Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.9% → 82.4%

Time: 22.2s

Alternatives: 18

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.9%

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

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

   1. Initial program 0.0%

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

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 49.8%

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

4. Final simplification 80.5%

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

Alternative 2: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-60} \lor \neg \left(x \leq 1.6 \cdot 10^{-75}\right):\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= x -2.6e+190)
     t_1
     (if (or (<= x -4.2e-60) (not (<= x 1.6e-75)))
       (+ t_1 t_2)
       (- t_2 (* 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (x <= -2.6e+190) {
		tmp = t_1;
	} else if ((x <= -4.2e-60) || !(x <= 1.6e-75)) {
		tmp = t_1 + t_2;
	} else {
		tmp = t_2 - (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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (x <= (-2.6d+190)) then
        tmp = t_1
    else if ((x <= (-4.2d-60)) .or. (.not. (x <= 1.6d-75))) then
        tmp = t_1 + t_2
    else
        tmp = t_2 - (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 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (x <= -2.6e+190) {
		tmp = t_1;
	} else if ((x <= -4.2e-60) || !(x <= 1.6e-75)) {
		tmp = t_1 + t_2;
	} else {
		tmp = t_2 - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if x <= -2.6e+190:
		tmp = t_1
	elif (x <= -4.2e-60) or not (x <= 1.6e-75):
		tmp = t_1 + t_2
	else:
		tmp = t_2 - (b * ((z * c) - (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -2.6e+190)
		tmp = t_1;
	elseif ((x <= -4.2e-60) || !(x <= 1.6e-75))
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(t_2 - 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 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (x <= -2.6e+190)
		tmp = t_1;
	elseif ((x <= -4.2e-60) || ~((x <= 1.6e-75)))
		tmp = t_1 + t_2;
	else
		tmp = t_2 - (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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+190], t$95$1, If[Or[LessEqual[x, -4.2e-60], N[Not[LessEqual[x, 1.6e-75]], $MachinePrecision]], N[(t$95$1 + t$95$2), $MachinePrecision], N[(t$95$2 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.60000000000000011e190

   1. Initial program 62.2%

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

      1. sub-neg 62.2%

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

      2. associate-+l+ 62.2%

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

      3. fma-def 62.2%

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

      4. +-commutative 62.2%

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

      5. fma-def 69.1%

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

      6. sub-neg 69.1%

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

      7. +-commutative 69.1%

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

      8. *-commutative 69.1%

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

      9. distribute-rgt-neg-in 69.1%

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

      10. fma-def 69.1%

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

      11. *-commutative 69.1%

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

      12. distribute-rgt-neg-in 69.1%

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

      13. sub-neg 69.1%

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

      14. distribute-neg-in 69.1%

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

      15. unsub-neg 69.1%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around inf 83.2%

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

   if -2.60000000000000011e190 < x < -4.19999999999999982e-60 or 1.59999999999999988e-75 < x

   1. Initial program 78.8%

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

      1. cancel-sign-sub 78.8%

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

      2. cancel-sign-sub-inv 78.8%

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

      3. *-commutative 78.8%

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

      4. *-commutative 78.8%

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

      5. remove-double-neg 78.8%

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

      6. *-commutative 78.8%

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

      7. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in b around 0 73.4%

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

   if -4.19999999999999982e-60 < x < 1.59999999999999988e-75

   1. Initial program 60.1%

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

      1. cancel-sign-sub 60.1%

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

      2. cancel-sign-sub-inv 60.1%

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

      3. *-commutative 60.1%

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

      4. *-commutative 60.1%

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

      5. remove-double-neg 60.1%

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

      6. *-commutative 60.1%

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

      7. *-commutative 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in x around 0 68.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-60} \lor \neg \left(x \leq 1.6 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \]

Alternative 3: 30.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ t_3 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -9.2 \cdot 10^{+218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.55 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+246} \lor \neg \left(i \leq 1.2 \cdot 10^{+297}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))) (t_2 (* a (* b i))) (t_3 (* y (* i (- j)))))
   (if (<= i -9.2e+218)
     t_3
     (if (<= i -1.9e+112)
       t_2
       (if (<= i -1e+79)
         (* j (* t c))
         (if (<= i -9e-23)
           t_1
           (if (<= i -2.55e-123)
             (* z (* x y))
             (if (<= i 4.2e-276)
               t_1
               (if (<= i 5.4e-24)
                 (* y (* x z))
                 (if (or (<= i 1.65e+246) (not (<= i 1.2e+297)))
                   t_3
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double t_2 = a * (b * i);
	double t_3 = y * (i * -j);
	double tmp;
	if (i <= -9.2e+218) {
		tmp = t_3;
	} else if (i <= -1.9e+112) {
		tmp = t_2;
	} else if (i <= -1e+79) {
		tmp = j * (t * c);
	} else if (i <= -9e-23) {
		tmp = t_1;
	} else if (i <= -2.55e-123) {
		tmp = z * (x * y);
	} else if (i <= 4.2e-276) {
		tmp = t_1;
	} else if (i <= 5.4e-24) {
		tmp = y * (x * z);
	} else if ((i <= 1.65e+246) || !(i <= 1.2e+297)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (x * -t)
    t_2 = a * (b * i)
    t_3 = y * (i * -j)
    if (i <= (-9.2d+218)) then
        tmp = t_3
    else if (i <= (-1.9d+112)) then
        tmp = t_2
    else if (i <= (-1d+79)) then
        tmp = j * (t * c)
    else if (i <= (-9d-23)) then
        tmp = t_1
    else if (i <= (-2.55d-123)) then
        tmp = z * (x * y)
    else if (i <= 4.2d-276) then
        tmp = t_1
    else if (i <= 5.4d-24) then
        tmp = y * (x * z)
    else if ((i <= 1.65d+246) .or. (.not. (i <= 1.2d+297))) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double t_2 = a * (b * i);
	double t_3 = y * (i * -j);
	double tmp;
	if (i <= -9.2e+218) {
		tmp = t_3;
	} else if (i <= -1.9e+112) {
		tmp = t_2;
	} else if (i <= -1e+79) {
		tmp = j * (t * c);
	} else if (i <= -9e-23) {
		tmp = t_1;
	} else if (i <= -2.55e-123) {
		tmp = z * (x * y);
	} else if (i <= 4.2e-276) {
		tmp = t_1;
	} else if (i <= 5.4e-24) {
		tmp = y * (x * z);
	} else if ((i <= 1.65e+246) || !(i <= 1.2e+297)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	t_2 = a * (b * i)
	t_3 = y * (i * -j)
	tmp = 0
	if i <= -9.2e+218:
		tmp = t_3
	elif i <= -1.9e+112:
		tmp = t_2
	elif i <= -1e+79:
		tmp = j * (t * c)
	elif i <= -9e-23:
		tmp = t_1
	elif i <= -2.55e-123:
		tmp = z * (x * y)
	elif i <= 4.2e-276:
		tmp = t_1
	elif i <= 5.4e-24:
		tmp = y * (x * z)
	elif (i <= 1.65e+246) or not (i <= 1.2e+297):
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	t_2 = Float64(a * Float64(b * i))
	t_3 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (i <= -9.2e+218)
		tmp = t_3;
	elseif (i <= -1.9e+112)
		tmp = t_2;
	elseif (i <= -1e+79)
		tmp = Float64(j * Float64(t * c));
	elseif (i <= -9e-23)
		tmp = t_1;
	elseif (i <= -2.55e-123)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 4.2e-276)
		tmp = t_1;
	elseif (i <= 5.4e-24)
		tmp = Float64(y * Float64(x * z));
	elseif ((i <= 1.65e+246) || !(i <= 1.2e+297))
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	t_2 = a * (b * i);
	t_3 = y * (i * -j);
	tmp = 0.0;
	if (i <= -9.2e+218)
		tmp = t_3;
	elseif (i <= -1.9e+112)
		tmp = t_2;
	elseif (i <= -1e+79)
		tmp = j * (t * c);
	elseif (i <= -9e-23)
		tmp = t_1;
	elseif (i <= -2.55e-123)
		tmp = z * (x * y);
	elseif (i <= 4.2e-276)
		tmp = t_1;
	elseif (i <= 5.4e-24)
		tmp = y * (x * z);
	elseif ((i <= 1.65e+246) || ~((i <= 1.2e+297)))
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.2e+218], t$95$3, If[LessEqual[i, -1.9e+112], t$95$2, If[LessEqual[i, -1e+79], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9e-23], t$95$1, If[LessEqual[i, -2.55e-123], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e-276], t$95$1, If[LessEqual[i, 5.4e-24], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 1.65e+246], N[Not[LessEqual[i, 1.2e+297]], $MachinePrecision]], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.2000000000000004e218 or 5.40000000000000014e-24 < i < 1.65e246 or 1.20000000000000005e297 < i

   1. Initial program 66.9%

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

      1. sub-neg 66.9%

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

      2. associate-+l+ 66.9%

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

      3. fma-def 68.2%

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

      4. +-commutative 68.2%

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

      5. fma-def 68.2%

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

      6. sub-neg 68.2%

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

      7. +-commutative 68.2%

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

      8. *-commutative 68.2%

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

      9. distribute-rgt-neg-in 68.2%

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

      10. fma-def 69.5%

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

      11. *-commutative 69.5%

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

      12. distribute-rgt-neg-in 69.5%

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

      13. sub-neg 69.5%

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

      14. distribute-neg-in 69.5%

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

      15. unsub-neg 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in y around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. +-commutative 54.9%

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

      4. mul-1-neg 54.9%

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

      5. unsub-neg 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in z around 0 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-*r* 51.8%

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

      3. neg-mul-1 51.8%

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

   9. Simplified 51.8%

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

   if -9.2000000000000004e218 < i < -1.90000000000000004e112 or 1.65e246 < i < 1.20000000000000005e297

   1. Initial program 55.9%

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

      1. sub-neg 55.9%

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

      2. associate-+l+ 55.9%

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

      3. fma-def 55.9%

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

      4. +-commutative 55.9%

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

      5. fma-def 62.8%

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

      6. sub-neg 62.8%

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

      7. +-commutative 62.8%

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

      8. *-commutative 62.8%

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

      9. distribute-rgt-neg-in 62.8%

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

      10. fma-def 62.8%

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

      11. *-commutative 62.8%

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

      12. distribute-rgt-neg-in 62.8%

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

      13. sub-neg 62.8%

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

      14. distribute-neg-in 62.8%

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

      15. unsub-neg 62.8%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in b around -inf 52.7%

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

   if -1.90000000000000004e112 < i < -9.99999999999999967e78

   1. Initial program 62.5%

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

      1. sub-neg 62.5%

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

      2. associate-+l+ 62.5%

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

      3. fma-def 62.5%

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

      4. +-commutative 62.5%

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

      5. fma-def 62.5%

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

      6. sub-neg 62.5%

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

      7. +-commutative 62.5%

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

      8. *-commutative 62.5%

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

      9. distribute-rgt-neg-in 62.5%

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

      10. fma-def 62.5%

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

      11. *-commutative 62.5%

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

      12. distribute-rgt-neg-in 62.5%

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

      13. sub-neg 62.5%

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

      14. distribute-neg-in 62.5%

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

      15. unsub-neg 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in y around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. *-commutative 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in c around 0 87.5%

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

   8. Taylor expanded in c around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 63.1%

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

      3. *-commutative 63.1%

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

      4. associate-*r* 63.1%

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

   10. Simplified 63.1%

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

   if -9.99999999999999967e78 < i < -8.9999999999999995e-23 or -2.55000000000000005e-123 < i < 4.2e-276

   1. Initial program 72.8%

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

      1. sub-neg 72.8%

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

      2. associate-+l+ 72.8%

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

      3. fma-def 74.2%

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

      4. +-commutative 74.2%

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

      5. fma-def 75.5%

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

      6. sub-neg 75.5%

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

      7. +-commutative 75.5%

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

      8. *-commutative 75.5%

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

      9. distribute-rgt-neg-in 75.5%

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

      10. fma-def 75.5%

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

      11. *-commutative 75.5%

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

      12. distribute-rgt-neg-in 75.5%

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

      13. sub-neg 75.5%

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

      14. distribute-neg-in 75.5%

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

      15. unsub-neg 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in y around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in x around inf 41.1%

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

      1. associate-*r* 41.1%

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

      2. neg-mul-1 41.1%

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

   9. Simplified 41.1%

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

   if -8.9999999999999995e-23 < i < -2.55000000000000005e-123

   1. Initial program 78.6%

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

      1. cancel-sign-sub 78.6%

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

      2. cancel-sign-sub-inv 78.6%

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

      3. *-commutative 78.6%

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

      4. *-commutative 78.6%

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

      5. remove-double-neg 78.6%

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

      6. *-commutative 78.6%

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

      7. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 73.5%

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

   5. Taylor expanded in y around inf 51.7%

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

   if 4.2e-276 < i < 5.40000000000000014e-24

   1. Initial program 75.7%

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

      1. sub-neg 75.7%

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

      2. associate-+l+ 75.7%

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

      3. fma-def 75.7%

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

      4. +-commutative 75.7%

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

      5. fma-def 77.7%

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

      6. sub-neg 77.7%

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

      7. +-commutative 77.7%

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

      8. *-commutative 77.7%

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

      9. distribute-rgt-neg-in 77.7%

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

      10. fma-def 77.7%

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

      11. *-commutative 77.7%

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

      12. distribute-rgt-neg-in 77.7%

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

      13. sub-neg 77.7%

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

      14. distribute-neg-in 77.7%

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

      15. unsub-neg 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in y around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. *-commutative 48.0%

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

      3. +-commutative 48.0%

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

      4. mul-1-neg 48.0%

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

      5. unsub-neg 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in z around inf 41.0%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+218}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq -2.55 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-276}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+246} \lor \neg \left(i \leq 1.2 \cdot 10^{+297}\right):\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 4: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -2.4e+142)
     t_3
     (if (<= y -3.1e+122)
       t_2
       (if (<= y -6.6e+72)
         t_3
         (if (<= y -1.16e-220)
           t_1
           (if (<= y 6.2e-123)
             (* t (- (* c j) (* x a)))
             (if (<= y 1.04e-82) t_2 (if (<= y 4.1e+104) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.4e+142) {
		tmp = t_3;
	} else if (y <= -3.1e+122) {
		tmp = t_2;
	} else if (y <= -6.6e+72) {
		tmp = t_3;
	} else if (y <= -1.16e-220) {
		tmp = t_1;
	} else if (y <= 6.2e-123) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.04e-82) {
		tmp = t_2;
	} else if (y <= 4.1e+104) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-2.4d+142)) then
        tmp = t_3
    else if (y <= (-3.1d+122)) then
        tmp = t_2
    else if (y <= (-6.6d+72)) then
        tmp = t_3
    else if (y <= (-1.16d-220)) then
        tmp = t_1
    else if (y <= 6.2d-123) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.04d-82) then
        tmp = t_2
    else if (y <= 4.1d+104) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.4e+142) {
		tmp = t_3;
	} else if (y <= -3.1e+122) {
		tmp = t_2;
	} else if (y <= -6.6e+72) {
		tmp = t_3;
	} else if (y <= -1.16e-220) {
		tmp = t_1;
	} else if (y <= 6.2e-123) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.04e-82) {
		tmp = t_2;
	} else if (y <= 4.1e+104) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.4e+142:
		tmp = t_3
	elif y <= -3.1e+122:
		tmp = t_2
	elif y <= -6.6e+72:
		tmp = t_3
	elif y <= -1.16e-220:
		tmp = t_1
	elif y <= 6.2e-123:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.04e-82:
		tmp = t_2
	elif y <= 4.1e+104:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.4e+142)
		tmp = t_3;
	elseif (y <= -3.1e+122)
		tmp = t_2;
	elseif (y <= -6.6e+72)
		tmp = t_3;
	elseif (y <= -1.16e-220)
		tmp = t_1;
	elseif (y <= 6.2e-123)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.04e-82)
		tmp = t_2;
	elseif (y <= 4.1e+104)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.4e+142)
		tmp = t_3;
	elseif (y <= -3.1e+122)
		tmp = t_2;
	elseif (y <= -6.6e+72)
		tmp = t_3;
	elseif (y <= -1.16e-220)
		tmp = t_1;
	elseif (y <= 6.2e-123)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.04e-82)
		tmp = t_2;
	elseif (y <= 4.1e+104)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+142], t$95$3, If[LessEqual[y, -3.1e+122], t$95$2, If[LessEqual[y, -6.6e+72], t$95$3, If[LessEqual[y, -1.16e-220], t$95$1, If[LessEqual[y, 6.2e-123], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.04e-82], t$95$2, If[LessEqual[y, 4.1e+104], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3999999999999999e142 or -3.09999999999999999e122 < y < -6.6e72 or 4.09999999999999985e104 < y

   1. Initial program 56.1%

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

      1. sub-neg 56.1%

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

      2. associate-+l+ 56.1%

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

      3. fma-def 57.2%

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

      4. +-commutative 57.2%

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

      5. fma-def 58.3%

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

      6. sub-neg 58.3%

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

      7. +-commutative 58.3%

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

      8. *-commutative 58.3%

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

      9. distribute-rgt-neg-in 58.3%

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

      10. fma-def 58.3%

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

      11. *-commutative 58.3%

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

      12. distribute-rgt-neg-in 58.3%

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

      13. sub-neg 58.3%

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

      14. distribute-neg-in 58.3%

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

      15. unsub-neg 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in y around inf 78.2%

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

      1. +-commutative 78.2%

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

      2. *-commutative 78.2%

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

      3. +-commutative 78.2%

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

      4. mul-1-neg 78.2%

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

      5. unsub-neg 78.2%

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

   6. Simplified 78.2%

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

   if -2.3999999999999999e142 < y < -3.09999999999999999e122 or 6.19999999999999996e-123 < y < 1.04000000000000004e-82

   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. cancel-sign-sub 82.9%

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

      2. cancel-sign-sub-inv 82.9%

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

      3. *-commutative 82.9%

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

      4. *-commutative 82.9%

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

      5. remove-double-neg 82.9%

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

      6. *-commutative 82.9%

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

      7. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in c around inf 80.0%

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

   if -6.6e72 < y < -1.15999999999999998e-220 or 1.04000000000000004e-82 < y < 4.09999999999999985e104

   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. sub-neg 77.2%

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

      2. associate-+l+ 77.2%

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

      3. fma-def 77.2%

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

      4. +-commutative 77.2%

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

      5. fma-def 80.2%

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

      6. sub-neg 80.2%

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

      7. +-commutative 80.2%

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

      8. *-commutative 80.2%

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

      9. distribute-rgt-neg-in 80.2%

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

      10. fma-def 81.2%

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

      11. *-commutative 81.2%

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

      12. distribute-rgt-neg-in 81.2%

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

      13. sub-neg 81.2%

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

      14. distribute-neg-in 81.2%

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

      15. unsub-neg 81.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in a around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   6. Simplified 58.8%

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

   if -1.15999999999999998e-220 < y < 6.19999999999999996e-123

   1. Initial program 75.3%

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

      1. sub-neg 75.3%

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

      2. associate-+l+ 75.3%

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

      3. fma-def 77.3%

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

      4. +-commutative 77.3%

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

      5. fma-def 77.3%

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

      6. sub-neg 77.3%

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

      7. +-commutative 77.3%

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

      8. *-commutative 77.3%

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

      9. distribute-rgt-neg-in 77.3%

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

      10. fma-def 77.3%

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

      11. *-commutative 77.3%

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

      12. distribute-rgt-neg-in 77.3%

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

      13. sub-neg 77.3%

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

      14. distribute-neg-in 77.3%

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

      15. unsub-neg 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in y around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in t around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

   9. Simplified 58.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-220}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 5: 59.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.3 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (* t c))))
        (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -4.3e+46)
     t_2
     (if (<= i 1.55e-183)
       t_1
       (if (<= i 4.9e-135)
         (* c (- (* t j) (* z b)))
         (if (<= i 8e+105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * (t * c));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -4.3e+46) {
		tmp = t_2;
	} else if (i <= 1.55e-183) {
		tmp = t_1;
	} else if (i <= 4.9e-135) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 8e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * (t * c))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-4.3d+46)) then
        tmp = t_2
    else if (i <= 1.55d-183) then
        tmp = t_1
    else if (i <= 4.9d-135) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 8d+105) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * (t * c));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -4.3e+46) {
		tmp = t_2;
	} else if (i <= 1.55e-183) {
		tmp = t_1;
	} else if (i <= 4.9e-135) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 8e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * (t * c))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -4.3e+46:
		tmp = t_2
	elif i <= 1.55e-183:
		tmp = t_1
	elif i <= 4.9e-135:
		tmp = c * ((t * j) - (z * b))
	elif i <= 8e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(t * c)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.3e+46)
		tmp = t_2;
	elseif (i <= 1.55e-183)
		tmp = t_1;
	elseif (i <= 4.9e-135)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 8e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * (t * c));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.3e+46)
		tmp = t_2;
	elseif (i <= 1.55e-183)
		tmp = t_1;
	elseif (i <= 4.9e-135)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 8e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.3e+46], t$95$2, If[LessEqual[i, 1.55e-183], t$95$1, If[LessEqual[i, 4.9e-135], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.30000000000000005e46 or 7.9999999999999995e105 < i

   1. Initial program 57.6%

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

      1. sub-neg 57.6%

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

      2. associate-+l+ 57.6%

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

      3. fma-def 58.7%

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

      4. +-commutative 58.7%

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

      5. fma-def 62.1%

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

      6. sub-neg 62.1%

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

      7. +-commutative 62.1%

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

      8. *-commutative 62.1%

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

      9. distribute-rgt-neg-in 62.1%

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

      10. fma-def 63.2%

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

      11. *-commutative 63.2%

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

      12. distribute-rgt-neg-in 63.2%

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

      13. sub-neg 63.2%

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

      14. distribute-neg-in 63.2%

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

      15. unsub-neg 63.2%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in i around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. unsub-neg 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

   6. Simplified 69.8%

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

   if -4.30000000000000005e46 < i < 1.55e-183 or 4.9000000000000003e-135 < i < 7.9999999999999995e105

   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 77.0%

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

      2. cancel-sign-sub-inv 77.0%

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

      3. *-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. remove-double-neg 77.0%

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

      6. *-commutative 77.0%

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

      7. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in b around 0 67.4%

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

   5. Taylor expanded in c around inf 60.5%

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

      1. associate-*r* 61.7%

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

      2. *-commutative 61.7%

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

   7. Simplified 61.7%

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

   if 1.55e-183 < i < 4.9000000000000003e-135

   1. Initial program 56.9%

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

      1. cancel-sign-sub 56.9%

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

      2. cancel-sign-sub-inv 56.9%

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

      3. *-commutative 56.9%

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

      4. *-commutative 56.9%

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

      5. remove-double-neg 56.9%

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

      6. *-commutative 56.9%

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

      7. *-commutative 56.9%

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

   3. Simplified 56.9%

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

   4. Taylor expanded in c around inf 86.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.3 \cdot 10^{+46}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 6: 61.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.35 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.35e+184)
   (* t (- (* c j) (* x a)))
   (if (<= c 4.2e+63)
     (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
     (* 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 (c <= -3.35e+184) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 4.2e+63) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} 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 (c <= (-3.35d+184)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 4.2d+63) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    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 (c <= -3.35e+184) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 4.2e+63) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.35e+184:
		tmp = t * ((c * j) - (x * a))
	elif c <= 4.2e+63:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	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 (c <= -3.35e+184)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 4.2e+63)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	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 (c <= -3.35e+184)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 4.2e+63)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.35e+184], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e+63], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.35e184

   1. Initial program 61.7%

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

      1. sub-neg 61.7%

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

      2. associate-+l+ 61.7%

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

      3. fma-def 64.6%

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

      4. +-commutative 64.6%

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

      5. fma-def 67.6%

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

      6. sub-neg 67.6%

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

      7. +-commutative 67.6%

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

      8. *-commutative 67.6%

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

      9. distribute-rgt-neg-in 67.6%

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

      10. fma-def 67.6%

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

      11. *-commutative 67.6%

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

      12. distribute-rgt-neg-in 67.6%

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

      13. sub-neg 67.6%

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

      14. distribute-neg-in 67.6%

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

      15. unsub-neg 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in y around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. *-commutative 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

   6. Simplified 70.5%

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

   7. Taylor expanded in t around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

   9. Simplified 68.6%

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

   if -3.35e184 < c < 4.2000000000000004e63

   1. Initial program 73.0%

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

      1. cancel-sign-sub 73.0%

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

      2. cancel-sign-sub-inv 73.0%

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

      3. *-commutative 73.0%

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

      4. *-commutative 73.0%

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

      5. remove-double-neg 73.0%

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

      6. *-commutative 73.0%

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

      7. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in b around 0 66.5%

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

   if 4.2000000000000004e63 < c

   1. Initial program 62.4%

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

      1. cancel-sign-sub 62.4%

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

      2. cancel-sign-sub-inv 62.4%

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

      3. *-commutative 62.4%

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

      4. *-commutative 62.4%

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

      5. remove-double-neg 62.4%

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

      6. *-commutative 62.4%

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

      7. *-commutative 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in c around inf 74.5%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.35 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 0.006:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.55e+36)
     t_2
     (if (<= a -3.3e-71)
       t_1
       (if (<= a -2.55e-135)
         (* y (* x z))
         (if (<= a 1e-236)
           t_1
           (if (<= a 1.15e-142) (* z (* x y)) (if (<= a 0.006) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.55e+36) {
		tmp = t_2;
	} else if (a <= -3.3e-71) {
		tmp = t_1;
	} else if (a <= -2.55e-135) {
		tmp = y * (x * z);
	} else if (a <= 1e-236) {
		tmp = t_1;
	} else if (a <= 1.15e-142) {
		tmp = z * (x * y);
	} else if (a <= 0.006) {
		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 = a * ((b * i) - (x * t))
    if (a <= (-1.55d+36)) then
        tmp = t_2
    else if (a <= (-3.3d-71)) then
        tmp = t_1
    else if (a <= (-2.55d-135)) then
        tmp = y * (x * z)
    else if (a <= 1d-236) then
        tmp = t_1
    else if (a <= 1.15d-142) then
        tmp = z * (x * y)
    else if (a <= 0.006d0) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.55e+36) {
		tmp = t_2;
	} else if (a <= -3.3e-71) {
		tmp = t_1;
	} else if (a <= -2.55e-135) {
		tmp = y * (x * z);
	} else if (a <= 1e-236) {
		tmp = t_1;
	} else if (a <= 1.15e-142) {
		tmp = z * (x * y);
	} else if (a <= 0.006) {
		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 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.55e+36:
		tmp = t_2
	elif a <= -3.3e-71:
		tmp = t_1
	elif a <= -2.55e-135:
		tmp = y * (x * z)
	elif a <= 1e-236:
		tmp = t_1
	elif a <= 1.15e-142:
		tmp = z * (x * y)
	elif a <= 0.006:
		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(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.55e+36)
		tmp = t_2;
	elseif (a <= -3.3e-71)
		tmp = t_1;
	elseif (a <= -2.55e-135)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1e-236)
		tmp = t_1;
	elseif (a <= 1.15e-142)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 0.006)
		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 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.55e+36)
		tmp = t_2;
	elseif (a <= -3.3e-71)
		tmp = t_1;
	elseif (a <= -2.55e-135)
		tmp = y * (x * z);
	elseif (a <= 1e-236)
		tmp = t_1;
	elseif (a <= 1.15e-142)
		tmp = z * (x * y);
	elseif (a <= 0.006)
		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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+36], t$95$2, If[LessEqual[a, -3.3e-71], t$95$1, If[LessEqual[a, -2.55e-135], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-236], t$95$1, If[LessEqual[a, 1.15e-142], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.006], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e36 or 0.0060000000000000001 < a

   1. Initial program 60.6%

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

      1. sub-neg 60.6%

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

      2. associate-+l+ 60.6%

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

      3. fma-def 62.3%

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

      4. +-commutative 62.3%

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

      5. fma-def 63.9%

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

      6. sub-neg 63.9%

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

      7. +-commutative 63.9%

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

      8. *-commutative 63.9%

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

      9. distribute-rgt-neg-in 63.9%

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

      10. fma-def 63.9%

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

      11. *-commutative 63.9%

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

      12. distribute-rgt-neg-in 63.9%

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

      13. sub-neg 63.9%

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

      14. distribute-neg-in 63.9%

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

      15. unsub-neg 63.9%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   if -1.55e36 < a < -3.3000000000000002e-71 or -2.5500000000000001e-135 < a < 1e-236 or 1.15000000000000001e-142 < a < 0.0060000000000000001

   1. Initial program 80.1%

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

      1. cancel-sign-sub 80.1%

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

      2. cancel-sign-sub-inv 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. remove-double-neg 80.1%

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

      6. *-commutative 80.1%

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

      7. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in c around inf 47.0%

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

   if -3.3000000000000002e-71 < a < -2.5500000000000001e-135

   1. Initial program 71.6%

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

      1. sub-neg 71.6%

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

      2. associate-+l+ 71.6%

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

      3. fma-def 71.6%

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

      4. +-commutative 71.6%

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

      5. fma-def 71.6%

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

      6. sub-neg 71.6%

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

      7. +-commutative 71.6%

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

      8. *-commutative 71.6%

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

      9. distribute-rgt-neg-in 71.6%

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

      10. fma-def 71.6%

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

      11. *-commutative 71.6%

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

      12. distribute-rgt-neg-in 71.6%

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

      13. sub-neg 71.6%

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

      14. distribute-neg-in 71.6%

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

      15. unsub-neg 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in y around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. +-commutative 80.3%

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

      4. mul-1-neg 80.3%

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

      5. unsub-neg 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in z around inf 56.5%

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

   if 1e-236 < a < 1.15000000000000001e-142

   1. Initial program 74.1%

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

      1. cancel-sign-sub 74.1%

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

      2. cancel-sign-sub-inv 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. remove-double-neg 74.1%

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

      6. *-commutative 74.1%

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

      7. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around inf 61.3%

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

   5. Taylor expanded in y around inf 52.5%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{-236}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 0.006:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 8: 47.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.3e-15)
   (* t (- (* c j) (* x a)))
   (if (<= c -1.3e-119)
     (* i (- (* a b) (* y j)))
     (if (<= c -7.5e-177)
       (* y (* x z))
       (if (<= c 3.8e+75)
         (* a (- (* b i) (* x t)))
         (* 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 (c <= -3.3e-15) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -1.3e-119) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -7.5e-177) {
		tmp = y * (x * z);
	} else if (c <= 3.8e+75) {
		tmp = a * ((b * i) - (x * t));
	} 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 (c <= (-3.3d-15)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-1.3d-119)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= (-7.5d-177)) then
        tmp = y * (x * z)
    else if (c <= 3.8d+75) then
        tmp = a * ((b * i) - (x * t))
    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 (c <= -3.3e-15) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -1.3e-119) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -7.5e-177) {
		tmp = y * (x * z);
	} else if (c <= 3.8e+75) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.3e-15:
		tmp = t * ((c * j) - (x * a))
	elif c <= -1.3e-119:
		tmp = i * ((a * b) - (y * j))
	elif c <= -7.5e-177:
		tmp = y * (x * z)
	elif c <= 3.8e+75:
		tmp = a * ((b * i) - (x * t))
	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 (c <= -3.3e-15)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -1.3e-119)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= -7.5e-177)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 3.8e+75)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	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 (c <= -3.3e-15)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -1.3e-119)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= -7.5e-177)
		tmp = y * (x * z);
	elseif (c <= 3.8e+75)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.3e-15], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-119], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.5e-177], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e+75], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.3e-15

   1. Initial program 60.1%

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

      1. sub-neg 60.1%

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

      2. associate-+l+ 60.1%

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

      3. fma-def 63.2%

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

      4. +-commutative 63.2%

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

      5. fma-def 64.8%

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

      6. sub-neg 64.8%

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

      7. +-commutative 64.8%

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

      8. *-commutative 64.8%

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

      9. distribute-rgt-neg-in 64.8%

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

      10. fma-def 64.8%

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

      11. *-commutative 64.8%

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

      12. distribute-rgt-neg-in 64.8%

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

      13. sub-neg 64.8%

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

      14. distribute-neg-in 64.8%

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

      15. unsub-neg 64.8%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in y around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in t around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

   9. Simplified 59.7%

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

   if -3.3e-15 < c < -1.30000000000000006e-119

   1. Initial program 80.3%

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

      1. sub-neg 80.3%

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

      2. associate-+l+ 80.3%

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

      3. fma-def 80.3%

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

      4. +-commutative 80.3%

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

      5. fma-def 83.2%

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

      6. sub-neg 83.2%

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

      7. +-commutative 83.2%

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

      8. *-commutative 83.2%

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

      9. distribute-rgt-neg-in 83.2%

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

      10. fma-def 83.2%

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

      11. *-commutative 83.2%

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

      12. distribute-rgt-neg-in 83.2%

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

      13. sub-neg 83.2%

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

      14. distribute-neg-in 83.2%

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

      15. unsub-neg 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in i around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. unsub-neg 49.4%

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

      3. *-commutative 49.4%

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

      4. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if -1.30000000000000006e-119 < c < -7.5e-177

   1. Initial program 66.0%

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

      1. sub-neg 66.0%

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

      2. associate-+l+ 66.0%

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

      3. fma-def 66.0%

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

      4. +-commutative 66.0%

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

      5. fma-def 66.0%

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

      6. sub-neg 66.0%

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

      7. +-commutative 66.0%

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

      8. *-commutative 66.0%

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

      9. distribute-rgt-neg-in 66.0%

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

      10. fma-def 66.0%

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

      11. *-commutative 66.0%

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

      12. distribute-rgt-neg-in 66.0%

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

      13. sub-neg 66.0%

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

      14. distribute-neg-in 66.0%

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

      15. unsub-neg 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in y around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. +-commutative 64.2%

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

      4. mul-1-neg 64.2%

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

      5. unsub-neg 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in z around inf 57.2%

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

   if -7.5e-177 < c < 3.8000000000000002e75

   1. Initial program 74.5%

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

      1. sub-neg 74.5%

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

      2. associate-+l+ 74.5%

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

      3. fma-def 74.5%

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

      4. +-commutative 74.5%

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

      5. fma-def 76.4%

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

      6. sub-neg 76.4%

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

      7. +-commutative 76.4%

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

      8. *-commutative 76.4%

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

      9. distribute-rgt-neg-in 76.4%

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

      10. fma-def 76.4%

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

      11. *-commutative 76.4%

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

      12. distribute-rgt-neg-in 76.4%

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

      13. sub-neg 76.4%

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

      14. distribute-neg-in 76.4%

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

      15. unsub-neg 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in a around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

      4. *-commutative 47.7%

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

   6. Simplified 47.7%

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

   if 3.8000000000000002e75 < c

   1. Initial program 65.5%

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

      1. cancel-sign-sub 65.5%

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

      2. cancel-sign-sub-inv 65.5%

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

      3. *-commutative 65.5%

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

      4. *-commutative 65.5%

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

      5. remove-double-neg 65.5%

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

      6. *-commutative 65.5%

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

      7. *-commutative 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in c around inf 78.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 9: 41.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+256}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.9e+256)
   (* i (* y (- j)))
   (if (<= y -5e+74)
     (* y (* x z))
     (if (<= y 6.2e+107) (* a (- (* b i) (* x t))) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.9e+256) {
		tmp = i * (y * -j);
	} else if (y <= -5e+74) {
		tmp = y * (x * z);
	} else if (y <= 6.2e+107) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.9d+256)) then
        tmp = i * (y * -j)
    else if (y <= (-5d+74)) then
        tmp = y * (x * z)
    else if (y <= 6.2d+107) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.9e+256) {
		tmp = i * (y * -j);
	} else if (y <= -5e+74) {
		tmp = y * (x * z);
	} else if (y <= 6.2e+107) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.9e+256:
		tmp = i * (y * -j)
	elif y <= -5e+74:
		tmp = y * (x * z)
	elif y <= 6.2e+107:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.9e+256)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -5e+74)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 6.2e+107)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.9e+256)
		tmp = i * (y * -j);
	elseif (y <= -5e+74)
		tmp = y * (x * z);
	elseif (y <= 6.2e+107)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.9e+256], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e+74], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+107], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9000000000000001e256

   1. Initial program 59.8%

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

      1. sub-neg 59.8%

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

      2. associate-+l+ 59.8%

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

      3. fma-def 59.8%

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

      4. +-commutative 59.8%

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

      5. fma-def 59.8%

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

      6. sub-neg 59.8%

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

      7. +-commutative 59.8%

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

      8. *-commutative 59.8%

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

      9. distribute-rgt-neg-in 59.8%

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

      10. fma-def 59.8%

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

      11. *-commutative 59.8%

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

      12. distribute-rgt-neg-in 59.8%

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

      13. sub-neg 59.8%

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

      14. distribute-neg-in 59.8%

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

      15. unsub-neg 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around inf 79.9%

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

      1. associate-*r* 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-*r* 80.0%

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

      4. associate-*r* 80.0%

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

      5. neg-mul-1 80.0%

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

      6. *-commutative 80.0%

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

   9. Simplified 80.0%

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

   if -1.9000000000000001e256 < y < -4.99999999999999963e74

   1. Initial program 66.2%

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

      1. sub-neg 66.2%

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

      2. associate-+l+ 66.2%

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

      3. fma-def 66.2%

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

      4. +-commutative 66.2%

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

      5. fma-def 66.2%

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

      6. sub-neg 66.2%

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

      7. +-commutative 66.2%

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

      8. *-commutative 66.2%

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

      9. distribute-rgt-neg-in 66.2%

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

      10. fma-def 66.2%

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

      11. *-commutative 66.2%

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

      12. distribute-rgt-neg-in 66.2%

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

      13. sub-neg 66.2%

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

      14. distribute-neg-in 66.2%

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

      15. unsub-neg 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in y around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. +-commutative 71.8%

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

      4. mul-1-neg 71.8%

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

      5. unsub-neg 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in z around inf 44.9%

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

   if -4.99999999999999963e74 < y < 6.20000000000000052e107

   1. Initial program 77.9%

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

      1. sub-neg 77.9%

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

      2. associate-+l+ 77.9%

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

      3. fma-def 78.5%

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

      4. +-commutative 78.5%

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

      5. fma-def 80.4%

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

      6. sub-neg 80.4%

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

      7. +-commutative 80.4%

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

      8. *-commutative 80.4%

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

      9. distribute-rgt-neg-in 80.4%

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

      10. fma-def 81.0%

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

      11. *-commutative 81.0%

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

      12. distribute-rgt-neg-in 81.0%

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

      13. sub-neg 81.0%

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

      14. distribute-neg-in 81.0%

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

      15. unsub-neg 81.0%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in a around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   6. Simplified 50.6%

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

   if 6.20000000000000052e107 < y

   1. Initial program 49.2%

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

      1. sub-neg 49.2%

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

      2. associate-+l+ 49.2%

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

      3. fma-def 51.2%

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

      4. +-commutative 51.2%

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

      5. fma-def 53.1%

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

      6. sub-neg 53.1%

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

      7. +-commutative 53.1%

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

      8. *-commutative 53.1%

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

      9. distribute-rgt-neg-in 53.1%

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

      10. fma-def 53.1%

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

      11. *-commutative 53.1%

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

      12. distribute-rgt-neg-in 53.1%

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

      13. sub-neg 53.1%

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

      14. distribute-neg-in 53.1%

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

      15. unsub-neg 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in x around inf 50.5%

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

   5. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

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

   7. Simplified 44.7%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+256}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 29.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -5.6e-55)
   (* c (* t j))
   (if (<= c -2.8e-272)
     (* y (* x z))
     (if (<= c 3.2e-252)
       (* y (* i (- j)))
       (if (<= c 1.15e+77) (* x (* y z)) (* c (* 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 (c <= -5.6e-55) {
		tmp = c * (t * j);
	} else if (c <= -2.8e-272) {
		tmp = y * (x * z);
	} else if (c <= 3.2e-252) {
		tmp = y * (i * -j);
	} else if (c <= 1.15e+77) {
		tmp = x * (y * z);
	} else {
		tmp = c * (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 (c <= (-5.6d-55)) then
        tmp = c * (t * j)
    else if (c <= (-2.8d-272)) then
        tmp = y * (x * z)
    else if (c <= 3.2d-252) then
        tmp = y * (i * -j)
    else if (c <= 1.15d+77) then
        tmp = x * (y * z)
    else
        tmp = c * (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 (c <= -5.6e-55) {
		tmp = c * (t * j);
	} else if (c <= -2.8e-272) {
		tmp = y * (x * z);
	} else if (c <= 3.2e-252) {
		tmp = y * (i * -j);
	} else if (c <= 1.15e+77) {
		tmp = x * (y * z);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.6e-55:
		tmp = c * (t * j)
	elif c <= -2.8e-272:
		tmp = y * (x * z)
	elif c <= 3.2e-252:
		tmp = y * (i * -j)
	elif c <= 1.15e+77:
		tmp = x * (y * z)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.6e-55)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= -2.8e-272)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 3.2e-252)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 1.15e+77)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.6e-55)
		tmp = c * (t * j);
	elseif (c <= -2.8e-272)
		tmp = y * (x * z);
	elseif (c <= 3.2e-252)
		tmp = y * (i * -j);
	elseif (c <= 1.15e+77)
		tmp = x * (y * z);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -5.6e-55], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.8e-272], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-252], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e+77], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.59999999999999968e-55

   1. Initial program 62.3%

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

      1. sub-neg 62.3%

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

      2. associate-+l+ 62.3%

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

      3. fma-def 65.0%

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

      4. +-commutative 65.0%

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

      5. fma-def 66.3%

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

      6. sub-neg 66.3%

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

      7. +-commutative 66.3%

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

      8. *-commutative 66.3%

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

      9. distribute-rgt-neg-in 66.3%

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

      10. fma-def 66.3%

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

      11. *-commutative 66.3%

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

      12. distribute-rgt-neg-in 66.3%

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

      13. sub-neg 66.3%

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

      14. distribute-neg-in 66.3%

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

      15. unsub-neg 66.3%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in y around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-commutative 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

   6. Simplified 68.2%

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

   7. Taylor expanded in c around 0 63.0%

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

   8. Taylor expanded in c around inf 36.8%

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

   if -5.59999999999999968e-55 < c < -2.79999999999999994e-272

   1. Initial program 75.4%

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

      1. sub-neg 75.4%

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

      2. associate-+l+ 75.4%

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

      3. fma-def 75.4%

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

      4. +-commutative 75.4%

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

      5. fma-def 77.2%

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

      6. sub-neg 77.2%

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

      7. +-commutative 77.2%

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

      8. *-commutative 77.2%

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

      9. distribute-rgt-neg-in 77.2%

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

      10. fma-def 77.2%

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

      11. *-commutative 77.2%

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

      12. distribute-rgt-neg-in 77.2%

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

      13. sub-neg 77.2%

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

      14. distribute-neg-in 77.2%

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

      15. unsub-neg 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in y around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. *-commutative 60.5%

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

      3. +-commutative 60.5%

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

      4. mul-1-neg 60.5%

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

      5. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in z around inf 38.0%

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

   if -2.79999999999999994e-272 < c < 3.2000000000000002e-252

   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. sub-neg 90.7%

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

      2. associate-+l+ 90.7%

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

      3. fma-def 90.6%

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

      4. +-commutative 90.6%

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

      5. fma-def 90.6%

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

      6. sub-neg 90.6%

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

      7. +-commutative 90.6%

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

      8. *-commutative 90.6%

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

      9. distribute-rgt-neg-in 90.6%

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

      10. fma-def 90.6%

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

      11. *-commutative 90.6%

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

      12. distribute-rgt-neg-in 90.6%

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

      13. sub-neg 90.6%

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

      14. distribute-neg-in 90.6%

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

      15. unsub-neg 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. +-commutative 57.6%

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

      4. mul-1-neg 57.6%

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

      5. unsub-neg 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in z around 0 46.3%

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

      1. *-commutative 46.3%

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

      2. associate-*r* 46.3%

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

      3. neg-mul-1 46.3%

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

   9. Simplified 46.3%

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

   if 3.2000000000000002e-252 < c < 1.14999999999999997e77

   1. Initial program 69.4%

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

      1. sub-neg 69.4%

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

      2. associate-+l+ 69.4%

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

      3. fma-def 69.4%

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

      4. +-commutative 69.4%

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

      5. fma-def 72.5%

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

      6. sub-neg 72.5%

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

      7. +-commutative 72.5%

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

      8. *-commutative 72.5%

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

      9. distribute-rgt-neg-in 72.5%

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

      10. fma-def 72.5%

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

      11. *-commutative 72.5%

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

      12. distribute-rgt-neg-in 72.5%

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

      13. sub-neg 72.5%

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

      14. distribute-neg-in 72.5%

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

      15. unsub-neg 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around inf 52.9%

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

   5. Taylor expanded in y around inf 33.6%

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

      1. *-commutative 33.6%

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

   7. Simplified 33.6%

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

   if 1.14999999999999997e77 < c

   1. Initial program 64.6%

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

      1. sub-neg 64.6%

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

      2. associate-+l+ 64.6%

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

      3. fma-def 64.6%

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

      4. +-commutative 64.6%

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

      5. fma-def 64.6%

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

      6. sub-neg 64.6%

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

      7. +-commutative 64.6%

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

      8. *-commutative 64.6%

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

      9. distribute-rgt-neg-in 64.6%

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

      10. fma-def 67.2%

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

      11. *-commutative 67.2%

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

      12. distribute-rgt-neg-in 67.2%

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

      13. sub-neg 67.2%

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

      14. distribute-neg-in 67.2%

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

      15. unsub-neg 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in y around 0 72.5%

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

      1. mul-1-neg 72.5%

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

      2. *-commutative 72.5%

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

      3. distribute-rgt-neg-in 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in z around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. distribute-lft-neg-in 57.6%

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

   9. Simplified 57.6%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 11: 29.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-202}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -5.6e-55)
   (* c (* t j))
   (if (<= c -2.6e-272)
     (* y (* x z))
     (if (<= c 1.9e-202)
       (* i (* y (- j)))
       (if (<= c 4.8e+76) (* x (* y z)) (* c (* 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 (c <= -5.6e-55) {
		tmp = c * (t * j);
	} else if (c <= -2.6e-272) {
		tmp = y * (x * z);
	} else if (c <= 1.9e-202) {
		tmp = i * (y * -j);
	} else if (c <= 4.8e+76) {
		tmp = x * (y * z);
	} else {
		tmp = c * (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 (c <= (-5.6d-55)) then
        tmp = c * (t * j)
    else if (c <= (-2.6d-272)) then
        tmp = y * (x * z)
    else if (c <= 1.9d-202) then
        tmp = i * (y * -j)
    else if (c <= 4.8d+76) then
        tmp = x * (y * z)
    else
        tmp = c * (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 (c <= -5.6e-55) {
		tmp = c * (t * j);
	} else if (c <= -2.6e-272) {
		tmp = y * (x * z);
	} else if (c <= 1.9e-202) {
		tmp = i * (y * -j);
	} else if (c <= 4.8e+76) {
		tmp = x * (y * z);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.6e-55:
		tmp = c * (t * j)
	elif c <= -2.6e-272:
		tmp = y * (x * z)
	elif c <= 1.9e-202:
		tmp = i * (y * -j)
	elif c <= 4.8e+76:
		tmp = x * (y * z)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.6e-55)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= -2.6e-272)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 1.9e-202)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 4.8e+76)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.6e-55)
		tmp = c * (t * j);
	elseif (c <= -2.6e-272)
		tmp = y * (x * z);
	elseif (c <= 1.9e-202)
		tmp = i * (y * -j);
	elseif (c <= 4.8e+76)
		tmp = x * (y * z);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -5.6e-55], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-272], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e-202], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+76], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.59999999999999968e-55

   1. Initial program 62.3%

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

      1. sub-neg 62.3%

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

      2. associate-+l+ 62.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 65.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 65.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 66.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 66.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 66.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 66.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 66.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 66.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 66.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 66.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 66.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 66.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 66.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 68.2%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 68.2%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 68.2%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 68.2%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 68.2%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 63.0%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 36.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -5.59999999999999968e-55 < c < -2.59999999999999992e-272

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 60.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 60.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 60.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 60.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 60.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 38.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -2.59999999999999992e-272 < c < 1.90000000000000007e-202

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 73.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 73.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 73.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 73.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in y around inf 45.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.2%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y \cdot i\right) \cdot j\right)} \]

      2. *-commutative 45.2%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(i \cdot y\right)} \cdot j\right) \]

      3. associate-*r* 46.3%

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y \cdot j\right)\right)} \]

      4. associate-*r* 46.3%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(y \cdot j\right)} \]

      5. neg-mul-1 46.3%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(y \cdot j\right) \]

      6. *-commutative 46.3%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(j \cdot y\right)} \]

   9. Simplified 46.3%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 1.90000000000000007e-202 < c < 4.8e76

   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. sub-neg 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 72.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 72.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 76.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 76.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 76.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 76.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 76.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 76.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 52.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 32.4%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   6. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   7. Simplified 32.4%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   if 4.8e76 < c

   1. Initial program 64.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 64.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 64.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 64.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 64.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 64.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 64.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 67.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 67.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 67.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 67.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 67.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 67.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 67.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 72.5%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 72.5%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 72.5%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 72.5%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in z around inf 57.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. distribute-lft-neg-in 57.6%

         \[\leadsto \color{blue}{\left(-c\right) \cdot \left(b \cdot z\right)} \]

   9. Simplified 57.6%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-202}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 12: 28.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= c -5.6e-55)
     t_1
     (if (<= c -1.1e-274)
       (* y (* x z))
       (if (<= c 8e-252)
         (* y (* i (- j)))
         (if (<= c 4.9e+55) (* 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 = c * (t * j);
	double tmp;
	if (c <= -5.6e-55) {
		tmp = t_1;
	} else if (c <= -1.1e-274) {
		tmp = y * (x * z);
	} else if (c <= 8e-252) {
		tmp = y * (i * -j);
	} else if (c <= 4.9e+55) {
		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 = c * (t * j)
    if (c <= (-5.6d-55)) then
        tmp = t_1
    else if (c <= (-1.1d-274)) then
        tmp = y * (x * z)
    else if (c <= 8d-252) then
        tmp = y * (i * -j)
    else if (c <= 4.9d+55) 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 = c * (t * j);
	double tmp;
	if (c <= -5.6e-55) {
		tmp = t_1;
	} else if (c <= -1.1e-274) {
		tmp = y * (x * z);
	} else if (c <= 8e-252) {
		tmp = y * (i * -j);
	} else if (c <= 4.9e+55) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if c <= -5.6e-55:
		tmp = t_1
	elif c <= -1.1e-274:
		tmp = y * (x * z)
	elif c <= 8e-252:
		tmp = y * (i * -j)
	elif c <= 4.9e+55:
		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(c * Float64(t * j))
	tmp = 0.0
	if (c <= -5.6e-55)
		tmp = t_1;
	elseif (c <= -1.1e-274)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 8e-252)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 4.9e+55)
		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 = c * (t * j);
	tmp = 0.0;
	if (c <= -5.6e-55)
		tmp = t_1;
	elseif (c <= -1.1e-274)
		tmp = y * (x * z);
	elseif (c <= 8e-252)
		tmp = y * (i * -j);
	elseif (c <= 4.9e+55)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.6e-55], t$95$1, If[LessEqual[c, -1.1e-274], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e-252], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e+55], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.59999999999999968e-55 or 4.90000000000000015e55 < c

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 62.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 62.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 64.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 64.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 69.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 69.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 69.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 58.5%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 36.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -5.59999999999999968e-55 < c < -1.09999999999999998e-274

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 60.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 60.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 60.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 60.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 60.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 38.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.09999999999999998e-274 < c < 7.99999999999999954e-252

   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. sub-neg 90.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 90.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 90.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 90.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 90.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 90.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 90.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 90.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 90.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 90.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 90.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 90.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 90.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 90.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 90.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 57.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 57.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 57.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 57.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 57.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 57.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 46.3%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto y \cdot \left(-1 \cdot \color{blue}{\left(j \cdot i\right)}\right) \]

      2. associate-*r* 46.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(-1 \cdot j\right) \cdot i\right)} \]

      3. neg-mul-1 46.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(-j\right)} \cdot i\right) \]

   9. Simplified 46.3%

      \[\leadsto y \cdot \color{blue}{\left(\left(-j\right) \cdot i\right)} \]

   if 7.99999999999999954e-252 < c < 4.90000000000000015e55

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 70.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 72.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 72.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 72.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 72.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 72.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 72.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 72.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 72.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 72.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 37.5%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   6. Step-by-step derivation

      1. *-commutative 37.5%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 13: 30.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-53} \lor \neg \left(t \leq 4.9 \cdot 10^{+48}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.5e-53) (not (<= t 4.9e+48))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.5e-53) || !(t <= 4.9e+48)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-4.5d-53)) .or. (.not. (t <= 4.9d+48))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.5e-53) || !(t <= 4.9e+48)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.5e-53) or not (t <= 4.9e+48):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.5e-53) || !(t <= 4.9e+48))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -4.5e-53) || ~((t <= 4.9e+48)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.5e-53], N[Not[LessEqual[t, 4.9e+48]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999985e-53 or 4.9000000000000003e48 < t

   1. Initial program 60.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 60.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 60.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 60.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 60.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 62.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 62.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 62.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 62.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 62.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 63.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 63.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 63.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 63.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 63.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 57.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 57.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 57.0%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 57.0%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 57.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 55.4%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 33.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.49999999999999985e-53 < t < 4.9000000000000003e48

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 80.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 80.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 38.4%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 38.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      4. *-commutative 38.4%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around -inf 27.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-53} \lor \neg \left(t \leq 4.9 \cdot 10^{+48}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 14: 28.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{-55} \lor \neg \left(c \leq 9.5 \cdot 10^{+55}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4.3e-55) (not (<= c 9.5e+55))) (* c (* t j)) (* y (* x z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.3e-55) || !(c <= 9.5e+55)) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-4.3d-55)) .or. (.not. (c <= 9.5d+55))) then
        tmp = c * (t * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.3e-55) || !(c <= 9.5e+55)) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -4.3e-55) or not (c <= 9.5e+55):
		tmp = c * (t * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -4.3e-55) || !(c <= 9.5e+55))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -4.3e-55) || ~((c <= 9.5e+55)))
		tmp = c * (t * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -4.3e-55], N[Not[LessEqual[c, 9.5e+55]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.3000000000000001e-55 or 9.49999999999999989e55 < c

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 62.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 62.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 64.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 64.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 69.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 69.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 69.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 58.5%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 36.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.3000000000000001e-55 < c < 9.49999999999999989e55

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 76.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 75.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 75.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 54.2%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 54.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 54.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 54.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 54.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 54.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 54.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 33.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{-55} \lor \neg \left(c \leq 9.5 \cdot 10^{+55}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 15: 28.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-55} \lor \neg \left(c \leq 4.6 \cdot 10^{+55}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -5.5e-55) (not (<= c 4.6e+55))) (* c (* t j)) (* z (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -5.5e-55) || !(c <= 4.6e+55)) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-5.5d-55)) .or. (.not. (c <= 4.6d+55))) then
        tmp = c * (t * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -5.5e-55) || !(c <= 4.6e+55)) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -5.5e-55) or not (c <= 4.6e+55):
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -5.5e-55) || !(c <= 4.6e+55))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -5.5e-55) || ~((c <= 4.6e+55)))
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -5.5e-55], N[Not[LessEqual[c, 4.6e+55]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.4999999999999999e-55 or 4.59999999999999975e55 < c

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 62.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 62.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 64.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 64.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 66.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 67.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 69.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 69.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 69.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 58.5%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 36.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -5.4999999999999999e-55 < c < 4.59999999999999975e55

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 39.8%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 34.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-55} \lor \neg \left(c \leq 4.6 \cdot 10^{+55}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 30.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.8e-53)
   (* j (* t c))
   (if (<= t 9.2e+49) (* a (* b i)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.8e-53) {
		tmp = j * (t * c);
	} else if (t <= 9.2e+49) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-2.8d-53)) then
        tmp = j * (t * c)
    else if (t <= 9.2d+49) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.8e-53) {
		tmp = j * (t * c);
	} else if (t <= 9.2e+49) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.8e-53:
		tmp = j * (t * c)
	elif t <= 9.2e+49:
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.8e-53)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 9.2e+49)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.8e-53)
		tmp = j * (t * c);
	elseif (t <= 9.2e+49)
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.8e-53], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+49], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999985e-53

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 62.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 62.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 63.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 64.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 64.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 64.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 64.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 64.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 54.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 54.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 54.8%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 54.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 53.5%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 29.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.8%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]

      2. associate-*r* 31.0%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      3. *-commutative 31.0%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

      4. associate-*r* 30.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   10. Simplified 30.9%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   if -2.79999999999999985e-53 < t < 9.20000000000000008e49

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 80.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 80.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 38.4%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 38.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      4. *-commutative 38.4%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around -inf 27.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 9.20000000000000008e49 < t

   1. Initial program 56.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 56.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 56.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 56.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 56.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 58.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 58.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 58.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 58.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 58.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 58.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 58.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 58.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 58.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 58.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 58.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 58.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 60.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 60.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 60.9%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 60.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 60.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in c around 0 58.8%

      \[\leadsto \mathsf{fma}\left(x, t \cdot \left(-a\right), \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(i \cdot a\right)}\right)\right) \]

   8. Taylor expanded in c around inf 39.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 17: 21.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -5.3e+213) (* c (* z b)) (* a (* b 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 (c <= -5.3e+213) {
		tmp = c * (z * b);
	} else {
		tmp = a * (b * 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 (c <= (-5.3d+213)) then
        tmp = c * (z * b)
    else
        tmp = a * (b * 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 (c <= -5.3e+213) {
		tmp = c * (z * b);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.3e+213:
		tmp = c * (z * b)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.3e+213)
		tmp = Float64(c * Float64(z * b));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.3e+213)
		tmp = c * (z * b);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -5.3e+213], N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.2999999999999998e213

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 63.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 63.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 66.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 66.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 66.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 66.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 66.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 66.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 66.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 66.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around 0 69.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left(a \cdot t\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-a \cdot t}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      2. *-commutative 69.9%

         \[\leadsto \mathsf{fma}\left(x, -\color{blue}{t \cdot a}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

      3. distribute-rgt-neg-in 69.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   6. Simplified 69.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{t \cdot \left(-a\right)}, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right) \]

   7. Taylor expanded in z around inf 18.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 18.2%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      2. *-commutative 18.2%

         \[\leadsto -c \cdot \color{blue}{\left(z \cdot b\right)} \]

      3. associate-*r* 21.2%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      4. distribute-rgt-neg-in 21.2%

         \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

   9. Simplified 21.2%

      \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 7.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(c \cdot z\right) \cdot \left(-b\right)\right)\right)} \]

       2. expm1-udef 7.4%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(c \cdot z\right) \cdot \left(-b\right)\right)} - 1} \]

   11. Applied egg-rr 14.0%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(c \cdot \left(b \cdot z\right)\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 14.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot z\right)\right)\right)} \]

       2. expm1-log1p 24.8%

          \[\leadsto \color{blue}{c \cdot \left(b \cdot z\right)} \]

   13. Simplified 24.8%

       \[\leadsto \color{blue}{c \cdot \left(b \cdot z\right)} \]

   if -5.2999999999999998e213 < c

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 70.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 72.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 73.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 73.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 73.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 73.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 73.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 73.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 39.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 39.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 39.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 39.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      4. *-commutative 39.2%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around -inf 19.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 19.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 18: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. sub-neg 69.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. associate-+l+ 69.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   3. fma-def 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   4. +-commutative 70.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   5. fma-def 72.1%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   6. sub-neg 72.1%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   7. +-commutative 72.1%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   8. *-commutative 72.1%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   9. distribute-rgt-neg-in 72.1%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   10. fma-def 72.5%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   11. *-commutative 72.5%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   12. distribute-rgt-neg-in 72.5%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

   13. sub-neg 72.5%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

   14. distribute-neg-in 72.5%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

   15. unsub-neg 72.5%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

3. Simplified 72.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

4. Taylor expanded in a around inf 40.1%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.1%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.1%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.1%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. *-commutative 40.1%

      \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

6. Simplified 40.1%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

7. Taylor expanded in b around -inf 18.2%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

8. Final simplification 18.2%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 69.1% 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 2023181 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))