Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.8% → 81.0%

Time: 17.0s

Alternatives: 21

Speedup: 0.5×

• 57.9% 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: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

      1. +-commutative 0.0%

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

      2. fma-define 2.0%

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

      3. *-commutative 2.0%

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

      4. *-commutative 2.0%

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

      5. cancel-sign-sub-inv 2.0%

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

      6. cancel-sign-sub 2.0%

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

      7. fmm-def 4.1%

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

      8. distribute-rgt-neg-out 4.1%

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

      9. remove-double-neg 4.1%

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

      10. *-commutative 4.1%

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

      11. *-commutative 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in y around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 86.2%

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

Alternative 2: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot j - x \cdot a\\ \mathbf{if}\;b \leq -4 \cdot 10^{-132}:\\ \;\;\;\;t \cdot t\_1 - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(\frac{y \cdot z}{t} - a\right)\right) - z \cdot \left(b \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \frac{t\_1}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* c j) (* x a))))
   (if (<= b -4e-132)
     (- (* t t_1) (* b (- (* z c) (* a i))))
     (if (<= b 3.2e+68)
       (+
        (- (* x (* t (- (/ (* y z) t) a))) (* z (* b c)))
        (* j (- (* t c) (* y i))))
       (* b (+ (* t (/ t_1 b)) (- (* a i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) - (x * a);
	double tmp;
	if (b <= -4e-132) {
		tmp = (t * t_1) - (b * ((z * c) - (a * i)));
	} else if (b <= 3.2e+68) {
		tmp = ((x * (t * (((y * z) / t) - a))) - (z * (b * c))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * ((t * (t_1 / b)) + ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * j) - (x * a)
    if (b <= (-4d-132)) then
        tmp = (t * t_1) - (b * ((z * c) - (a * i)))
    else if (b <= 3.2d+68) then
        tmp = ((x * (t * (((y * z) / t) - a))) - (z * (b * c))) + (j * ((t * c) - (y * i)))
    else
        tmp = b * ((t * (t_1 / b)) + ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) - (x * a);
	double tmp;
	if (b <= -4e-132) {
		tmp = (t * t_1) - (b * ((z * c) - (a * i)));
	} else if (b <= 3.2e+68) {
		tmp = ((x * (t * (((y * z) / t) - a))) - (z * (b * c))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * ((t * (t_1 / b)) + ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * j) - (x * a)
	tmp = 0
	if b <= -4e-132:
		tmp = (t * t_1) - (b * ((z * c) - (a * i)))
	elif b <= 3.2e+68:
		tmp = ((x * (t * (((y * z) / t) - a))) - (z * (b * c))) + (j * ((t * c) - (y * i)))
	else:
		tmp = b * ((t * (t_1 / b)) + ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * j) - Float64(x * a))
	tmp = 0.0
	if (b <= -4e-132)
		tmp = Float64(Float64(t * t_1) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	elseif (b <= 3.2e+68)
		tmp = Float64(Float64(Float64(x * Float64(t * Float64(Float64(Float64(y * z) / t) - a))) - Float64(z * Float64(b * c))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(Float64(t * Float64(t_1 / b)) + Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * j) - (x * a);
	tmp = 0.0;
	if (b <= -4e-132)
		tmp = (t * t_1) - (b * ((z * c) - (a * i)));
	elseif (b <= 3.2e+68)
		tmp = ((x * (t * (((y * z) / t) - a))) - (z * (b * c))) + (j * ((t * c) - (y * i)));
	else
		tmp = b * ((t * (t_1 / b)) + ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e-132], N[(N[(t * t$95$1), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+68], N[(N[(N[(x * N[(t * N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] + N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.9999999999999999e-132

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. fma-define 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. cancel-sign-sub-inv 75.7%

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

      6. cancel-sign-sub 75.7%

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

      7. fmm-def 76.9%

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

      8. distribute-rgt-neg-out 76.9%

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

      9. remove-double-neg 76.9%

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

      10. *-commutative 76.9%

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

      11. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-*r* 67.3%

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

      4. *-commutative 67.3%

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

      5. associate-*l* 69.6%

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

      6. mul-1-neg 69.6%

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

      7. *-commutative 69.6%

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

      8. associate-*r* 71.7%

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

      9. *-commutative 71.7%

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

      10. distribute-rgt-neg-in 71.7%

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

      11. mul-1-neg 71.7%

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

      12. distribute-lft-in 72.9%

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

      13. mul-1-neg 72.9%

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

      14. unsub-neg 72.9%

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

      15. *-commutative 72.9%

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

      16. *-commutative 72.9%

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

   7. Simplified 72.9%

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

   if -3.9999999999999999e-132 < b < 3.19999999999999994e68

   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. Add Preprocessing

   3. Taylor expanded in t around inf 73.4%

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

   4. Taylor expanded in c around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*l* 79.9%

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

      4. *-commutative 79.9%

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

   6. Simplified 79.9%

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

   if 3.19999999999999994e68 < b

   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 70.4%

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

      3. *-commutative 70.4%

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

      4. *-commutative 70.4%

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

      5. cancel-sign-sub-inv 70.4%

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

      6. cancel-sign-sub 70.4%

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

      7. fmm-def 70.4%

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

      8. distribute-rgt-neg-out 70.4%

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

      9. remove-double-neg 70.4%

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

      10. *-commutative 70.4%

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

      11. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in y around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*r* 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*l* 59.4%

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

      6. mul-1-neg 59.4%

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

      7. *-commutative 59.4%

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

      8. associate-*r* 61.4%

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

      9. *-commutative 61.4%

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

      10. distribute-rgt-neg-in 61.4%

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

      11. mul-1-neg 61.4%

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

      12. distribute-lft-in 63.7%

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

      13. mul-1-neg 63.7%

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

      14. unsub-neg 63.7%

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

      15. *-commutative 63.7%

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

      16. *-commutative 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in b around -inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. neg-mul-1 68.3%

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

      3. distribute-lft-out-- 68.3%

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

      4. associate-/l* 75.1%

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

      5. *-commutative 75.1%

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

      6. *-commutative 75.1%

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

   10. Simplified 75.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(\frac{y \cdot z}{t} - a\right)\right) - z \cdot \left(b \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \frac{c \cdot j - x \cdot a}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-86}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -6e+79)
     t_2
     (if (<= y -1.8e-86)
       (+ t_1 (* a (* b i)))
       (if (<= y 1.9e-190)
         (* t (- (* c j) (* x a)))
         (if (<= y 6.4e+34) (- t_1 (* b (* z c))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6e+79) {
		tmp = t_2;
	} else if (y <= -1.8e-86) {
		tmp = t_1 + (a * (b * i));
	} else if (y <= 1.9e-190) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 6.4e+34) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-6d+79)) then
        tmp = t_2
    else if (y <= (-1.8d-86)) then
        tmp = t_1 + (a * (b * i))
    else if (y <= 1.9d-190) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 6.4d+34) then
        tmp = t_1 - (b * (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6e+79) {
		tmp = t_2;
	} else if (y <= -1.8e-86) {
		tmp = t_1 + (a * (b * i));
	} else if (y <= 1.9e-190) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 6.4e+34) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6e+79:
		tmp = t_2
	elif y <= -1.8e-86:
		tmp = t_1 + (a * (b * i))
	elif y <= 1.9e-190:
		tmp = t * ((c * j) - (x * a))
	elif y <= 6.4e+34:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6e+79)
		tmp = t_2;
	elseif (y <= -1.8e-86)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (y <= 1.9e-190)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 6.4e+34)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6e+79)
		tmp = t_2;
	elseif (y <= -1.8e-86)
		tmp = t_1 + (a * (b * i));
	elseif (y <= 1.9e-190)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 6.4e+34)
		tmp = t_1 - (b * (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+79], t$95$2, If[LessEqual[y, -1.8e-86], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-190], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+34], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999948e79 or 6.3999999999999997e34 < y

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. fma-define 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

      5. cancel-sign-sub-inv 65.8%

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

      6. cancel-sign-sub 65.8%

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

      7. fmm-def 66.6%

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

      8. distribute-rgt-neg-out 66.6%

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

      9. remove-double-neg 66.6%

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

      10. *-commutative 66.6%

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

      11. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in y around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

   7. Simplified 70.3%

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

   if -5.99999999999999948e79 < y < -1.79999999999999983e-86

   1. Initial program 82.4%

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

      1. cancel-sign-sub-inv 82.4%

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

      2. cancel-sign-sub 82.4%

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

      3. *-commutative 82.4%

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

      4. fmm-def 82.4%

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

      5. distribute-rgt-neg-in 82.4%

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

      6. remove-double-neg 82.4%

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

      7. *-commutative 82.4%

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

      8. *-commutative 82.4%

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

      9. *-commutative 82.4%

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

      10. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in i around inf 59.8%

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

   if -1.79999999999999983e-86 < y < 1.8999999999999999e-190

   1. Initial program 82.9%

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

      1. +-commutative 82.9%

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

      2. fma-define 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. fmm-def 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 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

   7. Simplified 64.9%

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

   if 1.8999999999999999e-190 < y < 6.3999999999999997e34

   1. Initial program 90.7%

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

      1. cancel-sign-sub-inv 90.7%

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

      2. cancel-sign-sub 90.7%

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

      3. *-commutative 90.7%

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

      4. fmm-def 90.7%

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

      5. distribute-rgt-neg-in 90.7%

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

      6. remove-double-neg 90.7%

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

      7. *-commutative 90.7%

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

      8. *-commutative 90.7%

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

      9. *-commutative 90.7%

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

      10. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in c around inf 67.4%

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

      1. associate-*r* 67.4%

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

      2. neg-mul-1 67.4%

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

      3. *-commutative 67.4%

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

   7. Simplified 67.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-86}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -6.6e+22)
     t_3
     (if (<= b -6e-224)
       t_2
       (if (<= b 3.05e-118)
         t_1
         (if (<= b 1.16e-66) t_2 (if (<= b 4.9e+72) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.6e+22) {
		tmp = t_3;
	} else if (b <= -6e-224) {
		tmp = t_2;
	} else if (b <= 3.05e-118) {
		tmp = t_1;
	} else if (b <= 1.16e-66) {
		tmp = t_2;
	} else if (b <= 4.9e+72) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-6.6d+22)) then
        tmp = t_3
    else if (b <= (-6d-224)) then
        tmp = t_2
    else if (b <= 3.05d-118) then
        tmp = t_1
    else if (b <= 1.16d-66) then
        tmp = t_2
    else if (b <= 4.9d+72) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.6e+22) {
		tmp = t_3;
	} else if (b <= -6e-224) {
		tmp = t_2;
	} else if (b <= 3.05e-118) {
		tmp = t_1;
	} else if (b <= 1.16e-66) {
		tmp = t_2;
	} else if (b <= 4.9e+72) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -6.6e+22:
		tmp = t_3
	elif b <= -6e-224:
		tmp = t_2
	elif b <= 3.05e-118:
		tmp = t_1
	elif b <= 1.16e-66:
		tmp = t_2
	elif b <= 4.9e+72:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.6e+22)
		tmp = t_3;
	elseif (b <= -6e-224)
		tmp = t_2;
	elseif (b <= 3.05e-118)
		tmp = t_1;
	elseif (b <= 1.16e-66)
		tmp = t_2;
	elseif (b <= 4.9e+72)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.6e+22)
		tmp = t_3;
	elseif (b <= -6e-224)
		tmp = t_2;
	elseif (b <= 3.05e-118)
		tmp = t_1;
	elseif (b <= 1.16e-66)
		tmp = t_2;
	elseif (b <= 4.9e+72)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.6e+22], t$95$3, If[LessEqual[b, -6e-224], t$95$2, If[LessEqual[b, 3.05e-118], t$95$1, If[LessEqual[b, 1.16e-66], t$95$2, If[LessEqual[b, 4.9e+72], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.5999999999999996e22 or 4.90000000000000006e72 < b

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. fma-define 76.3%

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

      3. *-commutative 76.3%

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

      4. *-commutative 76.3%

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

      5. cancel-sign-sub-inv 76.3%

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

      6. cancel-sign-sub 76.3%

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

      7. fmm-def 77.4%

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

      8. distribute-rgt-neg-out 77.4%

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

      9. remove-double-neg 77.4%

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

      10. *-commutative 77.4%

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

      11. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-*r* 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-*l* 67.0%

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

      6. mul-1-neg 67.0%

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

      7. *-commutative 67.0%

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

      8. associate-*r* 68.0%

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

      9. *-commutative 68.0%

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

      10. distribute-rgt-neg-in 68.0%

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

      11. mul-1-neg 68.0%

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

      12. distribute-lft-in 69.0%

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

      13. mul-1-neg 69.0%

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

      14. unsub-neg 69.0%

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

      15. *-commutative 69.0%

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

      16. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in b around inf 70.3%

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

      1. *-commutative 70.3%

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

   10. Simplified 70.3%

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

   if -6.5999999999999996e22 < b < -5.99999999999999963e-224 or 3.04999999999999992e-118 < b < 1.16000000000000002e-66

   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. Step-by-step derivation

      1. +-commutative 69.3%

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

      2. fma-define 69.3%

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

      3. *-commutative 69.3%

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

      4. *-commutative 69.3%

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

      5. cancel-sign-sub-inv 69.3%

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

      6. cancel-sign-sub 69.3%

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

      7. fmm-def 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 t around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -5.99999999999999963e-224 < b < 3.04999999999999992e-118 or 1.16000000000000002e-66 < b < 4.90000000000000006e72

   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 80.2%

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

      3. *-commutative 80.2%

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

      4. *-commutative 80.2%

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

      5. cancel-sign-sub-inv 80.2%

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

      6. cancel-sign-sub 80.2%

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

      7. fmm-def 80.2%

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

      8. distribute-rgt-neg-out 80.2%

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

      9. remove-double-neg 80.2%

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

      10. *-commutative 80.2%

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

      11. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in y around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

   7. Simplified 65.1%

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

Alternative 5: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.6 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-251} \lor \neg \left(j \leq 6.6 \cdot 10^{-40}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -9.6e+210)
     t_1
     (if (or (<= j -4.7e-251) (not (<= j 6.6e-40)))
       (+ (* z (- (* x y) (* b c))) t_1)
       (- (* t (- (* c j) (* x a))) (* b (- (* z c) (* a i))))))))

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 tmp;
	if (j <= -9.6e+210) {
		tmp = t_1;
	} else if ((j <= -4.7e-251) || !(j <= 6.6e-40)) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-9.6d+210)) then
        tmp = t_1
    else if ((j <= (-4.7d-251)) .or. (.not. (j <= 6.6d-40))) then
        tmp = (z * ((x * y) - (b * c))) + t_1
    else
        tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -9.6e+210) {
		tmp = t_1;
	} else if ((j <= -4.7e-251) || !(j <= 6.6e-40)) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -9.6e+210:
		tmp = t_1
	elif (j <= -4.7e-251) or not (j <= 6.6e-40):
		tmp = (z * ((x * y) - (b * c))) + t_1
	else:
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
	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)))
	tmp = 0.0
	if (j <= -9.6e+210)
		tmp = t_1;
	elseif ((j <= -4.7e-251) || !(j <= 6.6e-40))
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1);
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	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));
	tmp = 0.0;
	if (j <= -9.6e+210)
		tmp = t_1;
	elseif ((j <= -4.7e-251) || ~((j <= 6.6e-40)))
		tmp = (z * ((x * y) - (b * c))) + t_1;
	else
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	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]}, If[LessEqual[j, -9.6e+210], t$95$1, If[Or[LessEqual[j, -4.7e-251], N[Not[LessEqual[j, 6.6e-40]], $MachinePrecision]], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.59999999999999953e210

   1. Initial program 66.6%

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

      1. +-commutative 66.6%

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

      2. fma-define 72.1%

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

      3. *-commutative 72.1%

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

      4. *-commutative 72.1%

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

      5. cancel-sign-sub-inv 72.1%

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

      6. cancel-sign-sub 72.1%

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

      7. fmm-def 72.1%

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

      8. distribute-rgt-neg-out 72.1%

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

      9. remove-double-neg 72.1%

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

      10. *-commutative 72.1%

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

      11. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in j around inf 94.4%

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

      1. *-commutative 94.4%

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

      2. *-commutative 94.4%

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

   7. Simplified 94.4%

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

   if -9.59999999999999953e210 < j < -4.7000000000000001e-251 or 6.59999999999999986e-40 < j

   1. Initial program 75.8%

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

      1. cancel-sign-sub-inv 75.8%

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

      2. cancel-sign-sub 75.8%

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

      3. *-commutative 75.8%

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

      4. fmm-def 76.4%

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

      5. distribute-rgt-neg-in 76.4%

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

      6. remove-double-neg 76.4%

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

      7. *-commutative 76.4%

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

      8. *-commutative 76.4%

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

      9. *-commutative 76.4%

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

      10. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -4.7000000000000001e-251 < j < 6.59999999999999986e-40

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

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

      2. fma-define 75.6%

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

      3. *-commutative 75.6%

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

      4. *-commutative 75.6%

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

      5. cancel-sign-sub-inv 75.6%

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

      6. cancel-sign-sub 75.6%

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

      7. fmm-def 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 y around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 71.0%

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

      4. *-commutative 71.0%

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

      5. associate-*l* 77.4%

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

      6. mul-1-neg 77.4%

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

      7. *-commutative 77.4%

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

      8. associate-*r* 79.8%

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

      9. *-commutative 79.8%

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

      10. distribute-rgt-neg-in 79.8%

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

      11. mul-1-neg 79.8%

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

      12. distribute-lft-in 79.8%

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

      13. mul-1-neg 79.8%

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

      14. unsub-neg 79.8%

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

      15. *-commutative 79.8%

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

      16. *-commutative 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.6 \cdot 10^{+210}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-251} \lor \neg \left(j \leq 6.6 \cdot 10^{-40}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+103} \lor \neg \left(a \leq -3 \cdot 10^{-23}\right) \land a \leq 8.5 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.55e+103) (and (not (<= a -3e-23)) (<= a 8.5e+114)))
   (+ (* z (- (* x y) (* b c))) (* j (- (* t c) (* y i))))
   (* 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 tmp;
	if ((a <= -1.55e+103) || (!(a <= -3e-23) && (a <= 8.5e+114))) {
		tmp = (z * ((x * y) - (b * c))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = a * ((b * i) - (x * 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 ((a <= (-1.55d+103)) .or. (.not. (a <= (-3d-23))) .and. (a <= 8.5d+114)) then
        tmp = (z * ((x * y) - (b * c))) + (j * ((t * c) - (y * i)))
    else
        tmp = a * ((b * i) - (x * 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 ((a <= -1.55e+103) || (!(a <= -3e-23) && (a <= 8.5e+114))) {
		tmp = (z * ((x * y) - (b * c))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.55e+103) or (not (a <= -3e-23) and (a <= 8.5e+114)):
		tmp = (z * ((x * y) - (b * c))) + (j * ((t * c) - (y * i)))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.55e+103) || (!(a <= -3e-23) && (a <= 8.5e+114)))
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	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)
	tmp = 0.0;
	if ((a <= -1.55e+103) || (~((a <= -3e-23)) && (a <= 8.5e+114)))
		tmp = (z * ((x * y) - (b * c))) + (j * ((t * c) - (y * i)));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.55e+103], And[N[Not[LessEqual[a, -3e-23]], $MachinePrecision], LessEqual[a, 8.5e+114]]], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5500000000000001e103 or -3.00000000000000003e-23 < a < 8.5000000000000001e114

   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. Step-by-step derivation

      1. cancel-sign-sub-inv 77.0%

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

      2. cancel-sign-sub 77.0%

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

      3. *-commutative 77.0%

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

      4. fmm-def 77.0%

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

      5. distribute-rgt-neg-in 77.0%

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

      6. remove-double-neg 77.0%

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

      7. *-commutative 77.0%

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

      8. *-commutative 77.0%

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

      9. *-commutative 77.0%

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

      10. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -1.5500000000000001e103 < a < -3.00000000000000003e-23 or 8.5000000000000001e114 < a

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. fma-define 71.3%

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

      3. *-commutative 71.3%

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

      4. *-commutative 71.3%

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

      5. cancel-sign-sub-inv 71.3%

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

      6. cancel-sign-sub 71.3%

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

      7. fmm-def 72.8%

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

      8. distribute-rgt-neg-out 72.8%

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

      9. remove-double-neg 72.8%

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

      10. *-commutative 72.8%

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

      11. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-*l* 75.9%

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

      6. mul-1-neg 75.9%

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

      7. *-commutative 75.9%

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

      8. associate-*r* 75.8%

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

      9. *-commutative 75.8%

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

      10. distribute-rgt-neg-in 75.8%

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

      11. mul-1-neg 75.8%

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

      12. distribute-lft-in 77.2%

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

      13. mul-1-neg 77.2%

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

      14. unsub-neg 77.2%

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

      15. *-commutative 77.2%

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

      16. *-commutative 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in a around -inf 72.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+103} \lor \neg \left(a \leq -3 \cdot 10^{-23}\right) \land a \leq 8.5 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{if}\;z \leq -3450000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(t \cdot \frac{c \cdot j - x \cdot a}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-52}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ (* z (- (* x y) (* b c))) t_1)))
   (if (<= z -3450000.0)
     t_2
     (if (<= z -1.02e-250)
       (* b (+ (* t (/ (- (* c j) (* x a)) b)) (- (* a i) (* z c))))
       (if (<= z 6.8e-52) (+ t_1 (* a (- (* b i) (* x t)))) 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 = (z * ((x * y) - (b * c))) + t_1;
	double tmp;
	if (z <= -3450000.0) {
		tmp = t_2;
	} else if (z <= -1.02e-250) {
		tmp = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)));
	} else if (z <= 6.8e-52) {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	} 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 = (z * ((x * y) - (b * c))) + t_1
    if (z <= (-3450000.0d0)) then
        tmp = t_2
    else if (z <= (-1.02d-250)) then
        tmp = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)))
    else if (z <= 6.8d-52) then
        tmp = t_1 + (a * ((b * i) - (x * t)))
    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 = (z * ((x * y) - (b * c))) + t_1;
	double tmp;
	if (z <= -3450000.0) {
		tmp = t_2;
	} else if (z <= -1.02e-250) {
		tmp = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)));
	} else if (z <= 6.8e-52) {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	} 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 = (z * ((x * y) - (b * c))) + t_1
	tmp = 0
	if z <= -3450000.0:
		tmp = t_2
	elif z <= -1.02e-250:
		tmp = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)))
	elif z <= 6.8e-52:
		tmp = t_1 + (a * ((b * i) - (x * t)))
	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(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1)
	tmp = 0.0
	if (z <= -3450000.0)
		tmp = t_2;
	elseif (z <= -1.02e-250)
		tmp = Float64(b * Float64(Float64(t * Float64(Float64(Float64(c * j) - Float64(x * a)) / b)) + Float64(Float64(a * i) - Float64(z * c))));
	elseif (z <= 6.8e-52)
		tmp = Float64(t_1 + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	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 = (z * ((x * y) - (b * c))) + t_1;
	tmp = 0.0;
	if (z <= -3450000.0)
		tmp = t_2;
	elseif (z <= -1.02e-250)
		tmp = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)));
	elseif (z <= 6.8e-52)
		tmp = t_1 + (a * ((b * i) - (x * t)));
	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[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[z, -3450000.0], t$95$2, If[LessEqual[z, -1.02e-250], N[(b * N[(N[(t * N[(N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] + N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-52], N[(t$95$1 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.45e6 or 6.80000000000000035e-52 < z

   1. Initial program 65.6%

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

      1. cancel-sign-sub-inv 65.6%

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

      2. cancel-sign-sub 65.6%

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

      3. *-commutative 65.6%

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

      4. fmm-def 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. *-commutative 66.4%

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

      10. *-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 77.8%

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

   if -3.45e6 < z < -1.02000000000000001e-250

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. fma-define 90.2%

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

      3. *-commutative 90.2%

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

      4. *-commutative 90.2%

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

      5. cancel-sign-sub-inv 90.2%

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

      6. cancel-sign-sub 90.2%

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

      7. fmm-def 90.2%

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

      8. distribute-rgt-neg-out 90.2%

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

      9. remove-double-neg 90.2%

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

      10. *-commutative 90.2%

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

      11. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 55.0%

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

      1. +-commutative 55.0%

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

      2. *-commutative 55.0%

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

      3. associate-*r* 55.1%

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

      4. *-commutative 55.1%

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

      5. associate-*l* 60.6%

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

      6. mul-1-neg 60.6%

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

      7. *-commutative 60.6%

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

      8. associate-*r* 69.6%

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

      9. *-commutative 69.6%

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

      10. distribute-rgt-neg-in 69.6%

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

      11. mul-1-neg 69.6%

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

      12. distribute-lft-in 69.6%

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

      13. mul-1-neg 69.6%

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

      14. unsub-neg 69.6%

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

      15. *-commutative 69.6%

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

      16. *-commutative 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in b around -inf 73.4%

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

      1. associate-*r* 73.4%

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

      2. neg-mul-1 73.4%

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

      3. distribute-lft-out-- 73.4%

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

      4. associate-/l* 75.3%

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

      5. *-commutative 75.3%

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

      6. *-commutative 75.3%

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

   10. Simplified 75.3%

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

   if -1.02000000000000001e-250 < z < 6.80000000000000035e-52

   1. Initial program 82.5%

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

      1. cancel-sign-sub-inv 82.5%

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

      2. cancel-sign-sub 82.5%

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

      3. *-commutative 82.5%

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

      4. fmm-def 82.5%

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

      5. distribute-rgt-neg-in 82.5%

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

      6. remove-double-neg 82.5%

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

      7. *-commutative 82.5%

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

      8. *-commutative 82.5%

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

      9. *-commutative 82.5%

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

      10. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in a around -inf 78.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3450000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(t \cdot \frac{c \cdot j - x \cdot a}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00022:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.25e+83)
     t_1
     (if (<= y -3e-87)
       (+ (* j (- (* t c) (* y i))) (* a (* b i)))
       (if (<= y 1.65e-170)
         (* t (- (* c j) (* x a)))
         (if (<= y 0.00022) (* b (- (* a i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.25e+83) {
		tmp = t_1;
	} else if (y <= -3e-87) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (y <= 1.65e-170) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 0.00022) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.25d+83)) then
        tmp = t_1
    else if (y <= (-3d-87)) then
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    else if (y <= 1.65d-170) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 0.00022d0) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.25e+83) {
		tmp = t_1;
	} else if (y <= -3e-87) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (y <= 1.65e-170) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 0.00022) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.25e+83:
		tmp = t_1
	elif y <= -3e-87:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	elif y <= 1.65e-170:
		tmp = t * ((c * j) - (x * a))
	elif y <= 0.00022:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.25e+83)
		tmp = t_1;
	elseif (y <= -3e-87)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	elseif (y <= 1.65e-170)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 0.00022)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.25e+83)
		tmp = t_1;
	elseif (y <= -3e-87)
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	elseif (y <= 1.65e-170)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 0.00022)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+83], t$95$1, If[LessEqual[y, -3e-87], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-170], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00022], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.25000000000000007e83 or 2.20000000000000008e-4 < y

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. fma-define 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

      5. cancel-sign-sub-inv 65.8%

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

      6. cancel-sign-sub 65.8%

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

      7. fmm-def 66.6%

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

      8. distribute-rgt-neg-out 66.6%

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

      9. remove-double-neg 66.6%

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

      10. *-commutative 66.6%

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

      11. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in y around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

   7. Simplified 70.3%

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

   if -1.25000000000000007e83 < y < -3.00000000000000016e-87

   1. Initial program 82.4%

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

      1. cancel-sign-sub-inv 82.4%

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

      2. cancel-sign-sub 82.4%

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

      3. *-commutative 82.4%

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

      4. fmm-def 82.4%

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

      5. distribute-rgt-neg-in 82.4%

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

      6. remove-double-neg 82.4%

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

      7. *-commutative 82.4%

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

      8. *-commutative 82.4%

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

      9. *-commutative 82.4%

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

      10. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in i around inf 59.8%

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

   if -3.00000000000000016e-87 < y < 1.65000000000000002e-170

   1. Initial program 82.7%

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

      1. +-commutative 82.7%

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

      2. fma-define 82.7%

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

      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. fmm-def 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 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   if 1.65000000000000002e-170 < y < 2.20000000000000008e-4

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      2. fma-define 92.7%

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

      3. *-commutative 92.7%

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

      4. *-commutative 92.7%

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

      5. cancel-sign-sub-inv 92.7%

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

      6. cancel-sign-sub 92.7%

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

      7. fmm-def 92.7%

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

      8. distribute-rgt-neg-out 92.7%

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

      9. remove-double-neg 92.7%

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

      10. *-commutative 92.7%

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

      11. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 78.9%

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

      4. *-commutative 78.9%

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

      5. associate-*l* 82.5%

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

      6. mul-1-neg 82.5%

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

      7. *-commutative 82.5%

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

      8. associate-*r* 82.4%

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

      9. *-commutative 82.4%

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

      10. distribute-rgt-neg-in 82.4%

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

      11. mul-1-neg 82.4%

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

      12. distribute-lft-in 82.4%

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

      13. mul-1-neg 82.4%

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

      14. unsub-neg 82.4%

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

      15. *-commutative 82.4%

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

      16. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in b around inf 68.6%

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

      1. *-commutative 68.6%

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

   10. Simplified 68.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00022:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-287}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.4e+23)
     t_2
     (if (<= b -8e-224)
       t_1
       (if (<= b 4.4e-287)
         (* j (- (* t c) (* y i)))
         (if (<= b 5.5e+28) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.4e+23) {
		tmp = t_2;
	} else if (b <= -8e-224) {
		tmp = t_1;
	} else if (b <= 4.4e-287) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 5.5e+28) {
		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 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.4d+23)) then
        tmp = t_2
    else if (b <= (-8d-224)) then
        tmp = t_1
    else if (b <= 4.4d-287) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 5.5d+28) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.4e+23) {
		tmp = t_2;
	} else if (b <= -8e-224) {
		tmp = t_1;
	} else if (b <= 4.4e-287) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 5.5e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.4e+23:
		tmp = t_2
	elif b <= -8e-224:
		tmp = t_1
	elif b <= 4.4e-287:
		tmp = j * ((t * c) - (y * i))
	elif b <= 5.5e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.4e+23)
		tmp = t_2;
	elseif (b <= -8e-224)
		tmp = t_1;
	elseif (b <= 4.4e-287)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 5.5e+28)
		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 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.4e+23)
		tmp = t_2;
	elseif (b <= -8e-224)
		tmp = t_1;
	elseif (b <= 4.4e-287)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 5.5e+28)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+23], t$95$2, If[LessEqual[b, -8e-224], t$95$1, If[LessEqual[b, 4.4e-287], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4e23 or 5.5000000000000003e28 < b

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. fma-define 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

      5. cancel-sign-sub-inv 76.2%

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

      6. cancel-sign-sub 76.2%

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

      7. fmm-def 77.2%

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

      8. distribute-rgt-neg-out 77.2%

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

      9. remove-double-neg 77.2%

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

      10. *-commutative 77.2%

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

      11. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in y around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*r* 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-*l* 64.8%

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

      6. mul-1-neg 64.8%

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

      7. *-commutative 64.8%

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

      8. associate-*r* 65.7%

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

      9. *-commutative 65.7%

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

      10. distribute-rgt-neg-in 65.7%

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

      11. mul-1-neg 65.7%

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

      12. distribute-lft-in 66.7%

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

      13. mul-1-neg 66.7%

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

      14. unsub-neg 66.7%

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

      15. *-commutative 66.7%

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

      16. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

   10. Simplified 66.9%

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

   if -1.4e23 < b < -8.0000000000000002e-224 or 4.4e-287 < b < 5.5000000000000003e28

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. fma-define 75.8%

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

      3. *-commutative 75.8%

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

      4. *-commutative 75.8%

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

      5. cancel-sign-sub-inv 75.8%

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

      6. cancel-sign-sub 75.8%

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

      7. fmm-def 75.8%

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

      8. distribute-rgt-neg-out 75.8%

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

      9. remove-double-neg 75.8%

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

      10. *-commutative 75.8%

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

      11. *-commutative 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   7. Simplified 58.2%

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

   if -8.0000000000000002e-224 < b < 4.4e-287

   1. Initial program 71.1%

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

      1. +-commutative 71.1%

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

      2. fma-define 71.1%

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

      3. *-commutative 71.1%

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

      4. *-commutative 71.1%

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

      5. cancel-sign-sub-inv 71.1%

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

      6. cancel-sign-sub 71.1%

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

      7. fmm-def 71.1%

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

      8. distribute-rgt-neg-out 71.1%

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

      9. remove-double-neg 71.1%

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

      10. *-commutative 71.1%

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

      11. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in j around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   7. Simplified 63.7%

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

Alternative 10: 45.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 32000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -8e+21)
     t_2
     (if (<= b -2.5e-209)
       t_1
       (if (<= b 1.9e-118) (* x (* y z)) (if (<= b 32000000000.0) 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 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8e+21) {
		tmp = t_2;
	} else if (b <= -2.5e-209) {
		tmp = t_1;
	} else if (b <= 1.9e-118) {
		tmp = x * (y * z);
	} else if (b <= 32000000000.0) {
		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 = c * ((t * j) - (z * b))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-8d+21)) then
        tmp = t_2
    else if (b <= (-2.5d-209)) then
        tmp = t_1
    else if (b <= 1.9d-118) then
        tmp = x * (y * z)
    else if (b <= 32000000000.0d0) 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 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8e+21) {
		tmp = t_2;
	} else if (b <= -2.5e-209) {
		tmp = t_1;
	} else if (b <= 1.9e-118) {
		tmp = x * (y * z);
	} else if (b <= 32000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -8e+21:
		tmp = t_2
	elif b <= -2.5e-209:
		tmp = t_1
	elif b <= 1.9e-118:
		tmp = x * (y * z)
	elif b <= 32000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8e+21)
		tmp = t_2;
	elseif (b <= -2.5e-209)
		tmp = t_1;
	elseif (b <= 1.9e-118)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 32000000000.0)
		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 = c * ((t * j) - (z * b));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -8e+21)
		tmp = t_2;
	elseif (b <= -2.5e-209)
		tmp = t_1;
	elseif (b <= 1.9e-118)
		tmp = x * (y * z);
	elseif (b <= 32000000000.0)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+21], t$95$2, If[LessEqual[b, -2.5e-209], t$95$1, If[LessEqual[b, 1.9e-118], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 32000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8e21 or 3.2e10 < b

   1. Initial program 77.2%

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

      1. +-commutative 77.2%

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

      2. fma-define 78.1%

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

      3. *-commutative 78.1%

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

      4. *-commutative 78.1%

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

      5. cancel-sign-sub-inv 78.1%

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

      6. cancel-sign-sub 78.1%

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

      7. fmm-def 79.0%

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

      8. distribute-rgt-neg-out 79.0%

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

      9. remove-double-neg 79.0%

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

      10. *-commutative 79.0%

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

      11. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in y around 0 64.1%

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

      1. +-commutative 64.1%

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

      2. *-commutative 64.1%

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

      3. associate-*r* 64.1%

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

      4. *-commutative 64.1%

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

      5. associate-*l* 64.1%

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

      6. mul-1-neg 64.1%

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

      7. *-commutative 64.1%

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

      8. associate-*r* 64.9%

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

      9. *-commutative 64.9%

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

      10. distribute-rgt-neg-in 64.9%

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

      11. mul-1-neg 64.9%

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

      12. distribute-lft-in 65.8%

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

      13. mul-1-neg 65.8%

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

      14. unsub-neg 65.8%

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

      15. *-commutative 65.8%

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

      16. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   10. Simplified 64.3%

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

   if -8e21 < b < -2.5000000000000002e-209 or 1.9e-118 < b < 3.2e10

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. fma-define 70.9%

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

      3. *-commutative 70.9%

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

      4. *-commutative 70.9%

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

      5. cancel-sign-sub-inv 70.9%

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

      6. cancel-sign-sub 70.9%

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

      7. fmm-def 70.9%

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

      8. distribute-rgt-neg-out 70.9%

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

      9. remove-double-neg 70.9%

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

      10. *-commutative 70.9%

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

      11. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in c around inf 44.4%

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

      1. *-commutative 44.4%

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

      2. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if -2.5000000000000002e-209 < b < 1.9e-118

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. fma-define 77.5%

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

      3. *-commutative 77.5%

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

      4. *-commutative 77.5%

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

      5. cancel-sign-sub-inv 77.5%

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

      6. cancel-sign-sub 77.5%

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

      7. fmm-def 77.5%

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

      8. distribute-rgt-neg-out 77.5%

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

      9. remove-double-neg 77.5%

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

      10. *-commutative 77.5%

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

      11. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in y around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in x around inf 42.6%

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

   9. Taylor expanded in y around 0 45.9%

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

Alternative 11: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+57} \lor \neg \left(z \leq 1.05 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (or (<= z -4.2e+57) (not (<= z 1.05e-57)))
     (+ (* z (- (* x y) (* b c))) t_1)
     (+ 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 = j * ((t * c) - (y * i));
	double tmp;
	if ((z <= -4.2e+57) || !(z <= 1.05e-57)) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else {
		tmp = t_1 + (a * ((b * i) - (x * 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) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if ((z <= (-4.2d+57)) .or. (.not. (z <= 1.05d-57))) then
        tmp = (z * ((x * y) - (b * c))) + t_1
    else
        tmp = t_1 + (a * ((b * i) - (x * 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 t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((z <= -4.2e+57) || !(z <= 1.05e-57)) {
		tmp = (z * ((x * y) - (b * c))) + t_1;
	} else {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if (z <= -4.2e+57) or not (z <= 1.05e-57):
		tmp = (z * ((x * y) - (b * c))) + t_1
	else:
		tmp = t_1 + (a * ((b * i) - (x * t)))
	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)))
	tmp = 0.0
	if ((z <= -4.2e+57) || !(z <= 1.05e-57))
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + t_1);
	else
		tmp = Float64(t_1 + 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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if ((z <= -4.2e+57) || ~((z <= 1.05e-57)))
		tmp = (z * ((x * y) - (b * c))) + t_1;
	else
		tmp = t_1 + (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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -4.2e+57], N[Not[LessEqual[z, 1.05e-57]], $MachinePrecision]], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999982e57 or 1.05e-57 < z

   1. Initial program 64.5%

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

      1. cancel-sign-sub-inv 64.5%

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

      2. cancel-sign-sub 64.5%

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

      3. *-commutative 64.5%

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

      4. fmm-def 65.3%

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

      5. distribute-rgt-neg-in 65.3%

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

      6. remove-double-neg 65.3%

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

      7. *-commutative 65.3%

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

      8. *-commutative 65.3%

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

      9. *-commutative 65.3%

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

      10. *-commutative 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in z around inf 79.0%

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

   if -4.19999999999999982e57 < z < 1.05e-57

   1. Initial program 85.4%

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

      1. cancel-sign-sub-inv 85.4%

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

      2. cancel-sign-sub 85.4%

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

      3. *-commutative 85.4%

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

      4. fmm-def 85.4%

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

      5. distribute-rgt-neg-in 85.4%

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

      6. remove-double-neg 85.4%

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

      7. *-commutative 85.4%

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

      8. *-commutative 85.4%

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

      9. *-commutative 85.4%

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

      10. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in a around -inf 72.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+57} \lor \neg \left(z \leq 1.05 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -5.8e+77)
     t_1
     (if (<= y -5.5e-56)
       (* b (* a i))
       (if (<= y 5.5e-233)
         (* c (* t j))
         (if (<= y 7.8e-22) (* 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 = x * (y * z);
	double tmp;
	if (y <= -5.8e+77) {
		tmp = t_1;
	} else if (y <= -5.5e-56) {
		tmp = b * (a * i);
	} else if (y <= 5.5e-233) {
		tmp = c * (t * j);
	} else if (y <= 7.8e-22) {
		tmp = 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) :: tmp
    t_1 = x * (y * z)
    if (y <= (-5.8d+77)) then
        tmp = t_1
    else if (y <= (-5.5d-56)) then
        tmp = b * (a * i)
    else if (y <= 5.5d-233) then
        tmp = c * (t * j)
    else if (y <= 7.8d-22) then
        tmp = 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 = x * (y * z);
	double tmp;
	if (y <= -5.8e+77) {
		tmp = t_1;
	} else if (y <= -5.5e-56) {
		tmp = b * (a * i);
	} else if (y <= 5.5e-233) {
		tmp = c * (t * j);
	} else if (y <= 7.8e-22) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -5.8e+77:
		tmp = t_1
	elif y <= -5.5e-56:
		tmp = b * (a * i)
	elif y <= 5.5e-233:
		tmp = c * (t * j)
	elif y <= 7.8e-22:
		tmp = z * (b * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -5.8e+77)
		tmp = t_1;
	elseif (y <= -5.5e-56)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 5.5e-233)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 7.8e-22)
		tmp = Float64(z * Float64(b * Float64(-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 = x * (y * z);
	tmp = 0.0;
	if (y <= -5.8e+77)
		tmp = t_1;
	elseif (y <= -5.5e-56)
		tmp = b * (a * i);
	elseif (y <= 5.5e-233)
		tmp = c * (t * j);
	elseif (y <= 7.8e-22)
		tmp = 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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+77], t$95$1, If[LessEqual[y, -5.5e-56], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-233], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-22], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8000000000000003e77 or 7.79999999999999996e-22 < y

   1. Initial program 66.1%

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

      1. +-commutative 66.1%

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

      2. fma-define 66.8%

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

      3. *-commutative 66.8%

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

      4. *-commutative 66.8%

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

      5. cancel-sign-sub-inv 66.8%

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

      6. cancel-sign-sub 66.8%

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

      7. fmm-def 67.6%

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

      8. distribute-rgt-neg-out 67.6%

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

      9. remove-double-neg 67.6%

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

      10. *-commutative 67.6%

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

      11. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in y around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in x around inf 42.5%

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

   9. Taylor expanded in y around 0 47.6%

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

   if -5.8000000000000003e77 < y < -5.4999999999999999e-56

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. fma-define 82.0%

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

      3. *-commutative 82.0%

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

      4. *-commutative 82.0%

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

      5. cancel-sign-sub-inv 82.0%

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

      6. cancel-sign-sub 82.0%

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

      7. fmm-def 82.0%

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

      8. distribute-rgt-neg-out 82.0%

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

      9. remove-double-neg 82.0%

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

      10. *-commutative 82.0%

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

      11. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*r* 75.6%

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

      4. *-commutative 75.6%

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

      5. associate-*l* 75.6%

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

      6. mul-1-neg 75.6%

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

      7. *-commutative 75.6%

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

      8. associate-*r* 75.6%

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

      9. *-commutative 75.6%

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

      10. distribute-rgt-neg-in 75.6%

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

      11. mul-1-neg 75.6%

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

      12. distribute-lft-in 75.6%

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

      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 b around inf 47.7%

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

      1. *-commutative 47.7%

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

   10. Simplified 47.7%

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

   11. Taylor expanded in a around inf 40.5%

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

       1. *-commutative 40.5%

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

   13. Simplified 40.5%

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

   if -5.4999999999999999e-56 < y < 5.50000000000000005e-233

   1. Initial program 83.0%

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

      1. +-commutative 83.0%

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

      2. fma-define 83.0%

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

      3. *-commutative 83.0%

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

      4. *-commutative 83.0%

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

      5. cancel-sign-sub-inv 83.0%

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

      6. cancel-sign-sub 83.0%

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

      7. fmm-def 83.0%

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

      8. distribute-rgt-neg-out 83.0%

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

      9. remove-double-neg 83.0%

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

      10. *-commutative 83.0%

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

      11. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in c around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in t around inf 34.4%

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

      1. *-commutative 34.4%

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

   10. Simplified 34.4%

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

   if 5.50000000000000005e-233 < y < 7.79999999999999996e-22

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. fma-define 88.4%

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

      3. *-commutative 88.4%

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

      4. *-commutative 88.4%

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

      5. cancel-sign-sub-inv 88.4%

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

      6. cancel-sign-sub 88.4%

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

      7. fmm-def 88.4%

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

      8. distribute-rgt-neg-out 88.4%

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

      9. remove-double-neg 88.4%

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

      10. *-commutative 88.4%

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

      11. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in c around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. *-commutative 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in t around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. *-commutative 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-*r* 44.2%

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

      5. distribute-rgt-neg-out 44.2%

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

   10. Simplified 44.2%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -2.2e+73)
     t_1
     (if (<= y -2.8e-49)
       (* b (* a i))
       (if (<= y 5.8e-170)
         (* c (* t j))
         (if (<= y 4e-22) (* c (* 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 = x * (y * z);
	double tmp;
	if (y <= -2.2e+73) {
		tmp = t_1;
	} else if (y <= -2.8e-49) {
		tmp = b * (a * i);
	} else if (y <= 5.8e-170) {
		tmp = c * (t * j);
	} else if (y <= 4e-22) {
		tmp = c * (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 = x * (y * z)
    if (y <= (-2.2d+73)) then
        tmp = t_1
    else if (y <= (-2.8d-49)) then
        tmp = b * (a * i)
    else if (y <= 5.8d-170) then
        tmp = c * (t * j)
    else if (y <= 4d-22) then
        tmp = c * (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 = x * (y * z);
	double tmp;
	if (y <= -2.2e+73) {
		tmp = t_1;
	} else if (y <= -2.8e-49) {
		tmp = b * (a * i);
	} else if (y <= 5.8e-170) {
		tmp = c * (t * j);
	} else if (y <= 4e-22) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -2.2e+73:
		tmp = t_1
	elif y <= -2.8e-49:
		tmp = b * (a * i)
	elif y <= 5.8e-170:
		tmp = c * (t * j)
	elif y <= 4e-22:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -2.2e+73)
		tmp = t_1;
	elseif (y <= -2.8e-49)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 5.8e-170)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 4e-22)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -2.2e+73)
		tmp = t_1;
	elseif (y <= -2.8e-49)
		tmp = b * (a * i);
	elseif (y <= 5.8e-170)
		tmp = c * (t * j);
	elseif (y <= 4e-22)
		tmp = c * (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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+73], t$95$1, If[LessEqual[y, -2.8e-49], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-170], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-22], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2e73 or 4.0000000000000002e-22 < y

   1. Initial program 66.1%

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

      1. +-commutative 66.1%

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

      2. fma-define 66.8%

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

      3. *-commutative 66.8%

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

      4. *-commutative 66.8%

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

      5. cancel-sign-sub-inv 66.8%

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

      6. cancel-sign-sub 66.8%

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

      7. fmm-def 67.6%

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

      8. distribute-rgt-neg-out 67.6%

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

      9. remove-double-neg 67.6%

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

      10. *-commutative 67.6%

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

      11. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in y around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in x around inf 42.5%

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

   9. Taylor expanded in y around 0 47.6%

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

   if -2.2e73 < y < -2.79999999999999997e-49

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. fma-define 82.0%

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

      3. *-commutative 82.0%

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

      4. *-commutative 82.0%

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

      5. cancel-sign-sub-inv 82.0%

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

      6. cancel-sign-sub 82.0%

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

      7. fmm-def 82.0%

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

      8. distribute-rgt-neg-out 82.0%

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

      9. remove-double-neg 82.0%

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

      10. *-commutative 82.0%

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

      11. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*r* 75.6%

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

      4. *-commutative 75.6%

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

      5. associate-*l* 75.6%

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

      6. mul-1-neg 75.6%

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

      7. *-commutative 75.6%

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

      8. associate-*r* 75.6%

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

      9. *-commutative 75.6%

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

      10. distribute-rgt-neg-in 75.6%

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

      11. mul-1-neg 75.6%

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

      12. distribute-lft-in 75.6%

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

      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 b around inf 47.7%

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

      1. *-commutative 47.7%

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

   10. Simplified 47.7%

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

   11. Taylor expanded in a around inf 40.5%

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

       1. *-commutative 40.5%

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

   13. Simplified 40.5%

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

   if -2.79999999999999997e-49 < y < 5.8000000000000001e-170

   1. Initial program 82.8%

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

      1. +-commutative 82.8%

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

      2. fma-define 82.8%

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

      3. *-commutative 82.8%

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

      4. *-commutative 82.8%

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

      5. cancel-sign-sub-inv 82.8%

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

      6. cancel-sign-sub 82.8%

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

      7. fmm-def 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 c around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. *-commutative 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in t around inf 32.3%

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

      1. *-commutative 32.3%

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

   10. Simplified 32.3%

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

   if 5.8000000000000001e-170 < y < 4.0000000000000002e-22

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-define 91.6%

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

      3. *-commutative 91.6%

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

      4. *-commutative 91.6%

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

      5. cancel-sign-sub-inv 91.6%

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

      6. cancel-sign-sub 91.6%

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

      7. fmm-def 91.6%

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

      8. distribute-rgt-neg-out 91.6%

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

      9. remove-double-neg 91.6%

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

      10. *-commutative 91.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 91.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 67.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 67.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 55.2%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. *-commutative 55.2%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

      3. distribute-rgt-neg-in 55.2%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   10. Simplified 55.2%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.55e-53)
     t_1
     (if (<= b -9.8e-207)
       (* c (* t j))
       (if (<= b 8.2e+72) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e-53) {
		tmp = t_1;
	} else if (b <= -9.8e-207) {
		tmp = c * (t * j);
	} else if (b <= 8.2e+72) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.55d-53)) then
        tmp = t_1
    else if (b <= (-9.8d-207)) then
        tmp = c * (t * j)
    else if (b <= 8.2d+72) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e-53) {
		tmp = t_1;
	} else if (b <= -9.8e-207) {
		tmp = c * (t * j);
	} else if (b <= 8.2e+72) {
		tmp = x * (y * z);
	} 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 <= -1.55e-53:
		tmp = t_1
	elif b <= -9.8e-207:
		tmp = c * (t * j)
	elif b <= 8.2e+72:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.55e-53)
		tmp = t_1;
	elseif (b <= -9.8e-207)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 8.2e+72)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.55e-53)
		tmp = t_1;
	elseif (b <= -9.8e-207)
		tmp = c * (t * j);
	elseif (b <= 8.2e+72)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e-53], t$95$1, If[LessEqual[b, -9.8e-207], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+72], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.55000000000000008e-53 or 8.19999999999999926e72 < b

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 77.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 77.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 77.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 77.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 77.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 68.9%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 67.3%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 67.3%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 68.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 68.2%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. *-commutative 68.2%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. associate-*r* 69.7%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 69.7%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 69.7%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 69.7%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 70.6%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 70.6%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 70.6%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 70.6%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 70.6%

          \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   8. Taylor expanded in b around inf 64.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -1.55000000000000008e-53 < b < -9.7999999999999999e-207

   1. Initial program 56.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 56.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 56.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 56.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 56.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 56.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.7%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 46.7%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 46.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 39.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 39.9%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -9.7999999999999999e-207 < b < 8.19999999999999926e72

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 79.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 79.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 58.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 58.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 58.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   7. Simplified 58.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   8. Taylor expanded in x around inf 35.3%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   9. Taylor expanded in y around 0 36.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+55} \lor \neg \left(j \leq 1.9 \cdot 10^{-40}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.1e+55) (not (<= j 1.9e-40)))
   (* j (- (* t c) (* y i)))
   (* b (- (* a i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.1e+55) || !(j <= 1.9e-40)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.1d+55)) .or. (.not. (j <= 1.9d-40))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.1e+55) || !(j <= 1.9e-40)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.1e+55) or not (j <= 1.9e-40):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.1e+55) || !(j <= 1.9e-40))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.1e+55) || ~((j <= 1.9e-40)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.1e+55], N[Not[LessEqual[j, 1.9e-40]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.10000000000000005e55 or 1.8999999999999999e-40 < j

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 65.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.8%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 65.8%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 65.8%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   if -1.10000000000000005e55 < j < 1.8999999999999999e-40

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 65.4%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 61.3%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 61.3%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 65.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 65.4%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. *-commutative 65.4%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. associate-*r* 68.7%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 68.7%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 68.7%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 68.7%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 69.5%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 69.5%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 69.5%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 69.5%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 69.5%

          \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   7. Simplified 69.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   8. Taylor expanded in b around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 46.1%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+55} \lor \neg \left(j \leq 1.9 \cdot 10^{-40}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{-47} \lor \neg \left(i \leq 1.05 \cdot 10^{+145}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -5.2e-47) (not (<= i 1.05e+145)))
   (* i (- (* a b) (* y j)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -5.2e-47) || !(i <= 1.05e+145)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-5.2d-47)) .or. (.not. (i <= 1.05d+145))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -5.2e-47) || !(i <= 1.05e+145)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -5.2e-47) or not (i <= 1.05e+145):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -5.2e-47) || !(i <= 1.05e+145))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -5.2e-47) || ~((i <= 1.05e+145)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -5.2e-47], N[Not[LessEqual[i, 1.05e+145]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.2e-47 or 1.04999999999999995e145 < i

   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 69.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 69.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 69.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 69.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 69.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 69.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in i around 0 69.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 69.4%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y - a \cdot b\right)} \]

      2. *-commutative 69.4%

         \[\leadsto -i \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right) \]

      3. distribute-rgt-neg-in 69.4%

         \[\leadsto \color{blue}{i \cdot \left(-\left(y \cdot j - a \cdot b\right)\right)} \]

      4. neg-sub0 69.4%

         \[\leadsto i \cdot \color{blue}{\left(0 - \left(y \cdot j - a \cdot b\right)\right)} \]

      5. associate--r- 69.4%

         \[\leadsto i \cdot \color{blue}{\left(\left(0 - y \cdot j\right) + a \cdot b\right)} \]

      6. neg-sub0 69.4%

         \[\leadsto i \cdot \left(\color{blue}{\left(-y \cdot j\right)} + a \cdot b\right) \]

      7. +-commutative 69.4%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + \left(-y \cdot j\right)\right)} \]

      8. unsub-neg 69.4%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      9. *-commutative 69.4%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

      10. *-commutative 69.4%

          \[\leadsto i \cdot \left(b \cdot a - \color{blue}{j \cdot y}\right) \]

   10. Simplified 69.4%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot a - j \cdot y\right)} \]

   if -5.2e-47 < i < 1.04999999999999995e145

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 79.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 79.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 79.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 45.4%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 45.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{-47} \lor \neg \left(i \leq 1.05 \cdot 10^{+145}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7600000 \lor \neg \left(z \leq 1.25 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -7600000.0) (not (<= z 1.25e+46))) (* x (* y z)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -7600000.0) || !(z <= 1.25e+46)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-7600000.0d0)) .or. (.not. (z <= 1.25d+46))) then
        tmp = x * (y * z)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -7600000.0) || !(z <= 1.25e+46)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -7600000.0) or not (z <= 1.25e+46):
		tmp = x * (y * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -7600000.0) || !(z <= 1.25e+46))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -7600000.0) || ~((z <= 1.25e+46)))
		tmp = x * (y * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -7600000.0], N[Not[LessEqual[z, 1.25e+46]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6e6 or 1.2500000000000001e46 < z

   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 63.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 64.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 64.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 64.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 56.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 56.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 56.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   7. Simplified 56.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   8. Taylor expanded in x around inf 45.1%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   9. Taylor expanded in y around 0 49.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -7.6e6 < z < 1.2500000000000001e46

   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 85.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 85.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 85.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 85.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 85.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 85.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 85.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 85.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 85.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 85.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 64.2%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 62.2%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 62.2%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 63.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 63.5%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. *-commutative 63.5%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. associate-*r* 66.8%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 66.8%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 66.8%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 66.8%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 68.2%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 68.2%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 68.2%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 68.2%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 68.2%

          \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   7. Simplified 68.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   8. Taylor expanded in b around inf 34.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 34.7%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   11. Taylor expanded in a around inf 28.6%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   12. Step-by-step derivation

       1. *-commutative 28.6%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   13. Simplified 28.6%

       \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600000 \lor \neg \left(z \leq 1.25 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+22} \lor \neg \left(b \leq 150000000000\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.4e+22) (not (<= b 150000000000.0)))
   (* b (* a i))
   (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.4e+22) || !(b <= 150000000000.0)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.4d+22)) .or. (.not. (b <= 150000000000.0d0))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.4e+22) || !(b <= 150000000000.0)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.4e+22) or not (b <= 150000000000.0):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.4e+22) || !(b <= 150000000000.0))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.4e+22) || ~((b <= 150000000000.0)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.4e+22], N[Not[LessEqual[b, 150000000000.0]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4e22 or 1.5e11 < b

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 79.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 79.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 64.1%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 64.1%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 64.1%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 64.1%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 64.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 64.1%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. *-commutative 64.1%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. associate-*r* 64.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 64.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 64.9%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 64.9%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 65.8%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 65.8%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 65.8%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 65.8%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 65.8%

          \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   7. Simplified 65.8%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   8. Taylor expanded in b around inf 64.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 64.3%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 64.3%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   11. Taylor expanded in a around inf 37.6%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   12. Step-by-step derivation

       1. *-commutative 37.6%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   13. Simplified 37.6%

       \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if -1.4e22 < b < 1.5e11

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 73.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 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 c around inf 35.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 35.8%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 35.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 29.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 29.2%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+22} \lor \neg \left(b \leq 150000000000\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 340000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.35e+22)
   (* b (* a i))
   (if (<= b 340000000.0) (* c (* t j)) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.35e+22) {
		tmp = b * (a * i);
	} else if (b <= 340000000.0) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.35d+22)) then
        tmp = b * (a * i)
    else if (b <= 340000000.0d0) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.35e+22) {
		tmp = b * (a * i);
	} else if (b <= 340000000.0) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.35e+22:
		tmp = b * (a * i)
	elif b <= 340000000.0:
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.35e+22)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 340000000.0)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.35e+22)
		tmp = b * (a * i);
	elseif (b <= 340000000.0)
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.35e+22], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 340000000.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3500000000000001e22

   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. Step-by-step derivation

      1. +-commutative 78.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 80.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 80.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 80.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 82.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 82.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 82.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 82.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 82.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 72.7%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 72.7%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 72.7%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 72.9%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 72.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. *-commutative 72.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. associate-*r* 72.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 72.9%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 72.9%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 72.9%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 72.9%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 72.9%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 72.9%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 72.9%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 72.9%

          \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   8. Taylor expanded in b around inf 67.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 67.0%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   11. Taylor expanded in a around inf 38.4%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   12. Step-by-step derivation

       1. *-commutative 38.4%

          \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   13. Simplified 38.4%

       \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if -1.3500000000000001e22 < b < 3.4e8

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 73.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 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 c around inf 35.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 35.8%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 35.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 29.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 29.2%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 3.4e8 < b

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 76.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 76.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 76.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 76.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 76.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 56.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 56.6%

         \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 56.7%

         \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. *-commutative 56.7%

         \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*l* 56.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. mul-1-neg 56.4%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. *-commutative 56.4%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. associate-*r* 58.0%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 58.0%

         \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. distribute-rgt-neg-in 58.0%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      11. mul-1-neg 58.0%

          \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      12. distribute-lft-in 59.7%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      13. mul-1-neg 59.7%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      14. unsub-neg 59.7%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      15. *-commutative 59.7%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      16. *-commutative 59.7%

          \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   8. Taylor expanded in b around inf 61.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 61.9%

       \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   11. Taylor expanded in a around inf 35.3%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   12. Step-by-step derivation

       1. *-commutative 35.3%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

       2. *-commutative 35.3%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

       3. associate-*r* 38.7%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   13. Simplified 38.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 340000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * 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 = b * (a * 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 b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 75.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-define 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 75.5%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 75.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. cancel-sign-sub-inv 75.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   6. cancel-sign-sub 75.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   7. fmm-def 75.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   8. distribute-rgt-neg-out 75.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   9. remove-double-neg 75.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   10. *-commutative 75.9%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

   11. *-commutative 75.9%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

3. Simplified 75.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 57.3%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
6. Step-by-step derivation

   1. +-commutative 57.3%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   2. *-commutative 57.3%

      \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   3. associate-*r* 56.4%

      \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   4. *-commutative 56.4%

      \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. associate-*l* 57.9%

      \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. mul-1-neg 57.9%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   7. *-commutative 57.9%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   8. associate-*r* 60.5%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   9. *-commutative 60.5%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   10. distribute-rgt-neg-in 60.5%

       \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   11. mul-1-neg 60.5%

       \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   12. distribute-lft-in 61.2%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   13. mul-1-neg 61.2%

       \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   14. unsub-neg 61.2%

       \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   15. *-commutative 61.2%

       \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   16. *-commutative 61.2%

       \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

7. Simplified 61.2%

   \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

8. Taylor expanded in b around inf 37.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
9. Step-by-step derivation

   1. *-commutative 37.8%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

10. Simplified 37.8%

    \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

11. Taylor expanded in a around inf 21.3%

    \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
12. Step-by-step derivation

    1. *-commutative 21.3%

       \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

13. Simplified 21.3%

    \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

14. Final simplification 21.3%

    \[\leadsto b \cdot \left(a \cdot i\right) \]
15. Add Preprocessing

Alternative 21: 22.1% 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 75.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 75.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-define 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 75.5%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 75.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. cancel-sign-sub-inv 75.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   6. cancel-sign-sub 75.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   7. fmm-def 75.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   8. distribute-rgt-neg-out 75.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   9. remove-double-neg 75.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   10. *-commutative 75.9%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

   11. *-commutative 75.9%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

3. Simplified 75.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 57.3%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
6. Step-by-step derivation

   1. +-commutative 57.3%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   2. *-commutative 57.3%

      \[\leadsto \left(\color{blue}{\left(j \cdot t\right) \cdot c} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   3. associate-*r* 56.4%

      \[\leadsto \left(\color{blue}{j \cdot \left(t \cdot c\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   4. *-commutative 56.4%

      \[\leadsto \left(\color{blue}{\left(t \cdot c\right) \cdot j} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. associate-*l* 57.9%

      \[\leadsto \left(\color{blue}{t \cdot \left(c \cdot j\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. mul-1-neg 57.9%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   7. *-commutative 57.9%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   8. associate-*r* 60.5%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-\color{blue}{t \cdot \left(x \cdot a\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   9. *-commutative 60.5%

      \[\leadsto \left(t \cdot \left(c \cdot j\right) + \left(-t \cdot \color{blue}{\left(a \cdot x\right)}\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   10. distribute-rgt-neg-in 60.5%

       \[\leadsto \left(t \cdot \left(c \cdot j\right) + \color{blue}{t \cdot \left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   11. mul-1-neg 60.5%

       \[\leadsto \left(t \cdot \left(c \cdot j\right) + t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   12. distribute-lft-in 61.2%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   13. mul-1-neg 61.2%

       \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   14. unsub-neg 61.2%

       \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   15. *-commutative 61.2%

       \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   16. *-commutative 61.2%

       \[\leadsto t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

7. Simplified 61.2%

   \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

8. Taylor expanded in i around inf 20.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
9. Add Preprocessing

Developer Target 1: 68.3% 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 2024163 
(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)))))