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

Percentage Accurate: 72.9% → 80.6%

Time: 21.8s

Alternatives: 26

Speedup: 0.9×

• 57.8% 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: 72.9% accurate, 1.0× speedup

Math

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

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: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{if}\;a \leq -1050000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, x \cdot y\right), t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (fma
          a
          (fma j c (- 0.0 (* t x)))
          (fma b (- (* t i) (* c z)) (* y (fma j (- 0.0 i) (* x z)))))))
   (if (<= a -1050000000.0)
     t_1
     (if (<= a 4.8e+14)
       (fma
        j
        (- (* a c) (* i y))
        (fma z (fma c (- 0.0 b) (* x y)) (* t (fma a (- 0.0 x) (* b 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 = fma(a, fma(j, c, (0.0 - (t * x))), fma(b, ((t * i) - (c * z)), (y * fma(j, (0.0 - i), (x * z)))));
	double tmp;
	if (a <= -1050000000.0) {
		tmp = t_1;
	} else if (a <= 4.8e+14) {
		tmp = fma(j, ((a * c) - (i * y)), fma(z, fma(c, (0.0 - b), (x * y)), (t * fma(a, (0.0 - x), (b * i)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), fma(b, Float64(Float64(t * i) - Float64(c * z)), Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)))))
	tmp = 0.0
	if (a <= -1050000000.0)
		tmp = t_1;
	elseif (a <= 4.8e+14)
		tmp = fma(j, Float64(Float64(a * c) - Float64(i * y)), fma(z, fma(c, Float64(0.0 - b), Float64(x * y)), Float64(t * fma(a, Float64(0.0 - x), Float64(b * i)))));
	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[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1050000000.0], t$95$1, If[LessEqual[a, 4.8e+14], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(c * N[(0.0 - b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * N[(0.0 - x), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05e9 or 4.8e14 < a

   1. Initial program 64.1%

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

   3. Taylor expanded in y around 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. Simplified 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   if -1.05e9 < a < 4.8e14

   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. accelerator-lowering-fma.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. +-commutative N/A

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

   5. Simplified 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, y \cdot x\right), t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1050000000:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, x \cdot y\right), t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\mathsf{fma}\left(j, \frac{a \cdot c - i \cdot y}{t}, \frac{z \cdot \mathsf{fma}\left(c, 0 - b, x \cdot y\right)}{t} + b \cdot i\right) - a \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t 6.5e-85)
   (fma
    a
    (fma j c (- 0.0 (* t x)))
    (fma b (- (* t i) (* c z)) (* y (fma j (- 0.0 i) (* x z)))))
   (*
    t
    (-
     (fma
      j
      (/ (- (* a c) (* i y)) t)
      (+ (/ (* z (fma c (- 0.0 b) (* x y))) t) (* b i)))
     (* a 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 (t <= 6.5e-85) {
		tmp = fma(a, fma(j, c, (0.0 - (t * x))), fma(b, ((t * i) - (c * z)), (y * fma(j, (0.0 - i), (x * z)))));
	} else {
		tmp = t * (fma(j, (((a * c) - (i * y)) / t), (((z * fma(c, (0.0 - b), (x * y))) / t) + (b * i))) - (a * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= 6.5e-85)
		tmp = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), fma(b, Float64(Float64(t * i) - Float64(c * z)), Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)))));
	else
		tmp = Float64(t * Float64(fma(j, Float64(Float64(Float64(a * c) - Float64(i * y)) / t), Float64(Float64(Float64(z * fma(c, Float64(0.0 - b), Float64(x * y))) / t) + Float64(b * i))) - Float64(a * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, 6.5e-85], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(j * N[(N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(N[(z * N[(c * N[(0.0 - b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.5e-85

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   if 6.5e-85 < t

   1. Initial program 70.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 89.1%

      \[\leadsto \color{blue}{t \cdot \left(\mathsf{fma}\left(j, \frac{a \cdot c - i \cdot y}{t}, \frac{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)}{t} + i \cdot b\right) - a \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\mathsf{fma}\left(j, \frac{a \cdot c - i \cdot y}{t}, \frac{z \cdot \mathsf{fma}\left(c, 0 - b, x \cdot y\right)}{t} + b \cdot i\right) - a \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\mathsf{fma}\left(j, \frac{a \cdot c - i \cdot y}{t}, \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(b, 0 - c, x \cdot y\right)}{t}, b \cdot i\right)\right) - a \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t 6.5e-85)
   (fma
    a
    (fma j c (- 0.0 (* t x)))
    (fma b (- (* t i) (* c z)) (* y (fma j (- 0.0 i) (* x z)))))
   (*
    t
    (-
     (fma
      j
      (/ (- (* a c) (* i y)) t)
      (fma z (/ (fma b (- 0.0 c) (* x y)) t) (* b i)))
     (* a 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 (t <= 6.5e-85) {
		tmp = fma(a, fma(j, c, (0.0 - (t * x))), fma(b, ((t * i) - (c * z)), (y * fma(j, (0.0 - i), (x * z)))));
	} else {
		tmp = t * (fma(j, (((a * c) - (i * y)) / t), fma(z, (fma(b, (0.0 - c), (x * y)) / t), (b * i))) - (a * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= 6.5e-85)
		tmp = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), fma(b, Float64(Float64(t * i) - Float64(c * z)), Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)))));
	else
		tmp = Float64(t * Float64(fma(j, Float64(Float64(Float64(a * c) - Float64(i * y)) / t), fma(z, Float64(fma(b, Float64(0.0 - c), Float64(x * y)) / t), Float64(b * i))) - Float64(a * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, 6.5e-85], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(j * N[(N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(z * N[(N[(b * N[(0.0 - c), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.5e-85

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   if 6.5e-85 < t

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. accelerator-lowering-fma.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. +-commutative N/A

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

   5. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, y \cdot x\right), t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)\right)\right)} \]

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

   8. Simplified 89.1%

      \[\leadsto \color{blue}{t \cdot \left(\mathsf{fma}\left(j, \frac{c \cdot a - i \cdot y}{t}, \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(b, 0 - c, y \cdot x\right)}{t}, b \cdot i\right)\right) - x \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\mathsf{fma}\left(j, \frac{a \cdot c - i \cdot y}{t}, \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(b, 0 - c, x \cdot y\right)}{t}, b \cdot i\right)\right) - a \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.7 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(c, 0 - b, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z 4.7e+198)
   (fma
    a
    (fma j c (- 0.0 (* t x)))
    (fma b (- (* t i) (* c z)) (* y (fma j (- 0.0 i) (* x z)))))
   (* z (fma c (- 0.0 b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 4.7e+198) {
		tmp = fma(a, fma(j, c, (0.0 - (t * x))), fma(b, ((t * i) - (c * z)), (y * fma(j, (0.0 - i), (x * z)))));
	} else {
		tmp = z * fma(c, (0.0 - b), (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= 4.7e+198)
		tmp = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), fma(b, Float64(Float64(t * i) - Float64(c * z)), Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)))));
	else
		tmp = Float64(z * fma(c, Float64(0.0 - b), Float64(x * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, 4.7e+198], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * N[(0.0 - b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.7000000000000002e198

   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 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. Simplified 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   if 4.7000000000000002e198 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 89.2

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.7 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, t \cdot i - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(c, 0 - b, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(c, 0 - b, x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 600000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.7e+121)
   (* y (- (* x z) (* j i)))
   (if (<= y -1.12e+43)
     (* z (fma c (- 0.0 b) (* x y)))
     (if (<= y -1.1e-139)
       (* t (fma a (- 0.0 x) (* b i)))
       (if (<= y -9e-250)
         (* c (- (* a j) (* b z)))
         (if (<= y 600000000.0)
           (* a (fma j c (- 0.0 (* t x))))
           (* y (fma j (- 0.0 i) (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.7e+121) {
		tmp = y * ((x * z) - (j * i));
	} else if (y <= -1.12e+43) {
		tmp = z * fma(c, (0.0 - b), (x * y));
	} else if (y <= -1.1e-139) {
		tmp = t * fma(a, (0.0 - x), (b * i));
	} else if (y <= -9e-250) {
		tmp = c * ((a * j) - (b * z));
	} else if (y <= 600000000.0) {
		tmp = a * fma(j, c, (0.0 - (t * x)));
	} else {
		tmp = y * fma(j, (0.0 - i), (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.7e+121)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (y <= -1.12e+43)
		tmp = Float64(z * fma(c, Float64(0.0 - b), Float64(x * y)));
	elseif (y <= -1.1e-139)
		tmp = Float64(t * fma(a, Float64(0.0 - x), Float64(b * i)));
	elseif (y <= -9e-250)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif (y <= 600000000.0)
		tmp = Float64(a * fma(j, c, Float64(0.0 - Float64(t * x))));
	else
		tmp = Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.7e+121], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.12e+43], N[(z * N[(c * N[(0.0 - b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-139], N[(t * N[(a * N[(0.0 - x), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-250], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 600000000.0], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.70000000000000005e121

   1. Initial program 66.8%

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

   3. Taylor expanded in 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. Simplified 82.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 77.0

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

   8. Simplified 77.0%

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

   if -1.70000000000000005e121 < y < -1.12e43

   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 z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 68.9

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 68.9%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   if -1.12e43 < y < -1.10000000000000005e-139

   1. Initial program 64.9%

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

   3. Taylor expanded in t around 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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      12. *-commutative N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

      13. *-lowering-*.f64 68.3

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)} \]

   if -1.10000000000000005e-139 < y < -8.99999999999999987e-250

   1. Initial program 73.2%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 77.1

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

   5. Simplified 77.1%

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

   if -8.99999999999999987e-250 < y < 6e8

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 53.7

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   if 6e8 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

      9. *-lowering-*.f64 77.4

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(c, 0 - b, x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 600000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - c \cdot z, x \cdot \left(z \cdot y - t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.55e+91)
   (+ (* y (* x z)) (* j (- (* a c) (* i y))))
   (if (<= y -5.3e-160)
     (fma b (- (* t i) (* c z)) (* x (- (* z y) (* t a))))
     (if (<= y 4.3e+63)
       (fma a (fma j c (- 0.0 (* t x))) (* b (* t i)))
       (* y (fma j (- 0.0 i) (* x z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.55e+91) {
		tmp = (y * (x * z)) + (j * ((a * c) - (i * y)));
	} else if (y <= -5.3e-160) {
		tmp = fma(b, ((t * i) - (c * z)), (x * ((z * y) - (t * a))));
	} else if (y <= 4.3e+63) {
		tmp = fma(a, fma(j, c, (0.0 - (t * x))), (b * (t * i)));
	} else {
		tmp = y * fma(j, (0.0 - i), (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.55e+91)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(j * Float64(Float64(a * c) - Float64(i * y))));
	elseif (y <= -5.3e-160)
		tmp = fma(b, Float64(Float64(t * i) - Float64(c * z)), Float64(x * Float64(Float64(z * y) - Float64(t * a))));
	elseif (y <= 4.3e+63)
		tmp = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), Float64(b * Float64(t * i)));
	else
		tmp = Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.55e+91], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.3e-160], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+63], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.54999999999999999e91

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 77.0

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

   5. Simplified 77.0%

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

   if -1.54999999999999999e91 < y < -5.3000000000000001e-160

   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 j around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. sub-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

      17. *-lowering-*.f64 N/A

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

      18. --lowering--.f64 N/A

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

      19. *-lowering-*.f64 N/A

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

      20. *-lowering-*.f64 79.6

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

   5. Simplified 79.6%

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

   if -5.3000000000000001e-160 < y < 4.3e63

   1. Initial program 75.8%

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

   3. Taylor expanded in 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. Simplified 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 70.1

         \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \color{blue}{\left(i \cdot t\right)}\right) \]

   8. Simplified 70.1%

      \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]

   if 4.3e63 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

      9. *-lowering-*.f64 81.2

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-160}:\\ \;\;\;\;\mathsf{fma}\left(b, t \cdot i - c \cdot z, x \cdot \left(z \cdot y - t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 520000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -4.2e+32)
   (fma j (- (* a c) (* i y)) (* x (* z y)))
   (if (<= y -4.2e-139)
     (* t (fma a (- 0.0 x) (* b i)))
     (if (<= y -6.2e-251)
       (* c (- (* a j) (* b z)))
       (if (<= y 520000000000.0)
         (* a (fma j c (- 0.0 (* t x))))
         (* y (fma j (- 0.0 i) (* x z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -4.2e+32) {
		tmp = fma(j, ((a * c) - (i * y)), (x * (z * y)));
	} else if (y <= -4.2e-139) {
		tmp = t * fma(a, (0.0 - x), (b * i));
	} else if (y <= -6.2e-251) {
		tmp = c * ((a * j) - (b * z));
	} else if (y <= 520000000000.0) {
		tmp = a * fma(j, c, (0.0 - (t * x)));
	} else {
		tmp = y * fma(j, (0.0 - i), (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -4.2e+32)
		tmp = fma(j, Float64(Float64(a * c) - Float64(i * y)), Float64(x * Float64(z * y)));
	elseif (y <= -4.2e-139)
		tmp = Float64(t * fma(a, Float64(0.0 - x), Float64(b * i)));
	elseif (y <= -6.2e-251)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif (y <= 520000000000.0)
		tmp = Float64(a * fma(j, c, Float64(0.0 - Float64(t * x))));
	else
		tmp = Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -4.2e+32], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-139], N[(t * N[(a * N[(0.0 - x), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-251], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 520000000000.0], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.2000000000000001e32

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. accelerator-lowering-fma.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. +-commutative N/A

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

   5. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, y \cdot x\right), t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)\right)\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 73.0

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

   8. Simplified 73.0%

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

   if -4.2000000000000001e32 < y < -4.20000000000000016e-139

   1. Initial program 64.9%

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

   3. Taylor expanded in t around 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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      12. *-commutative N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

      13. *-lowering-*.f64 68.3

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)} \]

   if -4.20000000000000016e-139 < y < -6.20000000000000006e-251

   1. Initial program 73.2%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 77.1

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

   5. Simplified 77.1%

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

   if -6.20000000000000006e-251 < y < 5.2e11

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 53.7

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   if 5.2e11 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

      9. *-lowering-*.f64 77.4

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 520000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 900000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.4e+47)
   (* y (- (* x z) (* j i)))
   (if (<= y -1.18e-138)
     (* t (fma a (- 0.0 x) (* b i)))
     (if (<= y -4e-251)
       (* c (- (* a j) (* b z)))
       (if (<= y 900000000000.0)
         (* a (fma j c (- 0.0 (* t x))))
         (* y (fma j (- 0.0 i) (* x z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.4e+47) {
		tmp = y * ((x * z) - (j * i));
	} else if (y <= -1.18e-138) {
		tmp = t * fma(a, (0.0 - x), (b * i));
	} else if (y <= -4e-251) {
		tmp = c * ((a * j) - (b * z));
	} else if (y <= 900000000000.0) {
		tmp = a * fma(j, c, (0.0 - (t * x)));
	} else {
		tmp = y * fma(j, (0.0 - i), (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.4e+47)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (y <= -1.18e-138)
		tmp = Float64(t * fma(a, Float64(0.0 - x), Float64(b * i)));
	elseif (y <= -4e-251)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif (y <= 900000000000.0)
		tmp = Float64(a * fma(j, c, Float64(0.0 - Float64(t * x))));
	else
		tmp = Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.4e+47], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.18e-138], N[(t * N[(a * N[(0.0 - x), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-251], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 900000000000.0], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.40000000000000019e47

   1. Initial program 67.4%

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

   3. Taylor expanded in y around 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. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 64.5

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

   8. Simplified 64.5%

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

   if -2.40000000000000019e47 < y < -1.18e-138

   1. Initial program 64.9%

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

   3. Taylor expanded in t around 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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      12. *-commutative N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

      13. *-lowering-*.f64 68.3

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)} \]

   if -1.18e-138 < y < -4.00000000000000006e-251

   1. Initial program 73.2%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 77.1

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

   5. Simplified 77.1%

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

   if -4.00000000000000006e-251 < y < 9e11

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 53.7

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   if 9e11 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

      9. *-lowering-*.f64 77.4

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 900000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-250}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 255000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* j i)))))
   (if (<= y -2.5e+44)
     t_1
     (if (<= y -2.4e-138)
       (* t (fma a (- 0.0 x) (* b i)))
       (if (<= y -1.06e-250)
         (* c (- (* a j) (* b z)))
         (if (<= y 255000000000.0) (* a (fma j c (- 0.0 (* t x)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (j * i));
	double tmp;
	if (y <= -2.5e+44) {
		tmp = t_1;
	} else if (y <= -2.4e-138) {
		tmp = t * fma(a, (0.0 - x), (b * i));
	} else if (y <= -1.06e-250) {
		tmp = c * ((a * j) - (b * z));
	} else if (y <= 255000000000.0) {
		tmp = a * fma(j, c, (0.0 - (t * x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(j * i)))
	tmp = 0.0
	if (y <= -2.5e+44)
		tmp = t_1;
	elseif (y <= -2.4e-138)
		tmp = Float64(t * fma(a, Float64(0.0 - x), Float64(b * i)));
	elseif (y <= -1.06e-250)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif (y <= 255000000000.0)
		tmp = Float64(a * fma(j, c, Float64(0.0 - Float64(t * x))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+44], t$95$1, If[LessEqual[y, -2.4e-138], N[(t * N[(a * N[(0.0 - x), $MachinePrecision] + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.06e-250], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 255000000000.0], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4999999999999998e44 or 2.55e11 < y

   1. Initial program 72.3%

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

   3. Taylor expanded in 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. Simplified 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 71.6

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

   8. Simplified 71.6%

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

   if -2.4999999999999998e44 < y < -2.3999999999999999e-138

   1. Initial program 64.9%

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

   3. Taylor expanded in t around 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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, \color{blue}{0 - x}, b \cdot i\right) \]

      12. *-commutative N/A

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

      13. *-lowering-*.f64 68.3

          \[\leadsto t \cdot \mathsf{fma}\left(a, 0 - x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)} \]

   if -2.3999999999999999e-138 < y < -1.05999999999999993e-250

   1. Initial program 73.2%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 77.1

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

   5. Simplified 77.1%

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

   if -1.05999999999999993e-250 < y < 2.55e11

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 53.7

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(a, 0 - x, b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-250}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 255000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1e+52)
   (+ (* y (* x z)) (* j (- (* a c) (* i y))))
   (if (<= y 3.3e+61)
     (fma a (fma j c (- 0.0 (* t x))) (* b (* t i)))
     (* y (fma j (- 0.0 i) (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1e+52) {
		tmp = (y * (x * z)) + (j * ((a * c) - (i * y)));
	} else if (y <= 3.3e+61) {
		tmp = fma(a, fma(j, c, (0.0 - (t * x))), (b * (t * i)));
	} else {
		tmp = y * fma(j, (0.0 - i), (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1e+52)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(j * Float64(Float64(a * c) - Float64(i * y))));
	elseif (y <= 3.3e+61)
		tmp = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), Float64(b * Float64(t * i)));
	else
		tmp = Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1e+52], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+61], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999999e51

   1. Initial program 66.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 76.1

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

   5. Simplified 76.1%

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

   if -9.9999999999999999e51 < y < 3.2999999999999998e61

   1. Initial program 73.4%

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

   3. Taylor expanded in y around 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. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 68.2

         \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \color{blue}{\left(i \cdot t\right)}\right) \]

   8. Simplified 68.2%

      \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]

   if 3.2999999999999998e61 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

      9. *-lowering-*.f64 81.2

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.6e+49)
   (fma j (- (* a c) (* i y)) (* x (* z y)))
   (if (<= y 1.65e+61)
     (fma a (fma j c (- 0.0 (* t x))) (* b (* t i)))
     (* y (fma j (- 0.0 i) (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.6e+49) {
		tmp = fma(j, ((a * c) - (i * y)), (x * (z * y)));
	} else if (y <= 1.65e+61) {
		tmp = fma(a, fma(j, c, (0.0 - (t * x))), (b * (t * i)));
	} else {
		tmp = y * fma(j, (0.0 - i), (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.6e+49)
		tmp = fma(j, Float64(Float64(a * c) - Float64(i * y)), Float64(x * Float64(z * y)));
	elseif (y <= 1.65e+61)
		tmp = fma(a, fma(j, c, Float64(0.0 - Float64(t * x))), Float64(b * Float64(t * i)));
	else
		tmp = Float64(y * fma(j, Float64(0.0 - i), Float64(x * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.6e+49], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+61], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * N[(0.0 - i), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999989e49

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. accelerator-lowering-fma.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. +-commutative N/A

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

   5. Simplified 61.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, y \cdot x\right), t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)\right)\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 74.1

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

   8. Simplified 74.1%

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

   if -2.59999999999999989e49 < y < 1.6499999999999999e61

   1. Initial program 73.4%

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

   3. Taylor expanded in y around 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. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]

      2. *-lowering-*.f64 68.2

         \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \color{blue}{\left(i \cdot t\right)}\right) \]

   8. Simplified 68.2%

      \[\leadsto \mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \color{blue}{b \cdot \left(i \cdot t\right)}\right) \]

   if 1.6499999999999999e61 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \color{blue}{0 - i}, x \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

      9. *-lowering-*.f64 81.2

         \[\leadsto y \cdot \mathsf{fma}\left(j, 0 - i, \color{blue}{z \cdot x}\right) \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), b \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(j, 0 - i, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;j \leq -1.26 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(x, z \cdot y - t \cdot a, i \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma j (- (* a c) (* i y)) (* x (* z y)))))
   (if (<= j -1.26e-129)
     t_1
     (if (<= j 2.65e-17) (fma x (- (* z y) (* t a)) (* i (* 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 = fma(j, ((a * c) - (i * y)), (x * (z * y)));
	double tmp;
	if (j <= -1.26e-129) {
		tmp = t_1;
	} else if (j <= 2.65e-17) {
		tmp = fma(x, ((z * y) - (t * a)), (i * (t * b)));
	} 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(i * y)), Float64(x * Float64(z * y)))
	tmp = 0.0
	if (j <= -1.26e-129)
		tmp = t_1;
	elseif (j <= 2.65e-17)
		tmp = fma(x, Float64(Float64(z * y) - Float64(t * a)), Float64(i * 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[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.26e-129], t$95$1, If[LessEqual[j, 2.65e-17], N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1.2599999999999999e-129 or 2.6499999999999999e-17 < j

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. accelerator-lowering-fma.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. +-commutative N/A

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

   5. Simplified 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - i \cdot y, \mathsf{fma}\left(z, \mathsf{fma}\left(c, 0 - b, y \cdot x\right), t \cdot \mathsf{fma}\left(a, 0 - x, i \cdot b\right)\right)\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 68.7

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

   8. Simplified 68.7%

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

   if -1.2599999999999999e-129 < j < 2.6499999999999999e-17

   1. Initial program 71.8%

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

   3. Taylor expanded in c around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-+l+ N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-in N/A

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

      13. *-lft-identity N/A

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

      14. metadata-eval N/A

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

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

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

   5. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, i \cdot \mathsf{fma}\left(j, 0 - y, b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0

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

      1. *-lowering-*.f64 64.0

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

   8. Simplified 64.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.26 \cdot 10^{-129}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(x, z \cdot y - t \cdot a, i \cdot \left(t \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;y \leq 9000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* j i)))))
   (if (<= y -1.7e+66)
     t_1
     (if (<= y -4.5e-250)
       (* b (- (* t i) (* c z)))
       (if (<= y 9000000000.0) (* a (fma j c (- 0.0 (* t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (j * i));
	double tmp;
	if (y <= -1.7e+66) {
		tmp = t_1;
	} else if (y <= -4.5e-250) {
		tmp = b * ((t * i) - (c * z));
	} else if (y <= 9000000000.0) {
		tmp = a * fma(j, c, (0.0 - (t * x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(j * i)))
	tmp = 0.0
	if (y <= -1.7e+66)
		tmp = t_1;
	elseif (y <= -4.5e-250)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(c * z)));
	elseif (y <= 9000000000.0)
		tmp = Float64(a * fma(j, c, Float64(0.0 - Float64(t * x))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+66], t$95$1, If[LessEqual[y, -4.5e-250], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9000000000.0], N[(a * N[(j * c + N[(0.0 - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000015e66 or 9e9 < y

   1. Initial program 72.1%

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

   3. Taylor expanded in y around 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. Simplified 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 73.8

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

   8. Simplified 73.8%

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

   if -1.70000000000000015e66 < y < -4.49999999999999993e-250

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 56.4%

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

   if -4.49999999999999993e-250 < y < 9e9

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 53.7

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;y \leq 9000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;y \leq 3800000000:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* j i)))))
   (if (<= y -2e+66)
     t_1
     (if (<= y -3e-101)
       (* b (- (* t i) (* c z)))
       (if (<= y 3800000000.0) (* c (- (* a j) (* b 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 = y * ((x * z) - (j * i));
	double tmp;
	if (y <= -2e+66) {
		tmp = t_1;
	} else if (y <= -3e-101) {
		tmp = b * ((t * i) - (c * z));
	} else if (y <= 3800000000.0) {
		tmp = c * ((a * j) - (b * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (j * i))
    if (y <= (-2d+66)) then
        tmp = t_1
    else if (y <= (-3d-101)) then
        tmp = b * ((t * i) - (c * z))
    else if (y <= 3800000000.0d0) then
        tmp = c * ((a * j) - (b * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (j * i));
	double tmp;
	if (y <= -2e+66) {
		tmp = t_1;
	} else if (y <= -3e-101) {
		tmp = b * ((t * i) - (c * z));
	} else if (y <= 3800000000.0) {
		tmp = c * ((a * j) - (b * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (j * i))
	tmp = 0
	if y <= -2e+66:
		tmp = t_1
	elif y <= -3e-101:
		tmp = b * ((t * i) - (c * z))
	elif y <= 3800000000.0:
		tmp = c * ((a * j) - (b * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(j * i)))
	tmp = 0.0
	if (y <= -2e+66)
		tmp = t_1;
	elseif (y <= -3e-101)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(c * z)));
	elseif (y <= 3800000000.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (j * i));
	tmp = 0.0;
	if (y <= -2e+66)
		tmp = t_1;
	elseif (y <= -3e-101)
		tmp = b * ((t * i) - (c * z));
	elseif (y <= 3800000000.0)
		tmp = c * ((a * j) - (b * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+66], t$95$1, If[LessEqual[y, -3e-101], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3800000000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999989e66 or 3.8e9 < y

   1. Initial program 72.1%

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

   3. Taylor expanded in y around 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. Simplified 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 73.8

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

   8. Simplified 73.8%

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

   if -1.99999999999999989e66 < y < -3.0000000000000003e-101

   1. Initial program 58.2%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 54.6%

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

   if -3.0000000000000003e-101 < y < 3.8e9

   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 c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 53.1

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

   5. Simplified 53.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;y \leq 3800000000:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a)))))
   (if (<= x -1.22e-71)
     t_1
     (if (<= x -3.9e-275)
       (* c (- (* a j) (* b z)))
       (if (<= x 1.02e+127) (* j (- (* a c) (* i y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double tmp;
	if (x <= -1.22e-71) {
		tmp = t_1;
	} else if (x <= -3.9e-275) {
		tmp = c * ((a * j) - (b * z));
	} else if (x <= 1.02e+127) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z * y) - (t * a))
    if (x <= (-1.22d-71)) then
        tmp = t_1
    else if (x <= (-3.9d-275)) then
        tmp = c * ((a * j) - (b * z))
    else if (x <= 1.02d+127) then
        tmp = j * ((a * c) - (i * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (t * a));
	double tmp;
	if (x <= -1.22e-71) {
		tmp = t_1;
	} else if (x <= -3.9e-275) {
		tmp = c * ((a * j) - (b * z));
	} else if (x <= 1.02e+127) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (t * a))
	tmp = 0
	if x <= -1.22e-71:
		tmp = t_1
	elif x <= -3.9e-275:
		tmp = c * ((a * j) - (b * z))
	elif x <= 1.02e+127:
		tmp = j * ((a * c) - (i * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.22e-71)
		tmp = t_1;
	elseif (x <= -3.9e-275)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif (x <= 1.02e+127)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(i * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * y) - (t * a));
	tmp = 0.0;
	if (x <= -1.22e-71)
		tmp = t_1;
	elseif (x <= -3.9e-275)
		tmp = c * ((a * j) - (b * z));
	elseif (x <= 1.02e+127)
		tmp = j * ((a * c) - (i * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e-71], t$95$1, If[LessEqual[x, -3.9e-275], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+127], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.21999999999999999e-71 or 1.02e127 < x

   1. Initial program 76.4%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 63.7

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

   5. Simplified 63.7%

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

   if -1.21999999999999999e-71 < x < -3.89999999999999973e-275

   1. Initial program 78.4%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 57.7

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

   5. Simplified 57.7%

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

   if -3.89999999999999973e-275 < x < 1.02e127

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 54.6

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

   5. Simplified 54.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;y \leq 420000000000:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.4e+70)
   (* z (* x y))
   (if (<= y -1.36e-103)
     (* b (- (* t i) (* c z)))
     (if (<= y 420000000000.0)
       (* c (- (* a j) (* b z)))
       (- 0.0 (* j (* i y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.4e+70) {
		tmp = z * (x * y);
	} else if (y <= -1.36e-103) {
		tmp = b * ((t * i) - (c * z));
	} else if (y <= 420000000000.0) {
		tmp = c * ((a * j) - (b * z));
	} else {
		tmp = 0.0 - (j * (i * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-5.4d+70)) then
        tmp = z * (x * y)
    else if (y <= (-1.36d-103)) then
        tmp = b * ((t * i) - (c * z))
    else if (y <= 420000000000.0d0) then
        tmp = c * ((a * j) - (b * z))
    else
        tmp = 0.0d0 - (j * (i * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.4e+70) {
		tmp = z * (x * y);
	} else if (y <= -1.36e-103) {
		tmp = b * ((t * i) - (c * z));
	} else if (y <= 420000000000.0) {
		tmp = c * ((a * j) - (b * z));
	} else {
		tmp = 0.0 - (j * (i * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.4e+70:
		tmp = z * (x * y)
	elif y <= -1.36e-103:
		tmp = b * ((t * i) - (c * z))
	elif y <= 420000000000.0:
		tmp = c * ((a * j) - (b * z))
	else:
		tmp = 0.0 - (j * (i * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.4e+70)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -1.36e-103)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(c * z)));
	elseif (y <= 420000000000.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	else
		tmp = Float64(0.0 - Float64(j * Float64(i * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5.4e+70)
		tmp = z * (x * y);
	elseif (y <= -1.36e-103)
		tmp = b * ((t * i) - (c * z));
	elseif (y <= 420000000000.0)
		tmp = c * ((a * j) - (b * z));
	else
		tmp = 0.0 - (j * (i * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.4e+70], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.36e-103], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 420000000000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 - N[(j * N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.3999999999999999e70

   1. Initial program 66.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 56.3

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 56.3%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.4

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

   8. Simplified 49.4%

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

   if -5.3999999999999999e70 < y < -1.36000000000000006e-103

   1. Initial program 58.2%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 54.6%

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

   if -1.36000000000000006e-103 < y < 4.2e11

   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 c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 53.1

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

   5. Simplified 53.1%

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

   if 4.2e11 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. Simplified 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 54.8

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

   8. Simplified 54.8%

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

   9. Taylor expanded in c around 0

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

       1. mul-1-neg N/A

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

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

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

       3. mul-1-neg N/A

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

       4. *-lowering-*.f64 N/A

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

       5. mul-1-neg N/A

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

       6. neg-sub0 N/A

          \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(0 - y\right)}\right) \]

       7. --lowering--.f64 49.5

          \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(0 - y\right)}\right) \]

   11. Simplified 49.5%

       \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(0 - y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;y \leq 420000000000:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3600000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.2e+50)
   (* z (* x y))
   (if (<= y -2.1e-293)
     (* i (* t b))
     (if (<= y 3600000000.0) (* j (* a c)) (- 0.0 (* j (* i y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.2e+50) {
		tmp = z * (x * y);
	} else if (y <= -2.1e-293) {
		tmp = i * (t * b);
	} else if (y <= 3600000000.0) {
		tmp = j * (a * c);
	} else {
		tmp = 0.0 - (j * (i * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7.2d+50)) then
        tmp = z * (x * y)
    else if (y <= (-2.1d-293)) then
        tmp = i * (t * b)
    else if (y <= 3600000000.0d0) then
        tmp = j * (a * c)
    else
        tmp = 0.0d0 - (j * (i * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.2e+50) {
		tmp = z * (x * y);
	} else if (y <= -2.1e-293) {
		tmp = i * (t * b);
	} else if (y <= 3600000000.0) {
		tmp = j * (a * c);
	} else {
		tmp = 0.0 - (j * (i * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7.2e+50:
		tmp = z * (x * y)
	elif y <= -2.1e-293:
		tmp = i * (t * b)
	elif y <= 3600000000.0:
		tmp = j * (a * c)
	else:
		tmp = 0.0 - (j * (i * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.2e+50)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -2.1e-293)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 3600000000.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(0.0 - Float64(j * Float64(i * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7.2e+50)
		tmp = z * (x * y);
	elseif (y <= -2.1e-293)
		tmp = i * (t * b);
	elseif (y <= 3600000000.0)
		tmp = j * (a * c);
	else
		tmp = 0.0 - (j * (i * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.2e+50], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-293], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3600000000.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(0.0 - N[(j * N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.19999999999999972e50

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 57.0

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 47.0

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

   8. Simplified 47.0%

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

   if -7.19999999999999972e50 < y < -2.10000000000000005e-293

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 53.4%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 33.2

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

   8. Simplified 33.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 36.1

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

   10. Applied egg-rr 36.1%

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

   if -2.10000000000000005e-293 < y < 3.6e9

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 54.0

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 36.8

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

   8. Simplified 36.8%

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

   if 3.6e9 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in 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. Simplified 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   6. Taylor expanded in j around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 54.8

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

   8. Simplified 54.8%

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

   9. Taylor expanded in c around 0

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

       1. mul-1-neg N/A

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

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

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

       3. mul-1-neg N/A

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

       4. *-lowering-*.f64 N/A

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

       5. mul-1-neg N/A

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

       6. neg-sub0 N/A

          \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(0 - y\right)}\right) \]

       7. --lowering--.f64 49.5

          \[\leadsto j \cdot \left(i \cdot \color{blue}{\left(0 - y\right)}\right) \]

   11. Simplified 49.5%

       \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(0 - y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3600000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;0 - j \cdot \left(i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-49}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(b, t, 0 - j \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* b z)))))
   (if (<= c -1.4e+87)
     t_1
     (if (<= c 1.75e-49) (* i (fma b t (- 0.0 (* j y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -1.4e+87) {
		tmp = t_1;
	} else if (c <= 1.75e-49) {
		tmp = i * fma(b, t, (0.0 - (j * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -1.4e+87)
		tmp = t_1;
	elseif (c <= 1.75e-49)
		tmp = Float64(i * fma(b, t, Float64(0.0 - Float64(j * y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.4e+87], t$95$1, If[LessEqual[c, 1.75e-49], N[(i * N[(b * t + N[(0.0 - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.40000000000000008e87 or 1.75000000000000003e-49 < c

   1. Initial program 62.7%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 60.4

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

   5. Simplified 60.4%

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

   if -1.40000000000000008e87 < c < 1.75000000000000003e-49

   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 i around -inf

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

   5. Simplified 72.7%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(b, t, -\mathsf{fma}\left(j, y, \frac{\mathsf{fma}\left(c, b \cdot z - j \cdot a, x \cdot \mathsf{fma}\left(a, t, 0 - y \cdot z\right)\right)}{i}\right)\right)} \]

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 51.0

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

   8. Simplified 51.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-49}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(b, t, 0 - j \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* c z)))))
   (if (<= b -1.4e+91)
     t_1
     (if (<= b 2.95e-74) (* j (- (* a c) (* i y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (b <= -1.4e+91) {
		tmp = t_1;
	} else if (b <= 2.95e-74) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (c * z))
    if (b <= (-1.4d+91)) then
        tmp = t_1
    else if (b <= 2.95d-74) then
        tmp = j * ((a * c) - (i * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (b <= -1.4e+91) {
		tmp = t_1;
	} else if (b <= 2.95e-74) {
		tmp = j * ((a * c) - (i * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (c * z))
	tmp = 0
	if b <= -1.4e+91:
		tmp = t_1
	elif b <= 2.95e-74:
		tmp = j * ((a * c) - (i * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(c * z)))
	tmp = 0.0
	if (b <= -1.4e+91)
		tmp = t_1;
	elseif (b <= 2.95e-74)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(i * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (c * z));
	tmp = 0.0;
	if (b <= -1.4e+91)
		tmp = t_1;
	elseif (b <= 2.95e-74)
		tmp = j * ((a * c) - (i * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+91], t$95$1, If[LessEqual[b, 2.95e-74], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3999999999999999e91 or 2.94999999999999983e-74 < b

   1. Initial program 64.5%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 61.3%

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

   if -1.3999999999999999e91 < b < 2.94999999999999983e-74

   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 j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 51.2

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

   5. Simplified 51.2%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - i\right) \cdot \left(j \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7e+63)
   (* z (* x y))
   (if (<= y 9.5e+164) (* b (- (* t i) (* c z))) (* (- 0.0 i) (* j y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7e+63) {
		tmp = z * (x * y);
	} else if (y <= 9.5e+164) {
		tmp = b * ((t * i) - (c * z));
	} else {
		tmp = (0.0 - i) * (j * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7d+63)) then
        tmp = z * (x * y)
    else if (y <= 9.5d+164) then
        tmp = b * ((t * i) - (c * z))
    else
        tmp = (0.0d0 - i) * (j * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7e+63) {
		tmp = z * (x * y);
	} else if (y <= 9.5e+164) {
		tmp = b * ((t * i) - (c * z));
	} else {
		tmp = (0.0 - i) * (j * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7e+63:
		tmp = z * (x * y)
	elif y <= 9.5e+164:
		tmp = b * ((t * i) - (c * z))
	else:
		tmp = (0.0 - i) * (j * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7e+63)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 9.5e+164)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(c * z)));
	else
		tmp = Float64(Float64(0.0 - i) * Float64(j * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7e+63)
		tmp = z * (x * y);
	elseif (y <= 9.5e+164)
		tmp = b * ((t * i) - (c * z));
	else
		tmp = (0.0 - i) * (j * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7e+63], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+164], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.0 - i), $MachinePrecision] * N[(j * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000059e63

   1. Initial program 66.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 56.3

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 56.3%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.4

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

   8. Simplified 49.4%

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

   if -7.00000000000000059e63 < y < 9.49999999999999976e164

   1. Initial program 73.8%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 45.1%

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

   if 9.49999999999999976e164 < y

   1. Initial program 75.4%

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

   3. Taylor expanded in y around 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. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 86.5

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

   8. Simplified 86.5%

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

   9. Taylor expanded in z 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. neg-sub0 N/A

          \[\leadsto \color{blue}{0 - i \cdot \left(j \cdot y\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \color{blue}{0 - i \cdot \left(j \cdot y\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto 0 - \color{blue}{i \cdot \left(j \cdot y\right)} \]

       5. *-lowering-*.f64 61.6

          \[\leadsto 0 - i \cdot \color{blue}{\left(j \cdot y\right)} \]

   11. Simplified 61.6%

       \[\leadsto \color{blue}{0 - i \cdot \left(j \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - i\right) \cdot \left(j \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 560000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.52e+52)
   (* z (* x y))
   (if (<= y -2.15e-292)
     (* i (* t b))
     (if (<= y 560000000.0) (* j (* a c)) (* x (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.52e+52) {
		tmp = z * (x * y);
	} else if (y <= -2.15e-292) {
		tmp = i * (t * b);
	} else if (y <= 560000000.0) {
		tmp = j * (a * c);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.52d+52)) then
        tmp = z * (x * y)
    else if (y <= (-2.15d-292)) then
        tmp = i * (t * b)
    else if (y <= 560000000.0d0) then
        tmp = j * (a * c)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.52e+52) {
		tmp = z * (x * y);
	} else if (y <= -2.15e-292) {
		tmp = i * (t * b);
	} else if (y <= 560000000.0) {
		tmp = j * (a * c);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.52e+52:
		tmp = z * (x * y)
	elif y <= -2.15e-292:
		tmp = i * (t * b)
	elif y <= 560000000.0:
		tmp = j * (a * c)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.52e+52)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -2.15e-292)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 560000000.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.52e+52)
		tmp = z * (x * y);
	elseif (y <= -2.15e-292)
		tmp = i * (t * b);
	elseif (y <= 560000000.0)
		tmp = j * (a * c);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.52e+52], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-292], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 560000000.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5199999999999999e52

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 57.0

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 47.0

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

   8. Simplified 47.0%

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

   if -1.5199999999999999e52 < y < -2.15e-292

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 53.4%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 33.2

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

   8. Simplified 33.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 36.1

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

   10. Applied egg-rr 36.1%

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

   if -2.15e-292 < y < 5.6e8

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 54.0

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 36.8

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

   8. Simplified 36.8%

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

   if 5.6e8 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 46.9

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-lowering-*.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. *-lowering-*.f64 37.1

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

   8. Simplified 37.1%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 560000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 10^{-297}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 2050000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -4.4e+49)
   (* z (* x y))
   (if (<= y 1e-297)
     (* t (* b i))
     (if (<= y 2050000000.0) (* j (* a c)) (* x (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -4.4e+49) {
		tmp = z * (x * y);
	} else if (y <= 1e-297) {
		tmp = t * (b * i);
	} else if (y <= 2050000000.0) {
		tmp = j * (a * c);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-4.4d+49)) then
        tmp = z * (x * y)
    else if (y <= 1d-297) then
        tmp = t * (b * i)
    else if (y <= 2050000000.0d0) then
        tmp = j * (a * c)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -4.4e+49) {
		tmp = z * (x * y);
	} else if (y <= 1e-297) {
		tmp = t * (b * i);
	} else if (y <= 2050000000.0) {
		tmp = j * (a * c);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -4.4e+49:
		tmp = z * (x * y)
	elif y <= 1e-297:
		tmp = t * (b * i)
	elif y <= 2050000000.0:
		tmp = j * (a * c)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -4.4e+49)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1e-297)
		tmp = Float64(t * Float64(b * i));
	elseif (y <= 2050000000.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -4.4e+49)
		tmp = z * (x * y);
	elseif (y <= 1e-297)
		tmp = t * (b * i);
	elseif (y <= 2050000000.0)
		tmp = j * (a * c);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -4.4e+49], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-297], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2050000000.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000001e49

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 57.0

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 47.0

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

   8. Simplified 47.0%

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

   if -4.4000000000000001e49 < y < 1.00000000000000004e-297

   1. Initial program 67.5%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 53.2%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 34.3

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

   8. Simplified 34.3%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 35.5

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

   10. Applied egg-rr 35.5%

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

   if 1.00000000000000004e-297 < y < 2.05e9

   1. Initial program 79.2%

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

   3. Taylor expanded in 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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 54.1

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 36.9

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

   8. Simplified 36.9%

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

   if 2.05e9 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 46.9

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-lowering-*.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. *-lowering-*.f64 37.1

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

   8. Simplified 37.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 10^{-297}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 2050000000:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 135000000:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.6e+20)
   (* y (* x z))
   (if (<= z 135000000.0) (* a (* j c)) (* x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.6e+20) {
		tmp = y * (x * z);
	} else if (z <= 135000000.0) {
		tmp = a * (j * c);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.6d+20)) then
        tmp = y * (x * z)
    else if (z <= 135000000.0d0) then
        tmp = a * (j * c)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.6e+20) {
		tmp = y * (x * z);
	} else if (z <= 135000000.0) {
		tmp = a * (j * c);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.6e+20:
		tmp = y * (x * z)
	elif z <= 135000000.0:
		tmp = a * (j * c)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.6e+20)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 135000000.0)
		tmp = Float64(a * Float64(j * c));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.6e+20)
		tmp = y * (x * z);
	elseif (z <= 135000000.0)
		tmp = a * (j * c);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.6e+20], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 135000000.0], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e20

   1. Initial program 69.7%

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

   3. Taylor expanded in 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. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, \mathsf{fma}\left(j, c, 0 - t \cdot x\right), \mathsf{fma}\left(b, i \cdot t - c \cdot z, y \cdot \mathsf{fma}\left(j, 0 - i, z \cdot x\right)\right)\right)} \]

   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. *-lowering-*.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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. --lowering--.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 53.7

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

   8. Simplified 53.7%

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

   9. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 39.2

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

   11. Simplified 39.2%

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

   if -1.6e20 < z < 1.35e8

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 50.8

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 33.0

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

   8. Simplified 33.0%

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

   if 1.35e8 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 73.7

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 73.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-lowering-*.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. *-lowering-*.f64 45.0

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

   8. Simplified 45.0%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 135000000:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1800000:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* z y))))
   (if (<= z -8.2e+19) t_1 (if (<= z 1800000.0) (* a (* j c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -8.2e+19) {
		tmp = t_1;
	} else if (z <= 1800000.0) {
		tmp = a * (j * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z * y)
    if (z <= (-8.2d+19)) then
        tmp = t_1
    else if (z <= 1800000.0d0) then
        tmp = a * (j * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -8.2e+19) {
		tmp = t_1;
	} else if (z <= 1800000.0) {
		tmp = a * (j * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (z * y)
	tmp = 0
	if z <= -8.2e+19:
		tmp = t_1
	elif z <= 1800000.0:
		tmp = a * (j * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (z <= -8.2e+19)
		tmp = t_1;
	elseif (z <= 1800000.0)
		tmp = Float64(a * Float64(j * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (z * y);
	tmp = 0.0;
	if (z <= -8.2e+19)
		tmp = t_1;
	elseif (z <= 1800000.0)
		tmp = a * (j * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+19], t$95$1, If[LessEqual[z, 1800000.0], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e19 or 1.8e6 < z

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{0 - b}, x \cdot y\right) \]

      11. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

      12. *-lowering-*.f64 66.0

          \[\leadsto z \cdot \mathsf{fma}\left(c, 0 - b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 66.0%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, 0 - b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

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

      1. *-lowering-*.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. *-lowering-*.f64 41.8

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

   8. Simplified 41.8%

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

   if -8.2e19 < z < 1.8e6

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 50.8

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 33.0

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

   8. Simplified 33.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1800000:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(j \cdot c\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.95 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* j c))))
   (if (<= c -4e-17) t_1 (if (<= c 2.95e+113) (* 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 * (j * c);
	double tmp;
	if (c <= -4e-17) {
		tmp = t_1;
	} else if (c <= 2.95e+113) {
		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 * (j * c)
    if (c <= (-4d-17)) then
        tmp = t_1
    else if (c <= 2.95d+113) 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 * (j * c);
	double tmp;
	if (c <= -4e-17) {
		tmp = t_1;
	} else if (c <= 2.95e+113) {
		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 * (j * c)
	tmp = 0
	if c <= -4e-17:
		tmp = t_1
	elif c <= 2.95e+113:
		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(j * c))
	tmp = 0.0
	if (c <= -4e-17)
		tmp = t_1;
	elseif (c <= 2.95e+113)
		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 * (j * c);
	tmp = 0.0;
	if (c <= -4e-17)
		tmp = t_1;
	elseif (c <= 2.95e+113)
		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[(j * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e-17], t$95$1, If[LessEqual[c, 2.95e+113], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -4.00000000000000029e-17 or 2.95000000000000011e113 < c

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

      8. *-lowering-*.f64 52.2

         \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 44.1

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

   8. Simplified 44.1%

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

   if -4.00000000000000029e-17 < c < 2.95000000000000011e113

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

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

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

      15. mul-1-neg N/A

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

      16. *-lowering-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. mul-1-neg N/A

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

   5. Simplified 36.3%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 27.0

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

   8. Simplified 27.0%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;c \leq 2.95 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.5% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(j \cdot c\right) \end{array} \]

FPCore

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

C

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

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 * (j * c)
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 * (j * c);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
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. *-lowering-*.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. accelerator-lowering-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. neg-sub0 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, \color{blue}{0 - t \cdot x}\right) \]

   8. *-lowering-*.f64 39.1

      \[\leadsto a \cdot \mathsf{fma}\left(j, c, 0 - \color{blue}{t \cdot x}\right) \]

5. Simplified 39.1%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(j, c, 0 - t \cdot x\right)} \]

6. Taylor expanded in j around inf

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

   1. *-lowering-*.f64 24.0

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

8. Simplified 24.0%

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

9. Final simplification 24.0%

   \[\leadsto a \cdot \left(j \cdot c\right) \]
10. Add Preprocessing

Developer Target 1: 59.2% 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 2024195 
(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)))))