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

Percentage Accurate: 73.5% → 82.5%

Time: 21.9s

Alternatives: 28

Speedup: 0.3×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot c - y \cdot i\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot t\_1\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_1, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, b \cdot i\right), z \cdot \mathsf{fma}\left(c, -b, x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a c) (* y i)))
        (t_2
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j t_1))))
   (if (<= t_2 2e+296)
     t_2
     (if (<= t_2 INFINITY)
       (fma j t_1 (fma t (fma a (- x) (* b i)) (* z (fma c (- b) (* x y)))))
       (* i (fma j (- y) (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * c) - (y * i);
	double t_2 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * t_1);
	double tmp;
	if (t_2 <= 2e+296) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma(j, t_1, fma(t, fma(a, -x, (b * i)), (z * fma(c, -b, (x * y)))));
	} else {
		tmp = i * fma(j, -y, (t * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * c) - Float64(y * i))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * t_1))
	tmp = 0.0
	if (t_2 <= 2e+296)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = fma(j, t_1, fma(t, fma(a, Float64(-x), Float64(b * i)), Float64(z * fma(c, Float64(-b), Float64(x * y)))));
	else
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+296], t$95$2, If[LessEqual[t$95$2, Infinity], N[(j * t$95$1 + N[(t * N[(a * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(z * N[(c * (-b) + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 1.99999999999999996e296

   1. Initial program 96.5%

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

   if 1.99999999999999996e296 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 89.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, b \cdot i\right), z \cdot \mathsf{fma}\left(c, -b, x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot i - z \cdot c\\ t_2 := a \cdot c - y \cdot i\\ t_3 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot t\_1\right) + j \cdot t\_2\\ \mathbf{if}\;t\_3 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right), \mathsf{fma}\left(b, t\_1, y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, b \cdot i\right), z \cdot \mathsf{fma}\left(c, -b, x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t i) (* z c)))
        (t_2 (- (* a c) (* y i)))
        (t_3 (+ (+ (* x (- (* y z) (* t a))) (* b t_1)) (* j t_2))))
   (if (<= t_3 5e+290)
     (fma a (fma j c (* x (- t))) (fma b t_1 (* y (fma j (- i) (* x z)))))
     (if (<= t_3 INFINITY)
       (fma j t_2 (fma t (fma a (- x) (* b i)) (* z (fma c (- b) (* x y)))))
       (* i (fma j (- y) (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * i) - (z * c);
	double t_2 = (a * c) - (y * i);
	double t_3 = ((x * ((y * z) - (t * a))) + (b * t_1)) + (j * t_2);
	double tmp;
	if (t_3 <= 5e+290) {
		tmp = fma(a, fma(j, c, (x * -t)), fma(b, t_1, (y * fma(j, -i, (x * z)))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = fma(j, t_2, fma(t, fma(a, -x, (b * i)), (z * fma(c, -b, (x * y)))));
	} else {
		tmp = i * fma(j, -y, (t * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * i) - Float64(z * c))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * t_1)) + Float64(j * t_2))
	tmp = 0.0
	if (t_3 <= 5e+290)
		tmp = fma(a, fma(j, c, Float64(x * Float64(-t))), fma(b, t_1, Float64(y * fma(j, Float64(-i), Float64(x * z)))));
	elseif (t_3 <= Inf)
		tmp = fma(j, t_2, fma(t, fma(a, Float64(-x), Float64(b * i)), Float64(z * fma(c, Float64(-b), Float64(x * y)))));
	else
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 5e+290], N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1 + N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(j * t$95$2 + N[(t * N[(a * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(z * N[(c * (-b) + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 4.9999999999999998e290

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 89.2%

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

   if 4.9999999999999998e290 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 82.3%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 89.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right), \mathsf{fma}\left(b, t \cdot i - z \cdot c, y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, b \cdot i\right), z \cdot \mathsf{fma}\left(c, -b, x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot i - z \cdot c\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := \left(t\_2 + b \cdot t\_1\right) + t\_3\\ \mathbf{if}\;t\_4 \leq 10^{+225}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right), \mathsf{fma}\left(b, t\_1, y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\left(t\_2 - c \cdot \left(z \cdot b\right)\right) + t\_3\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t i) (* z c)))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ (+ t_2 (* b t_1)) t_3)))
   (if (<= t_4 1e+225)
     (fma a (fma j c (* x (- t))) (fma b t_1 (* y (fma j (- i) (* x z)))))
     (if (<= t_4 INFINITY)
       (+ (- t_2 (* c (* z b))) t_3)
       (* i (fma j (- y) (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * i) - (z * c);
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (t_2 + (b * t_1)) + t_3;
	double tmp;
	if (t_4 <= 1e+225) {
		tmp = fma(a, fma(j, c, (x * -t)), fma(b, t_1, (y * fma(j, -i, (x * z)))));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (t_2 - (c * (z * b))) + t_3;
	} else {
		tmp = i * fma(j, -y, (t * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * i) - Float64(z * c))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(Float64(t_2 + Float64(b * t_1)) + t_3)
	tmp = 0.0
	if (t_4 <= 1e+225)
		tmp = fma(a, fma(j, c, Float64(x * Float64(-t))), fma(b, t_1, Float64(y * fma(j, Float64(-i), Float64(x * z)))));
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(t_2 - Float64(c * Float64(z * b))) + t_3);
	else
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, 1e+225], N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1 + N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(t$95$2 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 9.99999999999999928e224

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 90.3%

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

   if 9.99999999999999928e224 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 85.4%

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

   3. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 82.5

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

   5. Applied rewrites 82.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 10^{+225}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right), \mathsf{fma}\left(b, t \cdot i - z \cdot c, y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;\left(t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + t\_2 \leq \infty:\\ \;\;\;\;\left(t\_1 - c \cdot \left(z \cdot b\right)\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= (+ (+ t_1 (* b (- (* t i) (* z c)))) t_2) INFINITY)
     (+ (- t_1 (* c (* z b))) t_2)
     (* i (fma j (- y) (* t b))))))

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 * ((a * c) - (y * i));
	double tmp;
	if (((t_1 + (b * ((t * i) - (z * c)))) + t_2) <= ((double) INFINITY)) {
		tmp = (t_1 - (c * (z * b))) + t_2;
	} else {
		tmp = i * fma(j, -y, (t * b));
	}
	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(a * c) - Float64(y * i)))
	tmp = 0.0
	if (Float64(Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + t_2) <= Inf)
		tmp = Float64(Float64(t_1 - Float64(c * Float64(z * b))) + t_2);
	else
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	end
	return 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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], Infinity], N[(N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.4%

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

   3. Taylor expanded in c around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 81.3

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

   5. Applied rewrites 81.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(j, -y, b \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

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

Alternative 5: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.5e+131)
     t_2
     (if (<= j -5e+23)
       t_1
       (if (<= j -4.8e-30)
         (* y (fma j (- i) (* x z)))
         (if (<= j -7.5e-44)
           (* a (fma j c (* x (- t))))
           (if (<= j -5.5e-135)
             (* i (fma j (- y) (* t b)))
             (if (<= j 5.5e-229)
               (* z (* x (- y (/ (* b c) x))))
               (if (<= j 8.5e+80) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.5e+131) {
		tmp = t_2;
	} else if (j <= -5e+23) {
		tmp = t_1;
	} else if (j <= -4.8e-30) {
		tmp = y * fma(j, -i, (x * z));
	} else if (j <= -7.5e-44) {
		tmp = a * fma(j, c, (x * -t));
	} else if (j <= -5.5e-135) {
		tmp = i * fma(j, -y, (t * b));
	} else if (j <= 5.5e-229) {
		tmp = z * (x * (y - ((b * c) / x)));
	} else if (j <= 8.5e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.5e+131)
		tmp = t_2;
	elseif (j <= -5e+23)
		tmp = t_1;
	elseif (j <= -4.8e-30)
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	elseif (j <= -7.5e-44)
		tmp = Float64(a * fma(j, c, Float64(x * Float64(-t))));
	elseif (j <= -5.5e-135)
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	elseif (j <= 5.5e-229)
		tmp = Float64(z * Float64(x * Float64(y - Float64(Float64(b * c) / x))));
	elseif (j <= 8.5e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+131], t$95$2, If[LessEqual[j, -5e+23], t$95$1, If[LessEqual[j, -4.8e-30], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-44], N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.5e-135], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-229], N[(z * N[(x * N[(y - N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+80], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.49999999999999998e131 or 8.50000000000000007e80 < j

   1. Initial program 71.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if -2.49999999999999998e131 < j < -4.9999999999999999e23 or 5.5000000000000001e-229 < j < 8.50000000000000007e80

   1. Initial program 75.9%

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

   3. Taylor expanded in b around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 60.9

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

   5. Applied rewrites 60.9%

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

   if -4.9999999999999999e23 < j < -4.7999999999999997e-30

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if -4.7999999999999997e-30 < j < -7.50000000000000008e-44

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -7.50000000000000008e-44 < j < -5.4999999999999999e-135

   1. Initial program 83.6%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -5.4999999999999999e-135 < j < 5.5000000000000001e-229

   1. Initial program 66.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{x}\right)\right)}\right)\right) \]

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 65.2

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

   8. Applied rewrites 65.2%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(c, -b, x \cdot y\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.5e+131)
     t_2
     (if (<= j -5e+23)
       t_1
       (if (<= j -4.8e-30)
         (* y (fma j (- i) (* x z)))
         (if (<= j -7.5e-44)
           (* a (fma j c (* x (- t))))
           (if (<= j -5.5e-135)
             (* i (fma j (- y) (* t b)))
             (if (<= j 1.6e-231)
               (* z (fma c (- b) (* x y)))
               (if (<= j 8.5e+80) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.5e+131) {
		tmp = t_2;
	} else if (j <= -5e+23) {
		tmp = t_1;
	} else if (j <= -4.8e-30) {
		tmp = y * fma(j, -i, (x * z));
	} else if (j <= -7.5e-44) {
		tmp = a * fma(j, c, (x * -t));
	} else if (j <= -5.5e-135) {
		tmp = i * fma(j, -y, (t * b));
	} else if (j <= 1.6e-231) {
		tmp = z * fma(c, -b, (x * y));
	} else if (j <= 8.5e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.5e+131)
		tmp = t_2;
	elseif (j <= -5e+23)
		tmp = t_1;
	elseif (j <= -4.8e-30)
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	elseif (j <= -7.5e-44)
		tmp = Float64(a * fma(j, c, Float64(x * Float64(-t))));
	elseif (j <= -5.5e-135)
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	elseif (j <= 1.6e-231)
		tmp = Float64(z * fma(c, Float64(-b), Float64(x * y)));
	elseif (j <= 8.5e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+131], t$95$2, If[LessEqual[j, -5e+23], t$95$1, If[LessEqual[j, -4.8e-30], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-44], N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.5e-135], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e-231], N[(z * N[(c * (-b) + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+80], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.49999999999999998e131 or 8.50000000000000007e80 < j

   1. Initial program 71.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if -2.49999999999999998e131 < j < -4.9999999999999999e23 or 1.60000000000000004e-231 < j < 8.50000000000000007e80

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 60.7

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

   5. Applied rewrites 60.7%

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

   if -4.9999999999999999e23 < j < -4.7999999999999997e-30

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if -4.7999999999999997e-30 < j < -7.50000000000000008e-44

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -7.50000000000000008e-44 < j < -5.4999999999999999e-135

   1. Initial program 83.6%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -5.4999999999999999e-135 < j < 1.60000000000000004e-231

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(c, -b, x \cdot y\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.5e+131)
     t_2
     (if (<= j -5e+23)
       t_1
       (if (<= j -4.8e-30)
         (* y (fma j (- i) (* x z)))
         (if (<= j -7.5e-44)
           (* a (fma j c (* x (- t))))
           (if (<= j -4.5e-135)
             (* i (fma j (- y) (* t b)))
             (if (<= j 1.25e-203)
               (* x (fma a (- t) (* y z)))
               (if (<= j 8.5e+80) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.5e+131) {
		tmp = t_2;
	} else if (j <= -5e+23) {
		tmp = t_1;
	} else if (j <= -4.8e-30) {
		tmp = y * fma(j, -i, (x * z));
	} else if (j <= -7.5e-44) {
		tmp = a * fma(j, c, (x * -t));
	} else if (j <= -4.5e-135) {
		tmp = i * fma(j, -y, (t * b));
	} else if (j <= 1.25e-203) {
		tmp = x * fma(a, -t, (y * z));
	} else if (j <= 8.5e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.5e+131)
		tmp = t_2;
	elseif (j <= -5e+23)
		tmp = t_1;
	elseif (j <= -4.8e-30)
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	elseif (j <= -7.5e-44)
		tmp = Float64(a * fma(j, c, Float64(x * Float64(-t))));
	elseif (j <= -4.5e-135)
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	elseif (j <= 1.25e-203)
		tmp = Float64(x * fma(a, Float64(-t), Float64(y * z)));
	elseif (j <= 8.5e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+131], t$95$2, If[LessEqual[j, -5e+23], t$95$1, If[LessEqual[j, -4.8e-30], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-44], N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-135], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e-203], N[(x * N[(a * (-t) + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+80], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.49999999999999998e131 or 8.50000000000000007e80 < j

   1. Initial program 71.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if -2.49999999999999998e131 < j < -4.9999999999999999e23 or 1.25e-203 < j < 8.50000000000000007e80

   1. Initial program 76.9%

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

   3. Taylor expanded in b around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 63.5

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

   5. Applied rewrites 63.5%

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

   if -4.9999999999999999e23 < j < -4.7999999999999997e-30

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if -4.7999999999999997e-30 < j < -7.50000000000000008e-44

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -7.50000000000000008e-44 < j < -4.49999999999999987e-135

   1. Initial program 83.6%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -4.49999999999999987e-135 < j < 1.25e-203

   1. Initial program 66.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-*.f64 54.9

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

   5. Applied rewrites 54.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-168}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \mathsf{fma}\left(-c, \frac{z}{i}, t\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, z, i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 8000000:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, -x, b \cdot i\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, z \cdot \left(b \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma j c (* x (- t))))))
   (if (<= a -1.9e+44)
     t_1
     (if (<= a -9e-168)
       (* (* b i) (fma (- c) (/ z i) t))
       (if (<= a 5.2e-68)
         (* y (fma x z (* i (- j))))
         (if (<= a 8000000.0)
           (* t (fma a (- x) (* b i)))
           (if (<= a 9.5e+79) (fma (* y z) x (* z (* b (- c)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(j, c, (x * -t));
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_1;
	} else if (a <= -9e-168) {
		tmp = (b * i) * fma(-c, (z / i), t);
	} else if (a <= 5.2e-68) {
		tmp = y * fma(x, z, (i * -j));
	} else if (a <= 8000000.0) {
		tmp = t * fma(a, -x, (b * i));
	} else if (a <= 9.5e+79) {
		tmp = fma((y * z), x, (z * (b * -c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(j, c, Float64(x * Float64(-t))))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_1;
	elseif (a <= -9e-168)
		tmp = Float64(Float64(b * i) * fma(Float64(-c), Float64(z / i), t));
	elseif (a <= 5.2e-68)
		tmp = Float64(y * fma(x, z, Float64(i * Float64(-j))));
	elseif (a <= 8000000.0)
		tmp = Float64(t * fma(a, Float64(-x), Float64(b * i)));
	elseif (a <= 9.5e+79)
		tmp = fma(Float64(y * z), x, Float64(z * Float64(b * Float64(-c))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$1, If[LessEqual[a, -9e-168], N[(N[(b * i), $MachinePrecision] * N[((-c) * N[(z / i), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-68], N[(y * N[(x * z + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8000000.0], N[(t * N[(a * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+79], N[(N[(y * z), $MachinePrecision] * x + N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9000000000000001e44 or 9.49999999999999994e79 < a

   1. Initial program 67.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 70.2

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

   5. Applied rewrites 70.2%

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

   if -1.9000000000000001e44 < a < -9.0000000000000002e-168

   1. Initial program 72.2%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 76.0%

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

   9. Taylor expanded in i around -inf

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

   11. Applied rewrites 53.9%

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

   12. Taylor expanded in b around -inf

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

       1. *-commutative N/A

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

       2. *-commutative N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. associate-/l* N/A

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

       8. associate-*r* N/A

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

       9. lower-fma.f64 N/A

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

       10. mul-1-neg N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, \frac{z}{i}, t\right) \cdot \left(b \cdot i\right) \]

       11. lower-neg.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(c\right)}, \frac{z}{i}, t\right) \cdot \left(b \cdot i\right) \]

       12. lower-/.f64 N/A

           \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(c\right), \color{blue}{\frac{z}{i}}, t\right) \cdot \left(b \cdot i\right) \]

       13. lower-*.f64 60.8

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

   14. Applied rewrites 60.8%

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

   if -9.0000000000000002e-168 < a < 5.1999999999999996e-68

   1. Initial program 78.9%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 61.9

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

   8. Applied rewrites 61.9%

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

   if 5.1999999999999996e-68 < a < 8e6

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 66.6

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

   5. Applied rewrites 66.6%

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

   if 8e6 < a < 9.49999999999999994e79

   1. Initial program 80.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. neg-mul-1 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 60.8

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

   5. Applied rewrites 60.8%

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

      1. lift-neg.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-neg.f64 N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. distribute-lft-neg-out N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 60.9

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

   7. Applied rewrites 60.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-168}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \mathsf{fma}\left(-c, \frac{z}{i}, t\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, z, i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 8000000:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, -x, b \cdot i\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, x, z \cdot \left(b \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot c - y \cdot i\\ t_2 := \mathsf{fma}\left(j, t\_1, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \mathbf{if}\;j \leq -1.38 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot t\_1\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(c, z \cdot \left(-b\right), x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a c) (* y i))) (t_2 (fma j t_1 (* t (* a (- x))))))
   (if (<= j -1.38e+141)
     t_2
     (if (<= j -6.5e-135)
       (+ (* i (* t b)) (* j t_1))
       (if (<= j 8.5e+80)
         (fma c (* z (- b)) (* x (fma a (- t) (* y z))))
         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 * c) - (y * i);
	double t_2 = fma(j, t_1, (t * (a * -x)));
	double tmp;
	if (j <= -1.38e+141) {
		tmp = t_2;
	} else if (j <= -6.5e-135) {
		tmp = (i * (t * b)) + (j * t_1);
	} else if (j <= 8.5e+80) {
		tmp = fma(c, (z * -b), (x * fma(a, -t, (y * z))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * c) - Float64(y * i))
	t_2 = fma(j, t_1, Float64(t * Float64(a * Float64(-x))))
	tmp = 0.0
	if (j <= -1.38e+141)
		tmp = t_2;
	elseif (j <= -6.5e-135)
		tmp = Float64(Float64(i * Float64(t * b)) + Float64(j * t_1));
	elseif (j <= 8.5e+80)
		tmp = fma(c, Float64(z * Float64(-b)), Float64(x * fma(a, Float64(-t), Float64(y * z))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * t$95$1 + N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.38e+141], t$95$2, If[LessEqual[j, -6.5e-135], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+80], N[(c * N[(z * (-b)), $MachinePrecision] + N[(x * N[(a * (-t) + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.38e141 or 8.50000000000000007e80 < j

   1. Initial program 70.7%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 71.0%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 81.1

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

   8. Applied rewrites 81.1%

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

   if -1.38e141 < j < -6.50000000000000056e-135

   1. Initial program 79.1%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

   if -6.50000000000000056e-135 < j < 8.50000000000000007e80

   1. Initial program 73.6%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. associate-*l* N/A

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

      10. distribute-rgt-in N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in j around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 70.4

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

   8. Applied rewrites 70.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.38 \cdot 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(c, z \cdot \left(-b\right), x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, -x, b \cdot i\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t \cdot t\_1\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(t, t\_1, z \cdot \mathsf{fma}\left(b, -c, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma a (- x) (* b i))) (t_2 (- (* a c) (* y i))))
   (if (<= j -3.8e-65)
     (fma j t_2 (* t t_1))
     (if (<= j 9.2e+80)
       (fma t t_1 (* z (fma b (- c) (* x y))))
       (fma j t_2 (* t (* a (- x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(a, -x, (b * i));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if (j <= -3.8e-65) {
		tmp = fma(j, t_2, (t * t_1));
	} else if (j <= 9.2e+80) {
		tmp = fma(t, t_1, (z * fma(b, -c, (x * y))));
	} else {
		tmp = fma(j, t_2, (t * (a * -x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(a, Float64(-x), Float64(b * i))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -3.8e-65)
		tmp = fma(j, t_2, Float64(t * t_1));
	elseif (j <= 9.2e+80)
		tmp = fma(t, t_1, Float64(z * fma(b, Float64(-c), Float64(x * y))));
	else
		tmp = fma(j, t_2, Float64(t * Float64(a * Float64(-x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e-65], N[(j * t$95$2 + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.2e+80], N[(t * t$95$1 + N[(z * N[(b * (-c) + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * t$95$2 + N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.8000000000000002e-65

   1. Initial program 72.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. *-lft-identity N/A

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

      13. metadata-eval N/A

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

      14. cancel-sign-sub-inv N/A

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

      15. distribute-lft-out-- N/A

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

      16. mul-1-neg N/A

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

   5. Applied rewrites 69.6%

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

   if -3.8000000000000002e-65 < j < 9.20000000000000016e80

   1. Initial program 75.1%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in j around 0

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

      1. lower-fma.f64 N/A

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

      2. mul-1-neg N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-*.f64 80.6

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

   8. Applied rewrites 80.6%

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

   if 9.20000000000000016e80 < j

   1. Initial program 74.4%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 80.4

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

   8. Applied rewrites 80.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \mathsf{fma}\left(a, -x, b \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, b \cdot i\right), z \cdot \mathsf{fma}\left(b, -c, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \mathbf{if}\;j \leq -1.6 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - z \cdot c, y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma j (- (* a c) (* y i)) (* t (* a (- x))))))
   (if (<= j -1.6e+193)
     t_1
     (if (<= j 6e+82)
       (fma b (- (* t i) (* z c)) (* y (fma j (- i) (* x z))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(j, ((a * c) - (y * i)), (t * (a * -x)));
	double tmp;
	if (j <= -1.6e+193) {
		tmp = t_1;
	} else if (j <= 6e+82) {
		tmp = fma(b, ((t * i) - (z * c)), (y * fma(j, -i, (x * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(j, Float64(Float64(a * c) - Float64(y * i)), Float64(t * Float64(a * Float64(-x))))
	tmp = 0.0
	if (j <= -1.6e+193)
		tmp = t_1;
	elseif (j <= 6e+82)
		tmp = fma(b, Float64(Float64(t * i) - Float64(z * c)), Float64(y * fma(j, Float64(-i), Float64(x * z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.6e+193], t$95$1, If[LessEqual[j, 6e+82], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.60000000000000007e193 or 5.99999999999999978e82 < j

   1. Initial program 67.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. lower-neg.f64 81.7

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

   8. Applied rewrites 81.7%

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

   if -1.60000000000000007e193 < j < 5.99999999999999978e82

   1. Initial program 77.0%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. distribute-neg-in N/A

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

      9. remove-double-neg N/A

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

      10. +-commutative N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 72.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - z \cdot c, y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(a \cdot \left(-x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(t, i, c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, z, i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 4000000:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, -x, b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma j c (* x (- t))))))
   (if (<= a -1.9e+44)
     t_1
     (if (<= a -7.2e-115)
       (* b (fma t i (* c (- z))))
       (if (<= a 5.2e-68)
         (* y (fma x z (* i (- j))))
         (if (<= a 4000000.0)
           (* t (fma a (- x) (* b i)))
           (if (<= a 2.4e+65) (* y (fma j (- i) (* x z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(j, c, (x * -t));
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_1;
	} else if (a <= -7.2e-115) {
		tmp = b * fma(t, i, (c * -z));
	} else if (a <= 5.2e-68) {
		tmp = y * fma(x, z, (i * -j));
	} else if (a <= 4000000.0) {
		tmp = t * fma(a, -x, (b * i));
	} else if (a <= 2.4e+65) {
		tmp = y * fma(j, -i, (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(j, c, Float64(x * Float64(-t))))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_1;
	elseif (a <= -7.2e-115)
		tmp = Float64(b * fma(t, i, Float64(c * Float64(-z))));
	elseif (a <= 5.2e-68)
		tmp = Float64(y * fma(x, z, Float64(i * Float64(-j))));
	elseif (a <= 4000000.0)
		tmp = Float64(t * fma(a, Float64(-x), Float64(b * i)));
	elseif (a <= 2.4e+65)
		tmp = Float64(y * fma(j, Float64(-i), Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$1, If[LessEqual[a, -7.2e-115], N[(b * N[(t * i + N[(c * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-68], N[(y * N[(x * z + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4000000.0], N[(t * N[(a * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+65], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9000000000000001e44 or 2.4000000000000002e65 < a

   1. Initial program 67.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 69.5

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

   5. Applied rewrites 69.5%

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

   if -1.9000000000000001e44 < a < -7.20000000000000018e-115

   1. Initial program 73.7%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 62.6

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

   8. Applied rewrites 62.6%

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

   if -7.20000000000000018e-115 < a < 5.1999999999999996e-68

   1. Initial program 78.0%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 59.5

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

   8. Applied rewrites 59.5%

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

   if 5.1999999999999996e-68 < a < 4e6

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 66.6

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

   5. Applied rewrites 66.6%

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

   if 4e6 < a < 2.4000000000000002e65

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. neg-mul-1 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 58.3

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

   5. Applied rewrites 58.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(t, i, c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(x, z, i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 4000000:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, -x, b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, -i, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))) (t_2 (* a (fma j c (* x (- t))))))
   (if (<= a -1.9e+44)
     t_2
     (if (<= a -1.25e-167)
       t_1
       (if (<= a 5.5e-288)
         (* y (* i (- j)))
         (if (<= a 5.2e-68) (* x (* y z)) (if (<= a 5.2e-38) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double t_2 = a * fma(j, c, (x * -t));
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_2;
	} else if (a <= -1.25e-167) {
		tmp = t_1;
	} else if (a <= 5.5e-288) {
		tmp = y * (i * -j);
	} else if (a <= 5.2e-68) {
		tmp = x * (y * z);
	} else if (a <= 5.2e-38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(a * fma(j, c, Float64(x * Float64(-t))))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_2;
	elseif (a <= -1.25e-167)
		tmp = t_1;
	elseif (a <= 5.5e-288)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 5.2e-68)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 5.2e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$2, If[LessEqual[a, -1.25e-167], t$95$1, If[LessEqual[a, 5.5e-288], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-68], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-38], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9000000000000001e44 or 5.20000000000000022e-38 < a

   1. Initial program 69.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 60.9

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

   5. Applied rewrites 60.9%

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

   if -1.9000000000000001e44 < a < -1.25000000000000005e-167 or 5.1999999999999996e-68 < a < 5.20000000000000022e-38

   1. Initial program 76.9%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 51.2

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

   8. Applied rewrites 51.2%

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

   9. Taylor expanded in t around inf

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

       1. lower-*.f64 44.1

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

   11. Applied rewrites 44.1%

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

   if -1.25000000000000005e-167 < a < 5.5e-288

   1. Initial program 68.9%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+r+ N/A

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

      4. sub-neg N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-out-- N/A

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

      8. lower-fma.f64 N/A

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      10. lower-neg.f64 66.2

          \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-i\right)}\right) \]

   8. Applied rewrites 66.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, z, j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y \cdot \color{blue}{\left(\mathsf{neg}\left(i \cdot j\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto y \cdot \left(\mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(i\right)\right)\right)} \]

       4. mul-1-neg N/A

          \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-1 \cdot i\right)\right)} \]

       6. mul-1-neg N/A

          \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

       7. lower-neg.f64 44.5

          \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(-i\right)}\right) \]

   11. Applied rewrites 44.5%

       \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   if 5.5e-288 < a < 5.1999999999999996e-68

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 53.9

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 53.9%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      3. lower-*.f64 42.4

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Applied rewrites 42.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(c, z \cdot \left(-b\right), x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -6.5e-135)
     (+ (* i (* t b)) t_1)
     (if (<= j 2.6e+97) (fma c (* z (- b)) (* x (fma a (- t) (* 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6.5e-135) {
		tmp = (i * (t * b)) + t_1;
	} else if (j <= 2.6e+97) {
		tmp = fma(c, (z * -b), (x * fma(a, -t, (y * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.5e-135)
		tmp = Float64(Float64(i * Float64(t * b)) + t_1);
	elseif (j <= 2.6e+97)
		tmp = fma(c, Float64(z * Float64(-b)), Float64(x * fma(a, Float64(-t), Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e-135], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 2.6e+97], N[(c * N[(z * (-b)), $MachinePrecision] + N[(x * N[(a * (-t) + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.50000000000000056e-135

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. lower-*.f64 61.6

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Applied rewrites 61.6%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if -6.50000000000000056e-135 < j < 2.6e97

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) + a \cdot \left(c \cdot j\right)\right)} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \left(c \cdot j\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(a \cdot \color{blue}{\left(j \cdot c\right)} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\color{blue}{\left(a \cdot j\right) \cdot c} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \left(b \cdot \color{blue}{\left(z \cdot c\right)}\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + -1 \cdot \color{blue}{\left(\left(b \cdot z\right) \cdot c\right)}\right) \]

      9. associate-*l* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(a \cdot j\right) \cdot c + \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right) \cdot c}\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(b \cdot z\right)\right)} \]

      11. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \left(a \cdot j + \color{blue}{\left(\mathsf{neg}\left(b \cdot z\right)\right)}\right) \]

      12. sub-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + c \cdot \color{blue}{\left(a \cdot j - b \cdot z\right)} \]

      13. +-commutative N/A

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(c, a \cdot j - b \cdot z, x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, j \cdot a - b \cdot z, x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(c, \color{blue}{-1 \cdot \left(b \cdot z\right)}, x \cdot \mathsf{fma}\left(a, \mathsf{neg}\left(t\right), y \cdot z\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}, x \cdot \mathsf{fma}\left(a, \mathsf{neg}\left(t\right), y \cdot z\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}, x \cdot \mathsf{fma}\left(a, \mathsf{neg}\left(t\right), y \cdot z\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(c, b \cdot \color{blue}{\left(-1 \cdot z\right)}, x \cdot \mathsf{fma}\left(a, \mathsf{neg}\left(t\right), y \cdot z\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, \color{blue}{b \cdot \left(-1 \cdot z\right)}, x \cdot \mathsf{fma}\left(a, \mathsf{neg}\left(t\right), y \cdot z\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(c, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}, x \cdot \mathsf{fma}\left(a, \mathsf{neg}\left(t\right), y \cdot z\right)\right) \]

      6. lower-neg.f64 70.3

         \[\leadsto \mathsf{fma}\left(c, b \cdot \color{blue}{\left(-z\right)}, x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right) \]

   8. Applied rewrites 70.3%

      \[\leadsto \mathsf{fma}\left(c, \color{blue}{b \cdot \left(-z\right)}, x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right) \]

   if 2.6e97 < j

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 77.3

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 77.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(c, z \cdot \left(-b\right), x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(y, x, b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.4e+61)
   (* z (fma y x (* b (- c))))
   (if (<= z 3.4e+51)
     (+ (* i (* t b)) (* j (- (* a c) (* y i))))
     (* z (* x (- y (/ (* b c) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.4e+61) {
		tmp = z * fma(y, x, (b * -c));
	} else if (z <= 3.4e+51) {
		tmp = (i * (t * b)) + (j * ((a * c) - (y * i)));
	} else {
		tmp = z * (x * (y - ((b * c) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.4e+61)
		tmp = Float64(z * fma(y, x, Float64(b * Float64(-c))));
	elseif (z <= 3.4e+51)
		tmp = Float64(Float64(i * Float64(t * b)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(z * Float64(x * Float64(y - Float64(Float64(b * c) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.4e+61], N[(z * N[(y * x + N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+51], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y - N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e61

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 70.7

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 70.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto z \cdot \left(c \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} + y \cdot x\right) \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(c \cdot \left(\mathsf{neg}\left(b\right)\right) + \color{blue}{y \cdot x}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x + c \cdot \left(\mathsf{neg}\left(b\right)\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} + c \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(y, x, c \cdot \left(\mathsf{neg}\left(b\right)\right)\right)} \]

      6. lift-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, c \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\mathsf{neg}\left(c \cdot b\right)}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b}\right) \]

      10. lower-neg.f64 72.9

          \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(-c\right)} \cdot b\right) \]

   7. Applied rewrites 72.9%

      \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(y, x, \left(-c\right) \cdot b\right)} \]

   if -2.3999999999999999e61 < z < 3.39999999999999984e51

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. lower-*.f64 63.7

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Applied rewrites 63.7%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if 3.39999999999999984e51 < z

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 60.6

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 60.6%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1 \cdot \frac{b \cdot c}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1 \cdot \frac{b \cdot c}{x}\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{x}\right)\right)}\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(y - \frac{b \cdot c}{x}\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(y - \frac{b \cdot c}{x}\right)}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(x \cdot \left(y - \color{blue}{\frac{b \cdot c}{x}}\right)\right) \]

      6. lower-*.f64 60.6

         \[\leadsto z \cdot \left(x \cdot \left(y - \frac{\color{blue}{b \cdot c}}{x}\right)\right) \]

   8. Applied rewrites 60.6%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(y, x, b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.75e+124)
     t_1
     (if (<= j -4.5e-135)
       (* i (fma t b (* j (- y))))
       (if (<= j 1.25e-203)
         (* x (fma a (- t) (* y z)))
         (if (<= j 8.5e+80) (* b (- (* t i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.75e+124) {
		tmp = t_1;
	} else if (j <= -4.5e-135) {
		tmp = i * fma(t, b, (j * -y));
	} else if (j <= 1.25e-203) {
		tmp = x * fma(a, -t, (y * z));
	} else if (j <= 8.5e+80) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.75e+124)
		tmp = t_1;
	elseif (j <= -4.5e-135)
		tmp = Float64(i * fma(t, b, Float64(j * Float64(-y))));
	elseif (j <= 1.25e-203)
		tmp = Float64(x * fma(a, Float64(-t), Float64(y * z)));
	elseif (j <= 8.5e+80)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e+124], t$95$1, If[LessEqual[j, -4.5e-135], N[(i * N[(t * b + N[(j * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e-203], N[(x * N[(a * (-t) + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+80], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.7500000000000001e124 or 8.50000000000000007e80 < j

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 71.1

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 71.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.7500000000000001e124 < j < -4.49999999999999987e-135

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 54.4

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 54.4%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   if -4.49999999999999987e-135 < j < 1.25e-203

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. sub-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot t\right)\right) + y \cdot z\right)} \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\mathsf{neg}\left(t\right)\right)} + y \cdot z\right) \]

      5. mul-1-neg N/A

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(-1 \cdot t\right)} + y \cdot z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(a, -1 \cdot t, y \cdot z\right)} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(t\right)}, y \cdot z\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(t\right)}, y \cdot z\right) \]

      9. lower-*.f64 54.9

         \[\leadsto x \cdot \mathsf{fma}\left(a, -t, \color{blue}{y \cdot z}\right) \]

   5. Applied rewrites 54.9%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)} \]

   if 1.25e-203 < j < 8.50000000000000007e80

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c\right)\right) \cdot z + i \cdot t\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)} + i \cdot t\right) \]

      4. remove-double-neg N/A

         \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)}\right) \]

      5. distribute-neg-in N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot t\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot t\right)\right)\right)} \]

      10. sub-neg N/A

          \[\leadsto b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)}\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)} \]

      12. remove-double-neg N/A

          \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{i \cdot t}\right) \]

      13. +-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)} \]

      14. sub-neg N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. lower--.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      16. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\color{blue}{i \cdot t} - c \cdot z\right) \]

      17. lower-*.f64 61.5

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{c \cdot z}\right) \]

   5. Applied rewrites 61.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.75e+124)
     t_1
     (if (<= j -4.1e-135)
       (* i (fma t b (* j (- y))))
       (if (<= j -3.2e-268)
         (* y (* x z))
         (if (<= j 8.5e+80) (* b (- (* t i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.75e+124) {
		tmp = t_1;
	} else if (j <= -4.1e-135) {
		tmp = i * fma(t, b, (j * -y));
	} else if (j <= -3.2e-268) {
		tmp = y * (x * z);
	} else if (j <= 8.5e+80) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.75e+124)
		tmp = t_1;
	elseif (j <= -4.1e-135)
		tmp = Float64(i * fma(t, b, Float64(j * Float64(-y))));
	elseif (j <= -3.2e-268)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 8.5e+80)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e+124], t$95$1, If[LessEqual[j, -4.1e-135], N[(i * N[(t * b + N[(j * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.2e-268], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+80], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.7500000000000001e124 or 8.50000000000000007e80 < j

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 71.1

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 71.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.7500000000000001e124 < j < -4.1000000000000001e-135

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 54.4

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 54.4%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   if -4.1000000000000001e-135 < j < -3.1999999999999999e-268

   1. Initial program 53.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 61.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(x, z, -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{\mathsf{neg}\left(i \cdot j\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(-1 \cdot i\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      10. lower-neg.f64 53.3

          \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-i\right)}\right) \]

   8. Applied rewrites 53.3%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, z, j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 49.5

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   11. Applied rewrites 49.5%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -3.1999999999999999e-268 < j < 8.50000000000000007e80

   1. Initial program 80.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c\right)\right) \cdot z + i \cdot t\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)} + i \cdot t\right) \]

      4. remove-double-neg N/A

         \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)}\right) \]

      5. distribute-neg-in N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot t\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot t\right)\right)\right)} \]

      10. sub-neg N/A

          \[\leadsto b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)}\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)} \]

      12. remove-double-neg N/A

          \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{i \cdot t}\right) \]

      13. +-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)} \]

      14. sub-neg N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. lower--.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      16. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\color{blue}{i \cdot t} - c \cdot z\right) \]

      17. lower-*.f64 55.8

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{c \cdot z}\right) \]

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(y, x, b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -5e+60)
   (* z (fma y x (* b (- c))))
   (if (<= z 6.5e+46)
     (fma j (- (* a c) (* y i)) (* t (* b i)))
     (* z (* x (- y (/ (* b c) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5e+60) {
		tmp = z * fma(y, x, (b * -c));
	} else if (z <= 6.5e+46) {
		tmp = fma(j, ((a * c) - (y * i)), (t * (b * i)));
	} else {
		tmp = z * (x * (y - ((b * c) / x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -5e+60)
		tmp = Float64(z * fma(y, x, Float64(b * Float64(-c))));
	elseif (z <= 6.5e+46)
		tmp = fma(j, Float64(Float64(a * c) - Float64(y * i)), Float64(t * Float64(b * i)));
	else
		tmp = Float64(z * Float64(x * Float64(y - Float64(Float64(b * c) / x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -5e+60], N[(z * N[(y * x + N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+46], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y - N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999975e60

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 70.7

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 70.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto z \cdot \left(c \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} + y \cdot x\right) \]

      2. lift-*.f64 N/A

         \[\leadsto z \cdot \left(c \cdot \left(\mathsf{neg}\left(b\right)\right) + \color{blue}{y \cdot x}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x + c \cdot \left(\mathsf{neg}\left(b\right)\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} + c \cdot \left(\mathsf{neg}\left(b\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(y, x, c \cdot \left(\mathsf{neg}\left(b\right)\right)\right)} \]

      6. lift-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, c \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\mathsf{neg}\left(c \cdot b\right)}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(\mathsf{neg}\left(c\right)\right) \cdot b}\right) \]

      10. lower-neg.f64 72.9

          \[\leadsto z \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(-c\right)} \cdot b\right) \]

   7. Applied rewrites 72.9%

      \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(y, x, \left(-c\right) \cdot b\right)} \]

   if -4.99999999999999975e60 < z < 6.50000000000000008e46

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, b \cdot \color{blue}{\left(t \cdot i\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, \color{blue}{\left(b \cdot t\right) \cdot i}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, \color{blue}{\left(t \cdot b\right)} \cdot i\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, \color{blue}{t \cdot \left(b \cdot i\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, \color{blue}{t \cdot \left(b \cdot i\right)}\right) \]

      6. lower-*.f64 61.8

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

   8. Applied rewrites 61.8%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - i \cdot y, \color{blue}{t \cdot \left(b \cdot i\right)}\right) \]

   if 6.50000000000000008e46 < z

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 60.6

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 60.6%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1 \cdot \frac{b \cdot c}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1 \cdot \frac{b \cdot c}{x}\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot c}{x}\right)\right)}\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(y - \frac{b \cdot c}{x}\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(y - \frac{b \cdot c}{x}\right)}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto z \cdot \left(x \cdot \left(y - \color{blue}{\frac{b \cdot c}{x}}\right)\right) \]

      6. lower-*.f64 60.6

         \[\leadsto z \cdot \left(x \cdot \left(y - \frac{\color{blue}{b \cdot c}}{x}\right)\right) \]

   8. Applied rewrites 60.6%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(y, x, b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, t \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - \frac{b \cdot c}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.15 \cdot 10^{+195}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.15e+195)
   (* c (* a j))
   (if (<= j -6.5e-53)
     (* i (* j (- y)))
     (if (<= j -4.5e-135)
       (* i (* t b))
       (if (<= j 1.7e-231)
         (* y (* x z))
         (if (<= j 1.85e+81) (* b (* t i)) (* j (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.15e+195) {
		tmp = c * (a * j);
	} else if (j <= -6.5e-53) {
		tmp = i * (j * -y);
	} else if (j <= -4.5e-135) {
		tmp = i * (t * b);
	} else if (j <= 1.7e-231) {
		tmp = y * (x * z);
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.15d+195)) then
        tmp = c * (a * j)
    else if (j <= (-6.5d-53)) then
        tmp = i * (j * -y)
    else if (j <= (-4.5d-135)) then
        tmp = i * (t * b)
    else if (j <= 1.7d-231) then
        tmp = y * (x * z)
    else if (j <= 1.85d+81) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.15e+195) {
		tmp = c * (a * j);
	} else if (j <= -6.5e-53) {
		tmp = i * (j * -y);
	} else if (j <= -4.5e-135) {
		tmp = i * (t * b);
	} else if (j <= 1.7e-231) {
		tmp = y * (x * z);
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.15e+195:
		tmp = c * (a * j)
	elif j <= -6.5e-53:
		tmp = i * (j * -y)
	elif j <= -4.5e-135:
		tmp = i * (t * b)
	elif j <= 1.7e-231:
		tmp = y * (x * z)
	elif j <= 1.85e+81:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.15e+195)
		tmp = Float64(c * Float64(a * j));
	elseif (j <= -6.5e-53)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (j <= -4.5e-135)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 1.7e-231)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.85e+81)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.15e+195)
		tmp = c * (a * j);
	elseif (j <= -6.5e-53)
		tmp = i * (j * -y);
	elseif (j <= -4.5e-135)
		tmp = i * (t * b);
	elseif (j <= 1.7e-231)
		tmp = y * (x * z);
	elseif (j <= 1.85e+81)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.15e+195], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e-53], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-135], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-231], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e+81], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.14999999999999991e195

   1. Initial program 51.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 64.8

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 64.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

      2. lower-*.f64 41.2

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   8. Applied rewrites 41.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot j\right)} \cdot c \]

      4. lower-*.f64 41.6

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

   10. Applied rewrites 41.6%

       \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

   if -2.14999999999999991e195 < j < -6.4999999999999997e-53

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(x, z, -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{\mathsf{neg}\left(i \cdot j\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(-1 \cdot i\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      10. lower-neg.f64 48.2

          \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-i\right)}\right) \]

   8. Applied rewrites 48.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, z, j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot y\right)}\right) \]

       4. lower-*.f64 36.4

          \[\leadsto -i \cdot \color{blue}{\left(j \cdot y\right)} \]

   11. Applied rewrites 36.4%

       \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

   if -6.4999999999999997e-53 < j < -4.49999999999999987e-135

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 73.1

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 73.1%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 64.0

          \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   11. Applied rewrites 64.0%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -4.49999999999999987e-135 < j < 1.7e-231

   1. Initial program 65.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(x, z, -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{\mathsf{neg}\left(i \cdot j\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(-1 \cdot i\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      10. lower-neg.f64 49.6

          \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-i\right)}\right) \]

   8. Applied rewrites 49.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, z, j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 45.3

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   11. Applied rewrites 45.3%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if 1.7e-231 < j < 1.85e81

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 40.3

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 40.3%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

       2. *-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       3. lower-*.f64 39.8

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Applied rewrites 39.8%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.85e81 < j

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 75.0

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 53.6

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   8. Applied rewrites 53.6%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.15 \cdot 10^{+195}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -6.5e-53)
   (* y (* i (- j)))
   (if (<= j -4.5e-135)
     (* i (* t b))
     (if (<= j 1.7e-231)
       (* y (* x z))
       (if (<= j 1.85e+81) (* b (* t i)) (* j (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -6.5e-53) {
		tmp = y * (i * -j);
	} else if (j <= -4.5e-135) {
		tmp = i * (t * b);
	} else if (j <= 1.7e-231) {
		tmp = y * (x * z);
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-6.5d-53)) then
        tmp = y * (i * -j)
    else if (j <= (-4.5d-135)) then
        tmp = i * (t * b)
    else if (j <= 1.7d-231) then
        tmp = y * (x * z)
    else if (j <= 1.85d+81) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -6.5e-53) {
		tmp = y * (i * -j);
	} else if (j <= -4.5e-135) {
		tmp = i * (t * b);
	} else if (j <= 1.7e-231) {
		tmp = y * (x * z);
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -6.5e-53:
		tmp = y * (i * -j)
	elif j <= -4.5e-135:
		tmp = i * (t * b)
	elif j <= 1.7e-231:
		tmp = y * (x * z)
	elif j <= 1.85e+81:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -6.5e-53)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (j <= -4.5e-135)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 1.7e-231)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.85e+81)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -6.5e-53)
		tmp = y * (i * -j);
	elseif (j <= -4.5e-135)
		tmp = i * (t * b);
	elseif (j <= 1.7e-231)
		tmp = y * (x * z);
	elseif (j <= 1.85e+81)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -6.5e-53], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-135], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-231], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e+81], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.4999999999999997e-53

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(x, z, -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{\mathsf{neg}\left(i \cdot j\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(-1 \cdot i\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      10. lower-neg.f64 47.2

          \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-i\right)}\right) \]

   8. Applied rewrites 47.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, z, j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y \cdot \color{blue}{\left(\mathsf{neg}\left(i \cdot j\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto y \cdot \left(\mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(i\right)\right)\right)} \]

       4. mul-1-neg N/A

          \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

       5. lower-*.f64 N/A

          \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-1 \cdot i\right)\right)} \]

       6. mul-1-neg N/A

          \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

       7. lower-neg.f64 37.4

          \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(-i\right)}\right) \]

   11. Applied rewrites 37.4%

       \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   if -6.4999999999999997e-53 < j < -4.49999999999999987e-135

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 73.1

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 73.1%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 64.0

          \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   11. Applied rewrites 64.0%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -4.49999999999999987e-135 < j < 1.7e-231

   1. Initial program 65.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(x, z, -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{\mathsf{neg}\left(i \cdot j\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, \color{blue}{j \cdot \left(-1 \cdot i\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      10. lower-neg.f64 49.6

          \[\leadsto y \cdot \mathsf{fma}\left(x, z, j \cdot \color{blue}{\left(-i\right)}\right) \]

   8. Applied rewrites 49.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(x, z, j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 45.3

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   11. Applied rewrites 45.3%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if 1.7e-231 < j < 1.85e81

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 40.3

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 40.3%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

       2. *-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       3. lower-*.f64 39.8

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Applied rewrites 39.8%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.85e81 < j

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 75.0

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 53.6

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   8. Applied rewrites 53.6%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 53.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma j c (* x (- t))))))
   (if (<= a -1.4e+51)
     t_1
     (if (<= a 2.3e+51) (* i (fma j (- y) (* t b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(j, c, (x * -t));
	double tmp;
	if (a <= -1.4e+51) {
		tmp = t_1;
	} else if (a <= 2.3e+51) {
		tmp = i * fma(j, -y, (t * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(j, c, Float64(x * Float64(-t))))
	tmp = 0.0
	if (a <= -1.4e+51)
		tmp = t_1;
	elseif (a <= 2.3e+51)
		tmp = Float64(i * fma(j, Float64(-y), Float64(t * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+51], t$95$1, If[LessEqual[a, 2.3e+51], N[(i * N[(j * (-y) + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.40000000000000002e51 or 2.30000000000000005e51 < a

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 68.3

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 68.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   if -1.40000000000000002e51 < a < 2.30000000000000005e51

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto i \cdot \left(\color{blue}{\left(\mathsf{neg}\left(j \cdot y\right)\right)} + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \left(\color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \color{blue}{1} \cdot \left(b \cdot t\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \color{blue}{b \cdot t}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(j, -1 \cdot y, b \cdot t\right)} \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, b \cdot t\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, b \cdot t\right) \]

      11. lower-*.f64 46.1

          \[\leadsto i \cdot \mathsf{fma}\left(j, -y, \color{blue}{b \cdot t}\right) \]

   5. Applied rewrites 46.1%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(j, -y, b \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(t, i, c \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma j c (* x (- t))))))
   (if (<= a -1.9e+44)
     t_1
     (if (<= a 2.9e+87) (* b (fma t i (* c (- z)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(j, c, (x * -t));
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_1;
	} else if (a <= 2.9e+87) {
		tmp = b * fma(t, i, (c * -z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(j, c, Float64(x * Float64(-t))))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_1;
	elseif (a <= 2.9e+87)
		tmp = Float64(b * fma(t, i, Float64(c * Float64(-z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$1, If[LessEqual[a, 2.9e+87], N[(b * N[(t * i + N[(c * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9000000000000001e44 or 2.8999999999999998e87 < a

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 70.3

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 70.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   if -1.9000000000000001e44 < a < 2.8999999999999998e87

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + i \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + i \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t + -1 \cdot \left(c \cdot z\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} + -1 \cdot \left(c \cdot z\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto b \cdot \color{blue}{\mathsf{fma}\left(t, i, -1 \cdot \left(c \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto b \cdot \mathsf{fma}\left(t, i, \color{blue}{\mathsf{neg}\left(c \cdot z\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto b \cdot \mathsf{fma}\left(t, i, \mathsf{neg}\left(\color{blue}{z \cdot c}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \mathsf{fma}\left(t, i, \color{blue}{z \cdot \left(\mathsf{neg}\left(c\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \mathsf{fma}\left(t, i, z \cdot \color{blue}{\left(-1 \cdot c\right)}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto b \cdot \mathsf{fma}\left(t, i, \color{blue}{z \cdot \left(-1 \cdot c\right)}\right) \]

      10. mul-1-neg N/A

          \[\leadsto b \cdot \mathsf{fma}\left(t, i, z \cdot \color{blue}{\left(\mathsf{neg}\left(c\right)\right)}\right) \]

      11. lower-neg.f64 42.4

          \[\leadsto b \cdot \mathsf{fma}\left(t, i, z \cdot \color{blue}{\left(-c\right)}\right) \]

   8. Applied rewrites 42.4%

      \[\leadsto \color{blue}{b \cdot \mathsf{fma}\left(t, i, z \cdot \left(-c\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(t, i, c \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 52.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma j c (* x (- t))))))
   (if (<= a -1.9e+44) t_1 (if (<= a 2.9e+87) (* b (- (* t i) (* z c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(j, c, (x * -t));
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_1;
	} else if (a <= 2.9e+87) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(j, c, Float64(x * Float64(-t))))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_1;
	elseif (a <= 2.9e+87)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(j * c + N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$1, If[LessEqual[a, 2.9e+87], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9000000000000001e44 or 2.8999999999999998e87 < a

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 70.3

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 70.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   if -1.9000000000000001e44 < a < 2.8999999999999998e87

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(\mathsf{neg}\left(c\right)\right) \cdot z\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c\right)\right) \cdot z + i \cdot t\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)} + i \cdot t\right) \]

      4. remove-double-neg N/A

         \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)}\right) \]

      5. distribute-neg-in N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - i \cdot t\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      9. mul-1-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - i \cdot t\right)\right)\right)} \]

      10. sub-neg N/A

          \[\leadsto b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)}\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)} \]

      12. remove-double-neg N/A

          \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{i \cdot t}\right) \]

      13. +-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)} \]

      14. sub-neg N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      15. lower--.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      16. lower-*.f64 N/A

          \[\leadsto b \cdot \left(\color{blue}{i \cdot t} - c \cdot z\right) \]

      17. lower-*.f64 42.3

          \[\leadsto b \cdot \left(i \cdot t - \color{blue}{c \cdot z}\right) \]

   5. Applied rewrites 42.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.2e+116)
   (* c (* a j))
   (if (<= a -7e-115)
     (* i (* t b))
     (if (<= a 1.4e+94) (* x (* y z)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.2e+116) {
		tmp = c * (a * j);
	} else if (a <= -7e-115) {
		tmp = i * (t * b);
	} else if (a <= 1.4e+94) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.2d+116)) then
        tmp = c * (a * j)
    else if (a <= (-7d-115)) then
        tmp = i * (t * b)
    else if (a <= 1.4d+94) then
        tmp = x * (y * z)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.2e+116) {
		tmp = c * (a * j);
	} else if (a <= -7e-115) {
		tmp = i * (t * b);
	} else if (a <= 1.4e+94) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.2e+116:
		tmp = c * (a * j)
	elif a <= -7e-115:
		tmp = i * (t * b)
	elif a <= 1.4e+94:
		tmp = x * (y * z)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.2e+116)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= -7e-115)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 1.4e+94)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.2e+116)
		tmp = c * (a * j);
	elseif (a <= -7e-115)
		tmp = i * (t * b);
	elseif (a <= 1.4e+94)
		tmp = x * (y * z);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.2e+116], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-115], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+94], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2e116

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 70.6

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 70.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

      2. lower-*.f64 49.1

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   8. Applied rewrites 49.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot j\right)} \cdot c \]

      4. lower-*.f64 49.1

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

   10. Applied rewrites 49.1%

       \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

   if -2.2e116 < a < -7.0000000000000004e-115

   1. Initial program 70.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 67.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 52.4

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 52.4%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 44.3

          \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   11. Applied rewrites 44.3%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -7.0000000000000004e-115 < a < 1.39999999999999999e94

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 48.4

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 48.4%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      3. lower-*.f64 32.0

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Applied rewrites 32.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 1.39999999999999999e94 < a

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 54.6

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 54.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 47.4

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   8. Applied rewrites 47.4%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.2e+116)
   (* a (* c j))
   (if (<= a -7e-115)
     (* i (* t b))
     (if (<= a 1.4e+94) (* x (* y z)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.2e+116) {
		tmp = a * (c * j);
	} else if (a <= -7e-115) {
		tmp = i * (t * b);
	} else if (a <= 1.4e+94) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.2d+116)) then
        tmp = a * (c * j)
    else if (a <= (-7d-115)) then
        tmp = i * (t * b)
    else if (a <= 1.4d+94) then
        tmp = x * (y * z)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.2e+116) {
		tmp = a * (c * j);
	} else if (a <= -7e-115) {
		tmp = i * (t * b);
	} else if (a <= 1.4e+94) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.2e+116:
		tmp = a * (c * j)
	elif a <= -7e-115:
		tmp = i * (t * b)
	elif a <= 1.4e+94:
		tmp = x * (y * z)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.2e+116)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -7e-115)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 1.4e+94)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.2e+116)
		tmp = a * (c * j);
	elseif (a <= -7e-115)
		tmp = i * (t * b);
	elseif (a <= 1.4e+94)
		tmp = x * (y * z);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.2e+116], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-115], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+94], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2e116

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 70.6

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 70.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

      2. lower-*.f64 49.1

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   8. Applied rewrites 49.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -2.2e116 < a < -7.0000000000000004e-115

   1. Initial program 70.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 67.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 52.4

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 52.4%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 44.3

          \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   11. Applied rewrites 44.3%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -7.0000000000000004e-115 < a < 1.39999999999999999e94

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 48.4

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 48.4%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      3. lower-*.f64 32.0

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Applied rewrites 32.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 1.39999999999999999e94 < a

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 54.6

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 54.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 47.4

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   8. Applied rewrites 47.4%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.75e+124)
   (* a (* c j))
   (if (<= j 1.85e+81) (* b (* t i)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.75e+124) {
		tmp = a * (c * j);
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.75d+124)) then
        tmp = a * (c * j)
    else if (j <= 1.85d+81) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.75e+124) {
		tmp = a * (c * j);
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.75e+124:
		tmp = a * (c * j)
	elif j <= 1.85e+81:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.75e+124)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 1.85e+81)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.75e+124)
		tmp = a * (c * j);
	elseif (j <= 1.85e+81)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.75e+124], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e+81], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.7500000000000001e124

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 48.8

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 48.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

      2. lower-*.f64 33.2

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   8. Applied rewrites 33.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.7500000000000001e124 < j < 1.85e81

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 39.7

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 39.7%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

       2. *-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       3. lower-*.f64 28.2

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Applied rewrites 28.2%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.85e81 < j

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\color{blue}{a \cdot c} - i \cdot y\right) \]

      4. lower-*.f64 75.0

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{i \cdot y}\right) \]

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 53.6

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]

   8. Applied rewrites 53.6%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 27: 30.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1.75e+124) t_1 (if (<= j 1.85e+81) (* b (* t i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.75e+124) {
		tmp = t_1;
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-1.75d+124)) then
        tmp = t_1
    else if (j <= 1.85d+81) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.75e+124) {
		tmp = t_1;
	} else if (j <= 1.85e+81) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1.75e+124:
		tmp = t_1
	elif j <= 1.85e+81:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -1.75e+124)
		tmp = t_1;
	elseif (j <= 1.85e+81)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -1.75e+124)
		tmp = t_1;
	elseif (j <= 1.85e+81)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e+124], t$95$1, If[LessEqual[j, 1.85e+81], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.7500000000000001e124 or 1.85e81 < j

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 57.1

          \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Applied rewrites 57.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

      2. lower-*.f64 44.1

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   8. Applied rewrites 44.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.7500000000000001e124 < j < 1.85e81

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(x \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{\left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} \]

   5. Applied rewrites 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(t, \mathsf{fma}\left(a, -x, i \cdot b\right), z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)\right)\right)} \]

   6. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + -1 \cdot \left(j \cdot y\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(t, b, -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{\mathsf{neg}\left(j \cdot y\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, \color{blue}{j \cdot \left(-1 \cdot y\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 39.7

          \[\leadsto i \cdot \mathsf{fma}\left(t, b, j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Applied rewrites 39.7%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(t, b, j \cdot \left(-y\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

       2. *-commutative N/A

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

       3. lower-*.f64 28.2

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Applied rewrites 28.2%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 23.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   2. +-commutative N/A

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   3. *-commutative N/A

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right) \]

   4. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(t \cdot x\right)}\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

   7. mul-1-neg N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

   8. lower-*.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{t \cdot \left(-1 \cdot x\right)}\right) \]

   9. mul-1-neg N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

   10. lower-neg.f64 36.4

       \[\leadsto a \cdot \mathsf{fma}\left(j, c, t \cdot \color{blue}{\left(-x\right)}\right) \]

5. Applied rewrites 36.4%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, t \cdot \left(-x\right)\right)} \]

6. Taylor expanded in j around inf

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   2. lower-*.f64 22.1

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

8. Applied rewrites 22.1%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
9. Add Preprocessing

Developer Target 1: 59.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))