e-231)
         (* z (+ (* x y) (* t (/ (- (* c j) (* x a)) z))))
         (if (<= b 4.8e+120) (- t_2 (* z (* b c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -5.6e+63) {
		tmp = t_1;
	} else if (b <= -2.9e-65) {
		tmp = t_2 + (a * (b * i));
	} else if (b <= -3.3e-231) {
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)));
	} else if (b <= 4.8e+120) {
		tmp = t_2 - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)))
    t_2 = j * ((t * c) - (y * i))
    if (b <= (-5.6d+63)) then
        tmp = t_1
    else if (b <= (-2.9d-65)) then
        tmp = t_2 + (a * (b * i))
    else if (b <= (-3.3d-231)) then
        tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)))
    else if (b <= 4.8d+120) then
        tmp = t_2 - (z * (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -5.6e+63) {
		tmp = t_1;
	} else if (b <= -2.9e-65) {
		tmp = t_2 + (a * (b * i));
	} else if (b <= -3.3e-231) {
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)));
	} else if (b <= 4.8e+120) {
		tmp = t_2 - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -5.6e+63:
		tmp = t_1
	elif b <= -2.9e-65:
		tmp = t_2 + (a * (b * i))
	elif b <= -3.3e-231:
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)))
	elif b <= 4.8e+120:
		tmp = t_2 - (z * (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -5.6e+63)
		tmp = t_1;
	elseif (b <= -2.9e-65)
		tmp = Float64(t_2 + Float64(a * Float64(b * i)));
	elseif (b <= -3.3e-231)
		tmp = Float64(z * Float64(Float64(x * y) + Float64(t * Float64(Float64(Float64(c * j) - Float64(x * a)) / z))));
	elseif (b <= 4.8e+120)
		tmp = Float64(t_2 - Float64(z * Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (c * j)) + (b * ((a * i) - (z * c)));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -5.6e+63)
		tmp = t_1;
	elseif (b <= -2.9e-65)
		tmp = t_2 + (a * (b * i));
	elseif (b <= -3.3e-231)
		tmp = z * ((x * y) + (t * (((c * j) - (x * a)) / z)));
	elseif (b <= 4.8e+120)
		tmp = t_2 - (z * (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.6e+63], t$95$1, If[LessEqual[b, -2.9e-65], N[(t$95$2 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.3e-231], N[(z * N[(N[(x * y), $MachinePrecision] + N[(t * N[(N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+120], N[(t$95$2 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.59999999999999974e63 or 4.80000000000000002e120 < b

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. fma-define 71.5%

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

      3. *-commutative 71.5%

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

      4. *-commutative 71.5%

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

      5. cancel-sign-sub-inv 71.5%

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

      6. cancel-sign-sub 71.5%

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

      7. fma-neg 72.6%

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

      8. distribute-rgt-neg-out 72.6%

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

      9. remove-double-neg 72.6%

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

      10. *-commutative 72.6%

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

      11. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. *-commutative 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*r* 68.2%

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

      4. *-commutative 68.2%

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

      5. associate-*r* 68.2%

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

      6. *-commutative 68.2%

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

      7. *-commutative 68.2%

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

      8. associate-*r* 65.9%

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

      9. *-commutative 65.9%

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

      10. associate-*r* 69.3%

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

      11. distribute-lft-in 69.3%

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

      12. +-commutative 69.3%

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

      13. mul-1-neg 69.3%

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

      14. unsub-neg 69.3%

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

      15. *-commutative 69.3%

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

      16. *-commutative 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in c around inf 70.4%

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

   if -5.59999999999999974e63 < b < -2.8999999999999998e-65

   1. Initial program 71.5%

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

      1. cancel-sign-sub-inv 71.5%

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

      2. cancel-sign-sub 71.5%

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

      3. *-commutative 71.5%

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

      4. fma-neg 74.8%

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

      5. distribute-rgt-neg-in 74.8%

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

      6. remove-double-neg 74.8%

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

      7. *-commutative 74.8%

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

      8. *-commutative 74.8%

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

      9. sub-neg 74.8%

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

      10. sub-neg 74.8%

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

      11. *-commutative 74.8%

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

      12. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in i around inf 74.8%

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

   if -2.8999999999999998e-65 < b < -3.30000000000000028e-231

   1. Initial program 86.6%

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

      1. +-commutative 86.6%

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

      2. fma-define 86.6%

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

      3. *-commutative 86.6%

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

      4. *-commutative 86.6%

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

      5. cancel-sign-sub-inv 86.6%

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

      6. cancel-sign-sub 86.6%

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

      7. fma-neg 86.6%

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

      8. distribute-rgt-neg-out 86.6%

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

      9. remove-double-neg 86.6%

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

      10. *-commutative 86.6%

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

      11. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around -inf 76.0%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in x around inf 78.1%

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

   9. Taylor expanded in z around inf 80.2%

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

       1. +-commutative 80.2%

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

       2. mul-1-neg 80.2%

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

       3. unsub-neg 80.2%

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

       4. *-commutative 80.2%

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

       5. associate-/l* 78.1%

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

       6. *-commutative 78.1%

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

       7. *-commutative 78.1%

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

   11. Simplified 78.1%

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

   if -3.30000000000000028e-231 < b < 4.80000000000000002e120

   1. Initial program 70.3%

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

      1. cancel-sign-sub-inv 70.3%

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

      2. cancel-sign-sub 70.3%

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

      3. *-commutative 70.3%

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

      4. fma-neg 70.3%

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

      5. distribute-rgt-neg-in 70.3%

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

      6. remove-double-neg 70.3%

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

      7. *-commutative 70.3%

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

      8. *-commutative 70.3%

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

      9. sub-neg 70.3%

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

      10. sub-neg 70.3%

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

      11. *-commutative 70.3%

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

      12. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in c around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. *-commutative 65.8%

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

      3. *-commutative 65.8%

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

      4. associate-*r* 69.0%

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

      5. *-commutative 69.0%

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

      6. distribute-rgt-neg-out 69.0%

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

      7. distribute-rgt-neg-in 69.0%

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

   7. Simplified 69.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(x \cdot y + t \cdot \frac{c \cdot j - x \cdot a}{z}\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-179} \lor \neg \left(b \leq 8 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -7e+198)
     (+ (* t (* c j)) t_1)
     (if (or (<= b -1.6e-179) (not (<= b 8e+133)))
       (+ (* x (- (* y z) (* t a))) t_1)
       (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e+198) {
		tmp = (t * (c * j)) + t_1;
	} else if ((b <= -1.6e-179) || !(b <= 8e+133)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-7d+198)) then
        tmp = (t * (c * j)) + t_1
    else if ((b <= (-1.6d-179)) .or. (.not. (b <= 8d+133))) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e+198) {
		tmp = (t * (c * j)) + t_1;
	} else if ((b <= -1.6e-179) || !(b <= 8e+133)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7e+198:
		tmp = (t * (c * j)) + t_1
	elif (b <= -1.6e-179) or not (b <= 8e+133):
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	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 (b <= -7e+198)
		tmp = Float64(Float64(t * Float64(c * j)) + t_1);
	elseif ((b <= -1.6e-179) || !(b <= 8e+133))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e+198)
		tmp = (t * (c * j)) + t_1;
	elseif ((b <= -1.6e-179) || ~((b <= 8e+133)))
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+198], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[b, -1.6e-179], N[Not[LessEqual[b, 8e+133]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.00000000000000026e198

   1. Initial program 59.9%

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

      1. +-commutative 59.9%

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

      2. fma-define 59.9%

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

      3. *-commutative 59.9%

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

      4. *-commutative 59.9%

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

      5. cancel-sign-sub-inv 59.9%

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

      6. cancel-sign-sub 59.9%

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

      7. fma-neg 63.3%

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

      8. distribute-rgt-neg-out 63.3%

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

      9. remove-double-neg 63.3%

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

      10. *-commutative 63.3%

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

      11. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in y around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 58.5%

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

      4. *-commutative 58.5%

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

      5. associate-*r* 58.5%

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

      6. *-commutative 58.5%

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

      7. *-commutative 58.5%

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

      8. associate-*r* 55.2%

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

      9. *-commutative 55.2%

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

      10. associate-*r* 58.5%

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

      11. distribute-lft-in 58.5%

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

      12. +-commutative 58.5%

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

      13. mul-1-neg 58.5%

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

      14. unsub-neg 58.5%

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

      15. *-commutative 58.5%

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

      16. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in c around inf 71.9%

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

   if -7.00000000000000026e198 < b < -1.6e-179 or 8.0000000000000002e133 < b

   1. Initial program 76.7%

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

   3. Taylor expanded in j around 0 79.2%

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

   if -1.6e-179 < b < 8.0000000000000002e133

   1. Initial program 72.3%

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

      1. cancel-sign-sub-inv 72.3%

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

      2. cancel-sign-sub 72.3%

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

      3. *-commutative 72.3%

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

      4. fma-neg 72.3%

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

      5. distribute-rgt-neg-in 72.3%

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

      6. remove-double-neg 72.3%

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

      7. *-commutative 72.3%

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

      8. *-commutative 72.3%

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

      9. sub-neg 72.3%

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

      10. sub-neg 72.3%

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

      11. *-commutative 72.3%

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

      12. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in z around inf 71.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-179} \lor \neg \left(b \leq 8 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+195}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.55e+195)
     (+ (* t (* c j)) t_1)
     (if (<= b -3.8e-158)
       (+ (* x (- (* y z) (* t a))) t_1)
       (if (<= b 2e-30)
         (+ (* a (- (* b i) (* x t))) (* j (- (* t c) (* y i))))
         (+ (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e+195) {
		tmp = (t * (c * j)) + t_1;
	} else if (b <= -3.8e-158) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= 2e-30) {
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.55d+195)) then
        tmp = (t * (c * j)) + t_1
    else if (b <= (-3.8d-158)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (b <= 2d-30) then
        tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)))
    else
        tmp = (t * ((c * j) - (x * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e+195) {
		tmp = (t * (c * j)) + t_1;
	} else if (b <= -3.8e-158) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= 2e-30) {
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.55e+195:
		tmp = (t * (c * j)) + t_1
	elif b <= -3.8e-158:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif b <= 2e-30:
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)))
	else:
		tmp = (t * ((c * j) - (x * a))) + t_1
	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 (b <= -1.55e+195)
		tmp = Float64(Float64(t * Float64(c * j)) + t_1);
	elseif (b <= -3.8e-158)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (b <= 2e-30)
		tmp = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	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 (b <= -1.55e+195)
		tmp = (t * (c * j)) + t_1;
	elseif (b <= -3.8e-158)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (b <= 2e-30)
		tmp = (a * ((b * i) - (x * t))) + (j * ((t * c) - (y * i)));
	else
		tmp = (t * ((c * j) - (x * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+195], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -3.8e-158], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 2e-30], N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5500000000000001e195

   1. Initial program 59.9%

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

      1. +-commutative 59.9%

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

      2. fma-define 59.9%

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

      3. *-commutative 59.9%

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

      4. *-commutative 59.9%

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

      5. cancel-sign-sub-inv 59.9%

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

      6. cancel-sign-sub 59.9%

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

      7. fma-neg 63.3%

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

      8. distribute-rgt-neg-out 63.3%

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

      9. remove-double-neg 63.3%

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

      10. *-commutative 63.3%

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

      11. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in y around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 58.5%

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

      4. *-commutative 58.5%

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

      5. associate-*r* 58.5%

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

      6. *-commutative 58.5%

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

      7. *-commutative 58.5%

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

      8. associate-*r* 55.2%

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

      9. *-commutative 55.2%

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

      10. associate-*r* 58.5%

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

      11. distribute-lft-in 58.5%

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

      12. +-commutative 58.5%

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

      13. mul-1-neg 58.5%

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

      14. unsub-neg 58.5%

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

      15. *-commutative 58.5%

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

      16. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in c around inf 71.9%

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

   if -1.5500000000000001e195 < b < -3.7999999999999999e-158

   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. Add Preprocessing

   3. Taylor expanded in j around 0 74.7%

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

   if -3.7999999999999999e-158 < b < 2e-30

   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. Step-by-step derivation

      1. cancel-sign-sub-inv 78.7%

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

      2. cancel-sign-sub 78.7%

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

      3. *-commutative 78.7%

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

      4. fma-neg 78.7%

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

      5. distribute-rgt-neg-in 78.7%

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

      6. remove-double-neg 78.7%

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

      7. *-commutative 78.7%

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

      8. *-commutative 78.7%

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

      9. sub-neg 78.7%

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

      10. sub-neg 78.7%

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

      11. *-commutative 78.7%

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

      12. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in a around -inf 76.0%

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

   if 2e-30 < b

   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. Step-by-step derivation

      1. +-commutative 63.4%

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

      2. fma-define 65.2%

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

      3. *-commutative 65.2%

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

      4. *-commutative 65.2%

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

      5. cancel-sign-sub-inv 65.2%

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

      6. cancel-sign-sub 65.2%

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

      7. fma-neg 65.1%

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

      8. distribute-rgt-neg-out 65.1%

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

      9. remove-double-neg 65.1%

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

      10. *-commutative 65.1%

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

      11. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in y around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

      5. associate-*r* 75.9%

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

      6. *-commutative 75.9%

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

      7. *-commutative 75.9%

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

      8. associate-*r* 74.2%

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

      9. *-commutative 74.2%

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

      10. associate-*r* 79.4%

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

      11. distribute-lft-in 79.4%

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

      12. +-commutative 79.4%

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

      13. mul-1-neg 79.4%

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

      14. unsub-neg 79.4%

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

      15. *-commutative 79.4%

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

      16. *-commutative 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+195}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.2e+60)
   (* x (- (* y z) (* t a)))
   (if (<= x -7.2e-192)
     (+ (* j (- (* t c) (* y i))) (* a (* b i)))
     (if (<= x 9.2e+17)
       (+ (* t (* c j)) (* b (- (* a i) (* z c))))
       (* x (* a (- (/ (* y z) a) t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.2e+60) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= -7.2e-192) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (x <= 9.2e+17) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = x * (a * (((y * z) / a) - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-1.2d+60)) then
        tmp = x * ((y * z) - (t * a))
    else if (x <= (-7.2d-192)) then
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    else if (x <= 9.2d+17) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else
        tmp = x * (a * (((y * z) / a) - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.2e+60) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= -7.2e-192) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (x <= 9.2e+17) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = x * (a * (((y * z) / a) - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.2e+60:
		tmp = x * ((y * z) - (t * a))
	elif x <= -7.2e-192:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	elif x <= 9.2e+17:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	else:
		tmp = x * (a * (((y * z) / a) - t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.2e+60)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (x <= -7.2e-192)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	elseif (x <= 9.2e+17)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(x * Float64(a * Float64(Float64(Float64(y * z) / a) - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.2e+60)
		tmp = x * ((y * z) - (t * a));
	elseif (x <= -7.2e-192)
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	elseif (x <= 9.2e+17)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	else
		tmp = x * (a * (((y * z) / a) - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.2e+60], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-192], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+17], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * N[(N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e60

   1. Initial program 77.0%

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

   3. Taylor expanded in j around 0 74.0%

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

   4. Taylor expanded in x around inf 69.4%

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

      1. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if -1.2e60 < x < -7.1999999999999998e-192

   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. Step-by-step derivation

      1. cancel-sign-sub-inv 76.1%

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

      2. cancel-sign-sub 76.1%

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

      3. *-commutative 76.1%

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

      4. fma-neg 76.1%

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

      5. distribute-rgt-neg-in 76.1%

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

      6. remove-double-neg 76.1%

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

      7. *-commutative 76.1%

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

      8. *-commutative 76.1%

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

      9. sub-neg 76.1%

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

      10. sub-neg 76.1%

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

      11. *-commutative 76.1%

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

      12. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in i around inf 65.3%

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

   if -7.1999999999999998e-192 < x < 9.2e17

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. fma-define 67.1%

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

      3. *-commutative 67.1%

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

      4. *-commutative 67.1%

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

      5. cancel-sign-sub-inv 67.1%

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

      6. cancel-sign-sub 67.1%

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

      7. fma-neg 69.3%

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

      8. distribute-rgt-neg-out 69.3%

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

      9. remove-double-neg 69.3%

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

      10. *-commutative 69.3%

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

      11. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in y around 0 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-*r* 73.6%

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

      6. *-commutative 73.6%

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

      7. *-commutative 73.6%

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

      8. associate-*r* 70.1%

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

      9. *-commutative 70.1%

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

      10. associate-*r* 75.6%

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

      11. distribute-lft-in 75.6%

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

      12. +-commutative 75.6%

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

      13. mul-1-neg 75.6%

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

      14. unsub-neg 75.6%

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

      15. *-commutative 75.6%

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

      16. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in c around inf 73.3%

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

   if 9.2e17 < x

   1. Initial program 74.9%

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

   3. Taylor expanded in j around 0 69.3%

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

   4. Taylor expanded in x around inf 69.7%

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

      1. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in a around inf 69.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -3.7e+63)
     t_2
     (if (<= b -1.25e-40)
       t_1
       (if (<= b -3.2e-223) (* t (* x (- a))) (if (<= b 4.3e+120) 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 <= -3.7e+63) {
		tmp = t_2;
	} else if (b <= -1.25e-40) {
		tmp = t_1;
	} else if (b <= -3.2e-223) {
		tmp = t * (x * -a);
	} else if (b <= 4.3e+120) {
		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 <= (-3.7d+63)) then
        tmp = t_2
    else if (b <= (-1.25d-40)) then
        tmp = t_1
    else if (b <= (-3.2d-223)) then
        tmp = t * (x * -a)
    else if (b <= 4.3d+120) 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 <= -3.7e+63) {
		tmp = t_2;
	} else if (b <= -1.25e-40) {
		tmp = t_1;
	} else if (b <= -3.2e-223) {
		tmp = t * (x * -a);
	} else if (b <= 4.3e+120) {
		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 <= -3.7e+63:
		tmp = t_2
	elif b <= -1.25e-40:
		tmp = t_1
	elif b <= -3.2e-223:
		tmp = t * (x * -a)
	elif b <= 4.3e+120:
		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 <= -3.7e+63)
		tmp = t_2;
	elseif (b <= -1.25e-40)
		tmp = t_1;
	elseif (b <= -3.2e-223)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (b <= 4.3e+120)
		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 <= -3.7e+63)
		tmp = t_2;
	elseif (b <= -1.25e-40)
		tmp = t_1;
	elseif (b <= -3.2e-223)
		tmp = t * (x * -a);
	elseif (b <= 4.3e+120)
		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, -3.7e+63], t$95$2, If[LessEqual[b, -1.25e-40], t$95$1, If[LessEqual[b, -3.2e-223], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+120], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.69999999999999968e63 or 4.3000000000000002e120 < b

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

      3. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in b around inf 67.0%

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

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -3.69999999999999968e63 < b < -1.24999999999999991e-40 or -3.2000000000000001e-223 < b < 4.3000000000000002e120

   1. Initial program 70.2%

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

      1. +-commutative 70.2%

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

      2. fma-define 72.7%

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

      3. *-commutative 72.7%

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

      4. *-commutative 72.7%

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

      5. cancel-sign-sub-inv 72.7%

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

      6. cancel-sign-sub 72.7%

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

      7. fma-neg 73.5%

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

      8. distribute-rgt-neg-out 73.5%

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

      9. remove-double-neg 73.5%

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

      10. *-commutative 73.5%

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

      11. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in j around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. *-commutative 64.4%

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

      3. *-commutative 64.4%

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

      4. sub-neg 64.4%

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

   7. Simplified 64.4%

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

   if -1.24999999999999991e-40 < b < -3.2000000000000001e-223

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. fma-define 86.1%

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

      3. *-commutative 86.1%

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

      4. *-commutative 86.1%

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

      5. cancel-sign-sub-inv 86.1%

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

      6. cancel-sign-sub 86.1%

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

      7. fma-neg 86.1%

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

      8. distribute-rgt-neg-out 86.1%

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

      9. remove-double-neg 86.1%

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

      10. *-commutative 86.1%

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

      11. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in t around -inf 72.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in x around inf 72.2%

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

   9. Taylor expanded in a around inf 47.0%

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

       1. *-commutative 47.0%

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

   11. Simplified 47.0%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -5.6e-86)
     t_1
     (if (<= b -8.2e-234)
       (* t (* x (- a)))
       (if (<= b 1.75e+112) (* c (- (* t j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.6e-86) {
		tmp = t_1;
	} else if (b <= -8.2e-234) {
		tmp = t * (x * -a);
	} else if (b <= 1.75e+112) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-5.6d-86)) then
        tmp = t_1
    else if (b <= (-8.2d-234)) then
        tmp = t * (x * -a)
    else if (b <= 1.75d+112) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.6e-86) {
		tmp = t_1;
	} else if (b <= -8.2e-234) {
		tmp = t * (x * -a);
	} else if (b <= 1.75e+112) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.6e-86:
		tmp = t_1
	elif b <= -8.2e-234:
		tmp = t * (x * -a)
	elif b <= 1.75e+112:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	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 (b <= -5.6e-86)
		tmp = t_1;
	elseif (b <= -8.2e-234)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (b <= 1.75e+112)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.6e-86)
		tmp = t_1;
	elseif (b <= -8.2e-234)
		tmp = t * (x * -a);
	elseif (b <= 1.75e+112)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.6e-86], t$95$1, If[LessEqual[b, -8.2e-234], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e+112], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.60000000000000019e-86 or 1.74999999999999998e112 < b

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. unsub-neg 69.2%

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

      3. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in b around inf 60.6%

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

      1. *-commutative 60.6%

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

   8. Simplified 60.6%

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

   if -5.60000000000000019e-86 < b < -8.20000000000000021e-234

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. fma-define 86.3%

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

      3. *-commutative 86.3%

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

      4. *-commutative 86.3%

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

      5. cancel-sign-sub-inv 86.3%

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

      6. cancel-sign-sub 86.3%

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

      7. fma-neg 86.3%

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

      8. distribute-rgt-neg-out 86.3%

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

      9. remove-double-neg 86.3%

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

      10. *-commutative 86.3%

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

      11. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in t around -inf 77.6%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in x around inf 79.9%

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

   9. Taylor expanded in a around inf 52.5%

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

       1. *-commutative 52.5%

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

   11. Simplified 52.5%

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

   if -8.20000000000000021e-234 < b < 1.74999999999999998e112

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. fma-define 71.5%

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

      3. *-commutative 71.5%

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

      4. *-commutative 71.5%

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

      5. cancel-sign-sub-inv 71.5%

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

      6. cancel-sign-sub 71.5%

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

      7. fma-neg 71.5%

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

      8. distribute-rgt-neg-out 71.5%

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

      9. remove-double-neg 71.5%

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

      10. *-commutative 71.5%

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

      11. *-commutative 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in c around inf 42.5%

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

      1. *-commutative 42.5%

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

      2. *-commutative 42.5%

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

   7. Simplified 42.5%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 3.95 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -5e-78)
     t_1
     (if (<= b -7.6e-280)
       (* t (* x (- a)))
       (if (<= b 3.95e-22) (* i (* y (- j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5e-78) {
		tmp = t_1;
	} else if (b <= -7.6e-280) {
		tmp = t * (x * -a);
	} else if (b <= 3.95e-22) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-5d-78)) then
        tmp = t_1
    else if (b <= (-7.6d-280)) then
        tmp = t * (x * -a)
    else if (b <= 3.95d-22) then
        tmp = i * (y * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5e-78) {
		tmp = t_1;
	} else if (b <= -7.6e-280) {
		tmp = t * (x * -a);
	} else if (b <= 3.95e-22) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5e-78:
		tmp = t_1
	elif b <= -7.6e-280:
		tmp = t * (x * -a)
	elif b <= 3.95e-22:
		tmp = i * (y * -j)
	else:
		tmp = t_1
	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 (b <= -5e-78)
		tmp = t_1;
	elseif (b <= -7.6e-280)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (b <= 3.95e-22)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5e-78)
		tmp = t_1;
	elseif (b <= -7.6e-280)
		tmp = t * (x * -a);
	elseif (b <= 3.95e-22)
		tmp = i * (y * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e-78], t$95$1, If[LessEqual[b, -7.6e-280], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.95e-22], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.9999999999999996e-78 or 3.9499999999999999e-22 < b

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

      3. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in b around inf 55.7%

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

      1. *-commutative 55.7%

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

   8. Simplified 55.7%

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

   if -4.9999999999999996e-78 < b < -7.6000000000000003e-280

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. fma-define 83.1%

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

      3. *-commutative 83.1%

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

      4. *-commutative 83.1%

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

      5. cancel-sign-sub-inv 83.1%

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

      6. cancel-sign-sub 83.1%

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

      7. fma-neg 83.1%

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

      8. distribute-rgt-neg-out 83.1%

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

      9. remove-double-neg 83.1%

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

      10. *-commutative 83.1%

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

      11. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in t around -inf 72.2%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in x around inf 75.9%

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

   9. Taylor expanded in a around inf 49.4%

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

       1. *-commutative 49.4%

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

   11. Simplified 49.4%

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

   if -7.6000000000000003e-280 < b < 3.9499999999999999e-22

   1. Initial program 73.0%

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

      1. +-commutative 73.0%

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

      2. fma-define 74.8%

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

      3. *-commutative 74.8%

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

      4. *-commutative 74.8%

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

      5. cancel-sign-sub-inv 74.8%

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

      6. cancel-sign-sub 74.8%

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

      7. fma-neg 74.8%

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

      8. distribute-rgt-neg-out 74.8%

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

      9. remove-double-neg 74.8%

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

      10. *-commutative 74.8%

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

      11. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in i around inf 44.0%

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

      1. distribute-lft-out-- 44.0%

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

      2. *-commutative 44.0%

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

   7. Simplified 44.0%

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

   8. Taylor expanded in y around inf 40.5%

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

      1. associate-*r* 40.5%

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

      2. neg-mul-1 40.5%

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

      3. *-commutative 40.5%

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

   10. Simplified 40.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-78}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-280}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 3.95 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.1e+51)
   (* a (* b i))
   (if (<= i -2.15e-120)
     (* c (* t j))
     (if (<= i 9.5e+46) (* t (* x (- a))) (* y (* i (- 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 <= -3.1e+51) {
		tmp = a * (b * i);
	} else if (i <= -2.15e-120) {
		tmp = c * (t * j);
	} else if (i <= 9.5e+46) {
		tmp = t * (x * -a);
	} else {
		tmp = y * (i * -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 <= (-3.1d+51)) then
        tmp = a * (b * i)
    else if (i <= (-2.15d-120)) then
        tmp = c * (t * j)
    else if (i <= 9.5d+46) then
        tmp = t * (x * -a)
    else
        tmp = y * (i * -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 <= -3.1e+51) {
		tmp = a * (b * i);
	} else if (i <= -2.15e-120) {
		tmp = c * (t * j);
	} else if (i <= 9.5e+46) {
		tmp = t * (x * -a);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.1e+51:
		tmp = a * (b * i)
	elif i <= -2.15e-120:
		tmp = c * (t * j)
	elif i <= 9.5e+46:
		tmp = t * (x * -a)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.1e+51)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -2.15e-120)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 9.5e+46)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.1e+51)
		tmp = a * (b * i);
	elseif (i <= -2.15e-120)
		tmp = c * (t * j);
	elseif (i <= 9.5e+46)
		tmp = t * (x * -a);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.1e+51], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.15e-120], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e+46], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.10000000000000011e51

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. fma-define 65.7%

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

      3. *-commutative 65.7%

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

      4. *-commutative 65.7%

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

      5. cancel-sign-sub-inv 65.7%

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

      6. cancel-sign-sub 65.7%

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

      7. fma-neg 67.5%

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

      8. distribute-rgt-neg-out 67.5%

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

      9. remove-double-neg 67.5%

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

      10. *-commutative 67.5%

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

      11. *-commutative 67.5%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in i around inf 64.4%

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

      1. distribute-lft-out-- 64.4%

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

      2. *-commutative 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in y around 0 47.5%

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

   if -3.10000000000000011e51 < i < -2.14999999999999991e-120

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. fma-define 87.7%

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

      3. *-commutative 87.7%

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

      4. *-commutative 87.7%

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

      5. cancel-sign-sub-inv 87.7%

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

      6. cancel-sign-sub 87.7%

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

      7. fma-neg 87.7%

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

      8. distribute-rgt-neg-out 87.7%

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

      9. remove-double-neg 87.7%

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

      10. *-commutative 87.7%

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

      11. *-commutative 87.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 53.8%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 53.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -2.14999999999999991e-120 < i < 9.5000000000000008e46

   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. Step-by-step derivation

      1. +-commutative 78.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around -inf 63.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   7. Simplified 67.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)}{t}\right) - c \cdot j\right)} \]

   8. Taylor expanded in x around inf 65.4%

      \[\leadsto \left(-t\right) \cdot \left(\left(x \cdot a - \color{blue}{\frac{x \cdot \left(y \cdot z\right)}{t}}\right) - c \cdot j\right) \]

   9. Taylor expanded in a around inf 41.0%

      \[\leadsto \left(-t\right) \cdot \color{blue}{\left(a \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 41.0%

          \[\leadsto \left(-t\right) \cdot \color{blue}{\left(x \cdot a\right)} \]

   11. Simplified 41.0%

       \[\leadsto \left(-t\right) \cdot \color{blue}{\left(x \cdot a\right)} \]

   if 9.5000000000000008e46 < i

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 64.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 64.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 74.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 74.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 74.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 74.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.5%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 42.5%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.5%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   11. Taylor expanded in i around 0 42.5%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. neg-mul-1 42.5%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. distribute-lft-neg-in 42.5%

          \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

       3. associate-*r* 44.2%

          \[\leadsto \color{blue}{\left(\left(-i\right) \cdot j\right) \cdot y} \]

       4. *-commutative 44.2%

          \[\leadsto \color{blue}{\left(j \cdot \left(-i\right)\right)} \cdot y \]

   13. Simplified 44.2%

       \[\leadsto \color{blue}{\left(j \cdot \left(-i\right)\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.2e+49)
   (* a (* b i))
   (if (<= i -2.2e-120)
     (* c (* t j))
     (if (<= i 2.4e+47) (* t (* x (- a))) (* i (* y (- 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 <= -4.2e+49) {
		tmp = a * (b * i);
	} else if (i <= -2.2e-120) {
		tmp = c * (t * j);
	} else if (i <= 2.4e+47) {
		tmp = t * (x * -a);
	} else {
		tmp = i * (y * -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 <= (-4.2d+49)) then
        tmp = a * (b * i)
    else if (i <= (-2.2d-120)) then
        tmp = c * (t * j)
    else if (i <= 2.4d+47) then
        tmp = t * (x * -a)
    else
        tmp = i * (y * -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 <= -4.2e+49) {
		tmp = a * (b * i);
	} else if (i <= -2.2e-120) {
		tmp = c * (t * j);
	} else if (i <= 2.4e+47) {
		tmp = t * (x * -a);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.2e+49:
		tmp = a * (b * i)
	elif i <= -2.2e-120:
		tmp = c * (t * j)
	elif i <= 2.4e+47:
		tmp = t * (x * -a)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.2e+49)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -2.2e-120)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 2.4e+47)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.2e+49)
		tmp = a * (b * i);
	elseif (i <= -2.2e-120)
		tmp = c * (t * j);
	elseif (i <= 2.4e+47)
		tmp = t * (x * -a);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.2e+49], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.2e-120], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e+47], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.20000000000000022e49

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 65.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 64.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 64.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 47.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -4.20000000000000022e49 < i < -2.20000000000000012e-120

   1. Initial program 85.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 87.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 87.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 87.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 87.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 87.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 87.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 87.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 87.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 53.8%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 53.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -2.20000000000000012e-120 < i < 2.40000000000000019e47

   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. Step-by-step derivation

      1. +-commutative 78.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 81.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around -inf 63.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   7. Simplified 67.4%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)}{t}\right) - c \cdot j\right)} \]

   8. Taylor expanded in x around inf 65.4%

      \[\leadsto \left(-t\right) \cdot \left(\left(x \cdot a - \color{blue}{\frac{x \cdot \left(y \cdot z\right)}{t}}\right) - c \cdot j\right) \]

   9. Taylor expanded in a around inf 41.0%

      \[\leadsto \left(-t\right) \cdot \color{blue}{\left(a \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 41.0%

          \[\leadsto \left(-t\right) \cdot \color{blue}{\left(x \cdot a\right)} \]

   11. Simplified 41.0%

       \[\leadsto \left(-t\right) \cdot \color{blue}{\left(x \cdot a\right)} \]

   if 2.40000000000000019e47 < i

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 64.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 64.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 74.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 74.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 74.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 74.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.5%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 42.5%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.5%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.9 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.9e+50)
   (* a (* b i))
   (if (<= i -2.1e-113)
     (* c (* t j))
     (if (<= i 1.45e+47) (* (* t a) (- x)) (* i (* y (- 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 <= -5.9e+50) {
		tmp = a * (b * i);
	} else if (i <= -2.1e-113) {
		tmp = c * (t * j);
	} else if (i <= 1.45e+47) {
		tmp = (t * a) * -x;
	} else {
		tmp = i * (y * -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 <= (-5.9d+50)) then
        tmp = a * (b * i)
    else if (i <= (-2.1d-113)) then
        tmp = c * (t * j)
    else if (i <= 1.45d+47) then
        tmp = (t * a) * -x
    else
        tmp = i * (y * -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 <= -5.9e+50) {
		tmp = a * (b * i);
	} else if (i <= -2.1e-113) {
		tmp = c * (t * j);
	} else if (i <= 1.45e+47) {
		tmp = (t * a) * -x;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.9e+50:
		tmp = a * (b * i)
	elif i <= -2.1e-113:
		tmp = c * (t * j)
	elif i <= 1.45e+47:
		tmp = (t * a) * -x
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.9e+50)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -2.1e-113)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 1.45e+47)
		tmp = Float64(Float64(t * a) * Float64(-x));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5.9e+50)
		tmp = a * (b * i);
	elseif (i <= -2.1e-113)
		tmp = c * (t * j);
	elseif (i <= 1.45e+47)
		tmp = (t * a) * -x;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.9e+50], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.1e-113], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.45e+47], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.8999999999999998e50

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 65.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 64.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 64.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 47.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -5.8999999999999998e50 < i < -2.1e-113

   1. Initial program 84.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 87.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 52.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 52.6%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 52.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 42.9%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -2.1e-113 < i < 1.4499999999999999e47

   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. Add Preprocessing

   3. Taylor expanded in j around 0 66.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Taylor expanded in x around inf 57.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 57.5%

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   6. Simplified 57.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   7. Taylor expanded in y around 0 39.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. *-commutative 39.8%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      3. distribute-lft-neg-in 39.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(-t\right) \cdot a\right)} \]

   9. Simplified 39.8%

      \[\leadsto x \cdot \color{blue}{\left(\left(-t\right) \cdot a\right)} \]

   if 1.4499999999999999e47 < i

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 64.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 64.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 64.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 74.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 74.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 74.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 74.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.5%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 42.5%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.5%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.9 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+94}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -6.5e+47)
   (* a (* b i))
   (if (<= i -3.2e-117)
     (* c (* t j))
     (if (<= i 7e+94) (* (* t a) (- x)) (* 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 (i <= -6.5e+47) {
		tmp = a * (b * i);
	} else if (i <= -3.2e-117) {
		tmp = c * (t * j);
	} else if (i <= 7e+94) {
		tmp = (t * a) * -x;
	} 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 (i <= (-6.5d+47)) then
        tmp = a * (b * i)
    else if (i <= (-3.2d-117)) then
        tmp = c * (t * j)
    else if (i <= 7d+94) then
        tmp = (t * a) * -x
    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 (i <= -6.5e+47) {
		tmp = a * (b * i);
	} else if (i <= -3.2e-117) {
		tmp = c * (t * j);
	} else if (i <= 7e+94) {
		tmp = (t * a) * -x;
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -6.5e+47:
		tmp = a * (b * i)
	elif i <= -3.2e-117:
		tmp = c * (t * j)
	elif i <= 7e+94:
		tmp = (t * a) * -x
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -6.5e+47)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -3.2e-117)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 7e+94)
		tmp = Float64(Float64(t * a) * Float64(-x));
	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 (i <= -6.5e+47)
		tmp = a * (b * i);
	elseif (i <= -3.2e-117)
		tmp = c * (t * j);
	elseif (i <= 7e+94)
		tmp = (t * a) * -x;
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -6.5e+47], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.2e-117], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7e+94], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -6.49999999999999988e47

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 65.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 64.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 64.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 47.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -6.49999999999999988e47 < i < -3.19999999999999995e-117

   1. Initial program 84.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 87.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 52.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 52.6%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 52.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 42.9%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -3.19999999999999995e-117 < i < 6.9999999999999994e94

   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. Add Preprocessing

   3. Taylor expanded in j around 0 66.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Taylor expanded in x around inf 55.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   6. Simplified 55.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   7. Taylor expanded in y around 0 38.0%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. *-commutative 38.0%

         \[\leadsto x \cdot \left(-\color{blue}{t \cdot a}\right) \]

      3. distribute-lft-neg-in 38.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(-t\right) \cdot a\right)} \]

   9. Simplified 38.0%

      \[\leadsto x \cdot \color{blue}{\left(\left(-t\right) \cdot a\right)} \]

   if 6.9999999999999994e94 < i

   1. Initial program 58.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 60.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 60.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 60.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 79.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 79.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 79.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 79.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 43.5%

      \[\leadsto i \cdot \color{blue}{\left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+94}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.4 \cdot 10^{+48} \lor \neg \left(i \leq 1.9 \cdot 10^{+47}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -7.4e+48) (not (<= i 1.9e+47)))
   (* i (- (* a b) (* y j)))
   (* t (- (* c j) (* x 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 ((i <= -7.4e+48) || !(i <= 1.9e+47)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t * ((c * j) - (x * 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 ((i <= (-7.4d+48)) .or. (.not. (i <= 1.9d+47))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t * ((c * j) - (x * 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 ((i <= -7.4e+48) || !(i <= 1.9e+47)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -7.4e+48) or not (i <= 1.9e+47):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -7.4e+48) || !(i <= 1.9e+47))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -7.4e+48) || ~((i <= 1.9e+47)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -7.4e+48], N[Not[LessEqual[i, 1.9e+47]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.3999999999999998e48 or 1.9000000000000002e47 < i

   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. Step-by-step derivation

      1. +-commutative 63.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 64.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 64.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 64.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 64.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 64.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 69.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 69.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 69.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in i around 0 69.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 69.2%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y - a \cdot b\right)} \]

      2. *-commutative 69.2%

         \[\leadsto -i \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right) \]

      3. distribute-rgt-neg-out 69.2%

         \[\leadsto \color{blue}{i \cdot \left(-\left(y \cdot j - a \cdot b\right)\right)} \]

      4. neg-mul-1 69.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

      5. *-commutative 69.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{j \cdot y} - a \cdot b\right)\right) \]

      6. distribute-lft-out-- 69.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      7. sub-neg 69.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      8. neg-mul-1 69.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      9. remove-double-neg 69.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \]

      10. +-commutative 69.2%

          \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      11. mul-1-neg 69.2%

          \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      12. *-commutative 69.2%

          \[\leadsto i \cdot \left(a \cdot b + \left(-\color{blue}{y \cdot j}\right)\right) \]

      13. unsub-neg 69.2%

          \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

   10. Simplified 69.2%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if -7.3999999999999998e48 < i < 1.9000000000000002e47

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 59.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 59.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 59.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 59.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 59.4%

         \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) \]

   7. Simplified 59.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.4 \cdot 10^{+48} \lor \neg \left(i \leq 1.9 \cdot 10^{+47}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-11} \lor \neg \left(c \leq 1.45 \cdot 10^{-57}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.8e-11) (not (<= c 1.45e-57)))
   (* c (- (* t j) (* z b)))
   (* i (- (* a b) (* y 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 ((c <= -3.8e-11) || !(c <= 1.45e-57)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = i * ((a * b) - (y * 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 ((c <= (-3.8d-11)) .or. (.not. (c <= 1.45d-57))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = i * ((a * b) - (y * 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 ((c <= -3.8e-11) || !(c <= 1.45e-57)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.8e-11) or not (c <= 1.45e-57):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.8e-11) || !(c <= 1.45e-57))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.8e-11) || ~((c <= 1.45e-57)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.8e-11], N[Not[LessEqual[c, 1.45e-57]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.7999999999999998e-11 or 1.45000000000000013e-57 < c

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 68.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 68.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 68.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 70.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 70.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 70.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 57.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 57.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 57.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -3.7999999999999998e-11 < c < 1.45000000000000013e-57

   1. Initial program 78.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 81.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 81.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 81.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 81.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 81.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 57.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 57.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 57.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 57.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in i around 0 57.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.1%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y - a \cdot b\right)} \]

      2. *-commutative 57.1%

         \[\leadsto -i \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right) \]

      3. distribute-rgt-neg-out 57.1%

         \[\leadsto \color{blue}{i \cdot \left(-\left(y \cdot j - a \cdot b\right)\right)} \]

      4. neg-mul-1 57.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

      5. *-commutative 57.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{j \cdot y} - a \cdot b\right)\right) \]

      6. distribute-lft-out-- 57.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      7. sub-neg 57.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      8. neg-mul-1 57.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      9. remove-double-neg 57.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \]

      10. +-commutative 57.1%

          \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      11. mul-1-neg 57.1%

          \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      12. *-commutative 57.1%

          \[\leadsto i \cdot \left(a \cdot b + \left(-\color{blue}{y \cdot j}\right)\right) \]

      13. unsub-neg 57.1%

          \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

   10. Simplified 57.1%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-11} \lor \neg \left(c \leq 1.45 \cdot 10^{-57}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.05 \cdot 10^{+47} \lor \neg \left(i \leq 1.25 \cdot 10^{+126}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -3.05e+47) (not (<= i 1.25e+126))) (* 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 ((i <= -3.05e+47) || !(i <= 1.25e+126)) {
		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 ((i <= (-3.05d+47)) .or. (.not. (i <= 1.25d+126))) 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 ((i <= -3.05e+47) || !(i <= 1.25e+126)) {
		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 (i <= -3.05e+47) or not (i <= 1.25e+126):
		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 ((i <= -3.05e+47) || !(i <= 1.25e+126))
		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 ((i <= -3.05e+47) || ~((i <= 1.25e+126)))
		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[i, -3.05e+47], N[Not[LessEqual[i, 1.25e+126]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.05000000000000009e47 or 1.24999999999999994e126 < i

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 63.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 63.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 63.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 63.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 63.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 72.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 72.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 72.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 46.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -3.05000000000000009e47 < i < 1.24999999999999994e126

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 45.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 45.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 31.0%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.05 \cdot 10^{+47} \lor \neg \left(i \leq 1.25 \cdot 10^{+126}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+126}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.05e+49)
   (* a (* b i))
   (if (<= i 1.3e+126) (* 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 (i <= -1.05e+49) {
		tmp = a * (b * i);
	} else if (i <= 1.3e+126) {
		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 (i <= (-1.05d+49)) then
        tmp = a * (b * i)
    else if (i <= 1.3d+126) 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 (i <= -1.05e+49) {
		tmp = a * (b * i);
	} else if (i <= 1.3e+126) {
		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 i <= -1.05e+49:
		tmp = a * (b * i)
	elif i <= 1.3e+126:
		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 (i <= -1.05e+49)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= 1.3e+126)
		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 (i <= -1.05e+49)
		tmp = a * (b * i);
	elseif (i <= 1.3e+126)
		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[i, -1.05e+49], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+126], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.05000000000000005e49

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 65.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 65.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 67.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 64.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 64.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 47.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.05000000000000005e49 < i < 1.3e126

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 45.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 45.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 31.0%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 1.3e126 < i

   1. Initial program 54.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 54.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 56.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 56.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 56.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 56.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 56.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fma-neg 59.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 59.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 59.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 59.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 59.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 83.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 83.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 83.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 48.0%

      \[\leadsto i \cdot \color{blue}{\left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 22.5% 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 72.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 72.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-define 74.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 74.8%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 74.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. cancel-sign-sub-inv 74.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   6. cancel-sign-sub 74.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   7. fma-neg 75.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   8. distribute-rgt-neg-out 75.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   9. remove-double-neg 75.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   10. *-commutative 75.6%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

   11. *-commutative 75.6%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

3. Simplified 75.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in i around inf 41.1%

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
6. Step-by-step derivation

   1. distribute-lft-out-- 41.1%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   2. *-commutative 41.1%

      \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

7. Simplified 41.1%

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

8. Taylor expanded in y around 0 24.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
9. Add Preprocessing

Developer Target 1: 69.4% 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 2024146 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* 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)))))