Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.8% → 83.0%

Time: 11.7s

Alternatives: 17

Speedup: 0.5×

• 57.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 49.0

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

   5. Applied rewrites 49.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.9%

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

Alternative 2: 68.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+107} \lor \neg \left(a \leq 1.35 \cdot 10^{+101}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -7.5e+107) (not (<= a 1.35e+101)))
   (* (fma (- x) t (* i b)) a)
   (fma (fma (- i) y (* c t)) j (* (fma (- b) c (* y x)) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -7.5e+107) || !(a <= 1.35e+101)) {
		tmp = fma(-x, t, (i * b)) * a;
	} else {
		tmp = fma(fma(-i, y, (c * t)), j, (fma(-b, c, (y * x)) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -7.5e+107) || !(a <= 1.35e+101))
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	else
		tmp = fma(fma(Float64(-i), y, Float64(c * t)), j, Float64(fma(Float64(-b), c, Float64(y * x)) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -7.5e+107], N[Not[LessEqual[a, 1.35e+101]], $MachinePrecision]], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.4999999999999996e107 or 1.35000000000000003e101 < a

   1. Initial program 64.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   if -7.4999999999999996e107 < a < 1.35000000000000003e101

   1. Initial program 80.9%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+107} \lor \neg \left(a \leq 1.35 \cdot 10^{+101}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot t\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+96} \lor \neg \left(a \leq 1.15 \cdot 10^{+101}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3.4e+96) (not (<= a 1.15e+101)))
   (* (fma (- x) t (* i b)) a)
   (+ (* (* z x) y) (* j (- (* c t) (* i y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3.4e+96) || !(a <= 1.15e+101)) {
		tmp = fma(-x, t, (i * b)) * a;
	} else {
		tmp = ((z * x) * y) + (j * ((c * t) - (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -3.4e+96) || !(a <= 1.15e+101))
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	else
		tmp = Float64(Float64(Float64(z * x) * y) + Float64(j * Float64(Float64(c * t) - Float64(i * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -3.4e+96], N[Not[LessEqual[a, 1.15e+101]], $MachinePrecision]], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4000000000000001e96 or 1.1500000000000001e101 < a

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 72.4

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

   5. Applied rewrites 72.4%

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

   if -3.4000000000000001e96 < a < 1.1500000000000001e101

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+96} \lor \neg \left(a \leq 1.15 \cdot 10^{+101}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-75}:\\ \;\;\;\;\left(t \cdot c\right) \cdot j\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-133}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-293}:\\ \;\;\;\;\left(\left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+104}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-t\right) \cdot a\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.4e-75)
   (* (* t c) j)
   (if (<= t -3.8e-133)
     (* (* i a) b)
     (if (<= t -3e-293)
       (* (* (- j) i) y)
       (if (<= t 1.4e-76)
         (* (* z x) y)
         (if (<= t 3.3e+104) (* (* (- z) c) b) (* (* (- t) a) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.4e-75) {
		tmp = (t * c) * j;
	} else if (t <= -3.8e-133) {
		tmp = (i * a) * b;
	} else if (t <= -3e-293) {
		tmp = (-j * i) * y;
	} else if (t <= 1.4e-76) {
		tmp = (z * x) * y;
	} else if (t <= 3.3e+104) {
		tmp = (-z * c) * b;
	} else {
		tmp = (-t * a) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-4.4d-75)) then
        tmp = (t * c) * j
    else if (t <= (-3.8d-133)) then
        tmp = (i * a) * b
    else if (t <= (-3d-293)) then
        tmp = (-j * i) * y
    else if (t <= 1.4d-76) then
        tmp = (z * x) * y
    else if (t <= 3.3d+104) then
        tmp = (-z * c) * b
    else
        tmp = (-t * a) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.4e-75) {
		tmp = (t * c) * j;
	} else if (t <= -3.8e-133) {
		tmp = (i * a) * b;
	} else if (t <= -3e-293) {
		tmp = (-j * i) * y;
	} else if (t <= 1.4e-76) {
		tmp = (z * x) * y;
	} else if (t <= 3.3e+104) {
		tmp = (-z * c) * b;
	} else {
		tmp = (-t * a) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.4e-75:
		tmp = (t * c) * j
	elif t <= -3.8e-133:
		tmp = (i * a) * b
	elif t <= -3e-293:
		tmp = (-j * i) * y
	elif t <= 1.4e-76:
		tmp = (z * x) * y
	elif t <= 3.3e+104:
		tmp = (-z * c) * b
	else:
		tmp = (-t * a) * x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.4e-75)
		tmp = Float64(Float64(t * c) * j);
	elseif (t <= -3.8e-133)
		tmp = Float64(Float64(i * a) * b);
	elseif (t <= -3e-293)
		tmp = Float64(Float64(Float64(-j) * i) * y);
	elseif (t <= 1.4e-76)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 3.3e+104)
		tmp = Float64(Float64(Float64(-z) * c) * b);
	else
		tmp = Float64(Float64(Float64(-t) * a) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.4e-75)
		tmp = (t * c) * j;
	elseif (t <= -3.8e-133)
		tmp = (i * a) * b;
	elseif (t <= -3e-293)
		tmp = (-j * i) * y;
	elseif (t <= 1.4e-76)
		tmp = (z * x) * y;
	elseif (t <= 3.3e+104)
		tmp = (-z * c) * b;
	else
		tmp = (-t * a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.4e-75], N[(N[(t * c), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t, -3.8e-133], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, -3e-293], N[(N[((-j) * i), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.4e-76], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 3.3e+104], N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision], N[(N[((-t) * a), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.40000000000000011e-75

   1. Initial program 73.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 58.8

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 43.5%

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

   10. Applied rewrites 49.9%

       \[\leadsto \left(t \cdot c\right) \cdot j \]

   if -4.40000000000000011e-75 < t < -3.8000000000000003e-133

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 48.7%

      \[\leadsto \left(i \cdot a\right) \cdot b \]

   if -3.8000000000000003e-133 < t < -3.0000000000000002e-293

   1. Initial program 74.8%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 50.4

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

   5. Applied rewrites 50.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \left(i \cdot j\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 43.6%

      \[\leadsto \left(\left(-j\right) \cdot i\right) \cdot y \]

   if -3.0000000000000002e-293 < t < 1.40000000000000005e-76

   1. Initial program 78.5%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 53.0

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

   5. Applied rewrites 53.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 40.3%

      \[\leadsto \left(z \cdot x\right) \cdot y \]

   if 1.40000000000000005e-76 < t < 3.29999999999999985e104

   1. Initial program 87.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 56.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot z\right)\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 40.8%

      \[\leadsto \left(\left(-z\right) \cdot c\right) \cdot b \]

   if 3.29999999999999985e104 < t

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 41.9

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

   5. Applied rewrites 41.9%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 67.0

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

   8. Applied rewrites 67.0%

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

   9. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 53.9%

       \[\leadsto \left(\left(-t\right) \cdot a\right) \cdot x \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 5: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-75}:\\ \;\;\;\;\left(t \cdot c\right) \cdot j\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-133}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-293}:\\ \;\;\;\;\left(\left(-j\right) \cdot i\right) \cdot y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+104}:\\ \;\;\;\;\left(\left(-z\right) \cdot c\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.4e-75)
   (* (* t c) j)
   (if (<= t -3.8e-133)
     (* (* i a) b)
     (if (<= t -3e-293)
       (* (* (- j) i) y)
       (if (<= t 1.4e-76)
         (* (* z x) y)
         (if (<= t 3.3e+104) (* (* (- z) c) b) (* (* (- x) a) t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.4e-75) {
		tmp = (t * c) * j;
	} else if (t <= -3.8e-133) {
		tmp = (i * a) * b;
	} else if (t <= -3e-293) {
		tmp = (-j * i) * y;
	} else if (t <= 1.4e-76) {
		tmp = (z * x) * y;
	} else if (t <= 3.3e+104) {
		tmp = (-z * c) * b;
	} else {
		tmp = (-x * a) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-4.4d-75)) then
        tmp = (t * c) * j
    else if (t <= (-3.8d-133)) then
        tmp = (i * a) * b
    else if (t <= (-3d-293)) then
        tmp = (-j * i) * y
    else if (t <= 1.4d-76) then
        tmp = (z * x) * y
    else if (t <= 3.3d+104) then
        tmp = (-z * c) * b
    else
        tmp = (-x * a) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.4e-75) {
		tmp = (t * c) * j;
	} else if (t <= -3.8e-133) {
		tmp = (i * a) * b;
	} else if (t <= -3e-293) {
		tmp = (-j * i) * y;
	} else if (t <= 1.4e-76) {
		tmp = (z * x) * y;
	} else if (t <= 3.3e+104) {
		tmp = (-z * c) * b;
	} else {
		tmp = (-x * a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.4e-75:
		tmp = (t * c) * j
	elif t <= -3.8e-133:
		tmp = (i * a) * b
	elif t <= -3e-293:
		tmp = (-j * i) * y
	elif t <= 1.4e-76:
		tmp = (z * x) * y
	elif t <= 3.3e+104:
		tmp = (-z * c) * b
	else:
		tmp = (-x * a) * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.4e-75)
		tmp = Float64(Float64(t * c) * j);
	elseif (t <= -3.8e-133)
		tmp = Float64(Float64(i * a) * b);
	elseif (t <= -3e-293)
		tmp = Float64(Float64(Float64(-j) * i) * y);
	elseif (t <= 1.4e-76)
		tmp = Float64(Float64(z * x) * y);
	elseif (t <= 3.3e+104)
		tmp = Float64(Float64(Float64(-z) * c) * b);
	else
		tmp = Float64(Float64(Float64(-x) * a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.4e-75)
		tmp = (t * c) * j;
	elseif (t <= -3.8e-133)
		tmp = (i * a) * b;
	elseif (t <= -3e-293)
		tmp = (-j * i) * y;
	elseif (t <= 1.4e-76)
		tmp = (z * x) * y;
	elseif (t <= 3.3e+104)
		tmp = (-z * c) * b;
	else
		tmp = (-x * a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.4e-75], N[(N[(t * c), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t, -3.8e-133], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, -3e-293], N[(N[((-j) * i), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.4e-76], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 3.3e+104], N[(N[((-z) * c), $MachinePrecision] * b), $MachinePrecision], N[(N[((-x) * a), $MachinePrecision] * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.40000000000000011e-75

   1. Initial program 73.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 58.8

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 43.5%

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

   10. Applied rewrites 49.9%

       \[\leadsto \left(t \cdot c\right) \cdot j \]

   if -4.40000000000000011e-75 < t < -3.8000000000000003e-133

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 48.7%

      \[\leadsto \left(i \cdot a\right) \cdot b \]

   if -3.8000000000000003e-133 < t < -3.0000000000000002e-293

   1. Initial program 74.8%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 50.4

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

   5. Applied rewrites 50.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \left(i \cdot j\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 43.6%

      \[\leadsto \left(\left(-j\right) \cdot i\right) \cdot y \]

   if -3.0000000000000002e-293 < t < 1.40000000000000005e-76

   1. Initial program 78.5%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 53.0

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

   5. Applied rewrites 53.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 40.3%

      \[\leadsto \left(z \cdot x\right) \cdot y \]

   if 1.40000000000000005e-76 < t < 3.29999999999999985e104

   1. Initial program 87.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

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

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

      10. distribute-neg-in N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

   5. Applied rewrites 56.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot z\right)\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 40.8%

      \[\leadsto \left(\left(-z\right) \cdot c\right) \cdot b \]

   if 3.29999999999999985e104 < t

   1. Initial program 66.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot x\right)\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 51.8%

      \[\leadsto \left(\left(-x\right) \cdot a\right) \cdot t \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 6: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{if}\;x \leq -7 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-95}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;x \leq 920000000000:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- (* z y) (* a t)) x)))
   (if (<= x -7e-8)
     t_1
     (if (<= x 3e-95)
       (* (fma (- i) y (* c t)) j)
       (if (<= x 920000000000.0)
         (* (fma (- b) c (* y x)) z)
         (if (<= x 1.3e+193) (* (fma (- a) x (* j c)) t) 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 = ((z * y) - (a * t)) * x;
	double tmp;
	if (x <= -7e-8) {
		tmp = t_1;
	} else if (x <= 3e-95) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (x <= 920000000000.0) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (x <= 1.3e+193) {
		tmp = fma(-a, x, (j * c)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(z * y) - Float64(a * t)) * x)
	tmp = 0.0
	if (x <= -7e-8)
		tmp = t_1;
	elseif (x <= 3e-95)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (x <= 920000000000.0)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (x <= 1.3e+193)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7e-8], t$95$1, If[LessEqual[x, 3e-95], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[x, 920000000000.0], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 1.3e+193], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.00000000000000048e-8 or 1.30000000000000007e193 < x

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 68.5

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

   8. Applied rewrites 68.5%

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

   if -7.00000000000000048e-8 < x < 3e-95

   1. Initial program 75.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 73.9

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 53.4

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

   8. Applied rewrites 53.4%

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

   if 3e-95 < x < 9.2e11

   1. Initial program 70.7%

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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 47.8

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

   5. Applied rewrites 47.8%

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

   if 9.2e11 < x < 1.30000000000000007e193

   1. Initial program 83.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.4

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

   5. Applied rewrites 68.4%

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

Alternative 7: 60.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+107} \lor \neg \left(a \leq 1.9 \cdot 10^{+101}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot t, j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3.3e+107) (not (<= a 1.9e+101)))
   (* (fma (- x) t (* i b)) a)
   (fma (* c t) j (* (fma (- b) c (* y x)) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3.3e+107) || !(a <= 1.9e+101)) {
		tmp = fma(-x, t, (i * b)) * a;
	} else {
		tmp = fma((c * t), j, (fma(-b, c, (y * x)) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -3.3e+107) || !(a <= 1.9e+101))
		tmp = Float64(fma(Float64(-x), t, Float64(i * b)) * a);
	else
		tmp = fma(Float64(c * t), j, Float64(fma(Float64(-b), c, Float64(y * x)) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -3.3e+107], N[Not[LessEqual[a, 1.9e+101]], $MachinePrecision]], N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(c * t), $MachinePrecision] * j + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.30000000000000032e107 or 1.8999999999999999e101 < a

   1. Initial program 64.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   if -3.30000000000000032e107 < a < 1.8999999999999999e101

   1. Initial program 80.9%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+107} \lor \neg \left(a \leq 1.9 \cdot 10^{+101}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c \cdot t, j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, t, i \cdot b\right) \cdot a\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot t\right) \cdot j\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- x) t (* i b)) a)))
   (if (<= a -1.5e+96)
     t_1
     (if (<= a 6e-58)
       (* (fma (- i) y (* c t)) j)
       (if (<= a 1.9e+101) (* (fma (- a) x (* j c)) t) 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(-x, t, (i * b)) * a;
	double tmp;
	if (a <= -1.5e+96) {
		tmp = t_1;
	} else if (a <= 6e-58) {
		tmp = fma(-i, y, (c * t)) * j;
	} else if (a <= 1.9e+101) {
		tmp = fma(-a, x, (j * c)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-x), t, Float64(i * b)) * a)
	tmp = 0.0
	if (a <= -1.5e+96)
		tmp = t_1;
	elseif (a <= 6e-58)
		tmp = Float64(fma(Float64(-i), y, Float64(c * t)) * j);
	elseif (a <= 1.9e+101)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-x) * t + N[(i * b), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.5e+96], t$95$1, If[LessEqual[a, 6e-58], N[(N[((-i) * y + N[(c * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[a, 1.9e+101], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5e96 or 1.8999999999999999e101 < a

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 72.4

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

   5. Applied rewrites 72.4%

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

   if -1.5e96 < a < 6.00000000000000015e-58

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 80.9

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 58.4

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

   8. Applied rewrites 58.4%

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

   if 6.00000000000000015e-58 < a < 1.8999999999999999e101

   1. Initial program 84.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 56.7

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

   5. Applied rewrites 56.7%

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

Alternative 9: 53.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- a) x (* j c)) t)))
   (if (<= t -1.55e-22)
     t_1
     (if (<= t 1.05e-122)
       (* (fma (- j) i (* z x)) y)
       (if (<= t 1.8e-18) (* (fma (- b) c (* y x)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-a, x, (j * c)) * t;
	double tmp;
	if (t <= -1.55e-22) {
		tmp = t_1;
	} else if (t <= 1.05e-122) {
		tmp = fma(-j, i, (z * x)) * y;
	} else if (t <= 1.8e-18) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-a), x, Float64(j * c)) * t)
	tmp = 0.0
	if (t <= -1.55e-22)
		tmp = t_1;
	elseif (t <= 1.05e-122)
		tmp = Float64(fma(Float64(-j), i, Float64(z * x)) * y);
	elseif (t <= 1.8e-18)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.55e-22], t$95$1, If[LessEqual[t, 1.05e-122], N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.8e-18], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55000000000000006e-22 or 1.80000000000000005e-18 < t

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if -1.55000000000000006e-22 < t < 1.04999999999999996e-122

   1. Initial program 81.5%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 57.1

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

   5. Applied rewrites 57.1%

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

   if 1.04999999999999996e-122 < t < 1.80000000000000005e-18

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

Alternative 10: 52.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58} \lor \neg \left(z \leq 7.6 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -5e+58) (not (<= z 7.6e+27)))
   (* (fma (- b) c (* y x)) z)
   (* (fma (- a) x (* j c)) t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -5e+58) || !(z <= 7.6e+27)) {
		tmp = fma(-b, c, (y * x)) * z;
	} else {
		tmp = fma(-a, x, (j * c)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -5e+58) || !(z <= 7.6e+27))
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	else
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -5e+58], N[Not[LessEqual[z, 7.6e+27]], $MachinePrecision]], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999986e58 or 7.60000000000000043e27 < z

   1. Initial program 59.9%

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

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

      2. lower-*.f64 N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 60.8

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

   5. Applied rewrites 60.8%

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

   if -4.99999999999999986e58 < z < 7.60000000000000043e27

   1. Initial program 85.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 50.4

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

   5. Applied rewrites 50.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58} \lor \neg \left(z \leq 7.6 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-j\right) \cdot i\right) \cdot y\\ \mathbf{if}\;i \leq -4.4 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{+274}:\\ \;\;\;\;\left(b \cdot a\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- j) i) y)))
   (if (<= i -4.4e+104)
     t_1
     (if (<= i 3.5e+94)
       (* (fma (- a) x (* j c)) t)
       (if (<= i 4.9e+274) (* (* b a) 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 = (-j * i) * y;
	double tmp;
	if (i <= -4.4e+104) {
		tmp = t_1;
	} else if (i <= 3.5e+94) {
		tmp = fma(-a, x, (j * c)) * t;
	} else if (i <= 4.9e+274) {
		tmp = (b * a) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-j) * i) * y)
	tmp = 0.0
	if (i <= -4.4e+104)
		tmp = t_1;
	elseif (i <= 3.5e+94)
		tmp = Float64(fma(Float64(-a), x, Float64(j * c)) * t);
	elseif (i <= 4.9e+274)
		tmp = Float64(Float64(b * a) * 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[(N[((-j) * i), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[i, -4.4e+104], t$95$1, If[LessEqual[i, 3.5e+94], N[(N[((-a) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[i, 4.9e+274], N[(N[(b * a), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.40000000000000001e104 or 4.90000000000000025e274 < i

   1. Initial program 68.5%

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

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \left(i \cdot j\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 57.1%

      \[\leadsto \left(\left(-j\right) \cdot i\right) \cdot y \]

   if -4.40000000000000001e104 < i < 3.4999999999999997e94

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 53.1

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

   5. Applied rewrites 53.1%

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

   if 3.4999999999999997e94 < i < 4.90000000000000025e274

   1. Initial program 72.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 64.5

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

   5. Applied rewrites 64.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(a \cdot b\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 51.4%

      \[\leadsto \left(b \cdot a\right) \cdot i \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 42.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-j\right) \cdot i\right) \cdot y\\ \mathbf{if}\;i \leq -9 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+141}:\\ \;\;\;\;\left(z \cdot y - a \cdot t\right) \cdot x\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+274}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* (- j) i) y)))
   (if (<= i -9e+105)
     t_1
     (if (<= i 2.3e+141)
       (* (- (* z y) (* a t)) x)
       (if (<= i 8e+274) (* (* i b) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (-j * i) * y;
	double tmp;
	if (i <= -9e+105) {
		tmp = t_1;
	} else if (i <= 2.3e+141) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (i <= 8e+274) {
		tmp = (i * b) * a;
	} 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 = (-j * i) * y
    if (i <= (-9d+105)) then
        tmp = t_1
    else if (i <= 2.3d+141) then
        tmp = ((z * y) - (a * t)) * x
    else if (i <= 8d+274) then
        tmp = (i * b) * a
    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 = (-j * i) * y;
	double tmp;
	if (i <= -9e+105) {
		tmp = t_1;
	} else if (i <= 2.3e+141) {
		tmp = ((z * y) - (a * t)) * x;
	} else if (i <= 8e+274) {
		tmp = (i * b) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (-j * i) * y
	tmp = 0
	if i <= -9e+105:
		tmp = t_1
	elif i <= 2.3e+141:
		tmp = ((z * y) - (a * t)) * x
	elif i <= 8e+274:
		tmp = (i * b) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(-j) * i) * y)
	tmp = 0.0
	if (i <= -9e+105)
		tmp = t_1;
	elseif (i <= 2.3e+141)
		tmp = Float64(Float64(Float64(z * y) - Float64(a * t)) * x);
	elseif (i <= 8e+274)
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (-j * i) * y;
	tmp = 0.0;
	if (i <= -9e+105)
		tmp = t_1;
	elseif (i <= 2.3e+141)
		tmp = ((z * y) - (a * t)) * x;
	elseif (i <= 8e+274)
		tmp = (i * b) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-j) * i), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[i, -9e+105], t$95$1, If[LessEqual[i, 2.3e+141], N[(N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[i, 8e+274], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.0000000000000002e105 or 7.99999999999999937e274 < i

   1. Initial program 67.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 60.3

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

   5. Applied rewrites 60.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \left(i \cdot j\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 58.3%

      \[\leadsto \left(\left(-j\right) \cdot i\right) \cdot y \]

   if -9.0000000000000002e105 < i < 2.3000000000000002e141

   1. Initial program 78.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. +-commutative N/A

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

      18. mul-1-neg N/A

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

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

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

      20. lower-fma.f64 N/A

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

      21. lower-neg.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 67.1

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

   5. Applied rewrites 67.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 44.5

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

   8. Applied rewrites 44.5%

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

   if 2.3000000000000002e141 < i < 7.99999999999999937e274

   1. Initial program 68.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 58.0%

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

Alternative 13: 28.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+113}:\\ \;\;\;\;\left(t \cdot c\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -6.6e+88)
   (* (* i b) a)
   (if (<= a -1.2e+24)
     (* (* z x) y)
     (if (<= a 2.9e+113) (* (* t c) j) (* (* i a) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6.6e+88) {
		tmp = (i * b) * a;
	} else if (a <= -1.2e+24) {
		tmp = (z * x) * y;
	} else if (a <= 2.9e+113) {
		tmp = (t * c) * j;
	} else {
		tmp = (i * a) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-6.6d+88)) then
        tmp = (i * b) * a
    else if (a <= (-1.2d+24)) then
        tmp = (z * x) * y
    else if (a <= 2.9d+113) then
        tmp = (t * c) * j
    else
        tmp = (i * a) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6.6e+88) {
		tmp = (i * b) * a;
	} else if (a <= -1.2e+24) {
		tmp = (z * x) * y;
	} else if (a <= 2.9e+113) {
		tmp = (t * c) * j;
	} else {
		tmp = (i * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -6.6e+88:
		tmp = (i * b) * a
	elif a <= -1.2e+24:
		tmp = (z * x) * y
	elif a <= 2.9e+113:
		tmp = (t * c) * j
	else:
		tmp = (i * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -6.6e+88)
		tmp = Float64(Float64(i * b) * a);
	elseif (a <= -1.2e+24)
		tmp = Float64(Float64(z * x) * y);
	elseif (a <= 2.9e+113)
		tmp = Float64(Float64(t * c) * j);
	else
		tmp = Float64(Float64(i * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -6.6e+88)
		tmp = (i * b) * a;
	elseif (a <= -1.2e+24)
		tmp = (z * x) * y;
	elseif (a <= 2.9e+113)
		tmp = (t * c) * j;
	else
		tmp = (i * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -6.6e+88], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, -1.2e+24], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 2.9e+113], N[(N[(t * c), $MachinePrecision] * j), $MachinePrecision], N[(N[(i * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.6000000000000006e88

   1. Initial program 63.3%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 48.2%

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

   if -6.6000000000000006e88 < a < -1.2e24

   1. Initial program 77.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 63.0

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.7%

      \[\leadsto \left(z \cdot x\right) \cdot y \]

   if -1.2e24 < a < 2.89999999999999984e113

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 44.1

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

   5. Applied rewrites 44.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 34.1%

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

   10. Applied rewrites 37.4%

       \[\leadsto \left(t \cdot c\right) \cdot j \]

   if 2.89999999999999984e113 < a

   1. Initial program 64.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. mul-1-neg N/A

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

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)}\right) \cdot b \]

      10. distribute-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(a\right)\right) \cdot i\right)\right)\right)} \cdot b \]

      11. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z - a \cdot i\right)}\right)\right) \cdot b \]

      12. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)} \cdot b \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right) \cdot b} \]

   5. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, c, i \cdot a\right) \cdot b} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot i\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 52.9%

      \[\leadsto \left(i \cdot a\right) \cdot b \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 28.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot b\right) \cdot a\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+113}:\\ \;\;\;\;\left(t \cdot c\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i b) a)))
   (if (<= a -6.6e+88)
     t_1
     (if (<= a -1.2e+24)
       (* (* z x) y)
       (if (<= a 2.9e+113) (* (* t c) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (a <= -6.6e+88) {
		tmp = t_1;
	} else if (a <= -1.2e+24) {
		tmp = (z * x) * y;
	} else if (a <= 2.9e+113) {
		tmp = (t * c) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * b) * a
    if (a <= (-6.6d+88)) then
        tmp = t_1
    else if (a <= (-1.2d+24)) then
        tmp = (z * x) * y
    else if (a <= 2.9d+113) then
        tmp = (t * c) * j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * b) * a;
	double tmp;
	if (a <= -6.6e+88) {
		tmp = t_1;
	} else if (a <= -1.2e+24) {
		tmp = (z * x) * y;
	} else if (a <= 2.9e+113) {
		tmp = (t * c) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * b) * a
	tmp = 0
	if a <= -6.6e+88:
		tmp = t_1
	elif a <= -1.2e+24:
		tmp = (z * x) * y
	elif a <= 2.9e+113:
		tmp = (t * c) * j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * b) * a)
	tmp = 0.0
	if (a <= -6.6e+88)
		tmp = t_1;
	elseif (a <= -1.2e+24)
		tmp = Float64(Float64(z * x) * y);
	elseif (a <= 2.9e+113)
		tmp = Float64(Float64(t * c) * j);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * b) * a;
	tmp = 0.0;
	if (a <= -6.6e+88)
		tmp = t_1;
	elseif (a <= -1.2e+24)
		tmp = (z * x) * y;
	elseif (a <= 2.9e+113)
		tmp = (t * c) * j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -6.6e+88], t$95$1, If[LessEqual[a, -1.2e+24], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 2.9e+113], N[(N[(t * c), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.6000000000000006e88 or 2.89999999999999984e113 < a

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 58.1

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 58.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.6%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -6.6000000000000006e88 < a < -1.2e24

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right) \cdot y} \]

      3. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(i \cdot j\right)\right)} + x \cdot z\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{j \cdot i}\right)\right) + x \cdot z\right) \cdot y \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot i} + x \cdot z\right) \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j\right), i, x \cdot z\right)} \cdot y \]

      7. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-j}, i, x \cdot z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-j, i, \color{blue}{z \cdot x}\right) \cdot y \]

      9. lower-*.f64 63.0

         \[\leadsto \mathsf{fma}\left(-j, i, \color{blue}{z \cdot x}\right) \cdot y \]

   5. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 54.7%

      \[\leadsto \left(z \cdot x\right) \cdot y \]

   if -1.2e24 < a < 2.89999999999999984e113

   1. Initial program 81.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 44.1

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 34.1%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 37.4%

       \[\leadsto \left(t \cdot c\right) \cdot j \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 28.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{+88} \lor \neg \left(a \leq 2.9 \cdot 10^{+113}\right):\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot j\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6.1e+88) (not (<= a 2.9e+113))) (* (* i b) a) (* (* t c) j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.1e+88) || !(a <= 2.9e+113)) {
		tmp = (i * b) * a;
	} else {
		tmp = (t * c) * j;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-6.1d+88)) .or. (.not. (a <= 2.9d+113))) then
        tmp = (i * b) * a
    else
        tmp = (t * c) * j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.1e+88) || !(a <= 2.9e+113)) {
		tmp = (i * b) * a;
	} else {
		tmp = (t * c) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -6.1e+88) or not (a <= 2.9e+113):
		tmp = (i * b) * a
	else:
		tmp = (t * c) * j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6.1e+88) || !(a <= 2.9e+113))
		tmp = Float64(Float64(i * b) * a);
	else
		tmp = Float64(Float64(t * c) * j);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -6.1e+88) || ~((a <= 2.9e+113)))
		tmp = (i * b) * a;
	else
		tmp = (t * c) * j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6.1e+88], N[Not[LessEqual[a, 2.9e+113]], $MachinePrecision]], N[(N[(i * b), $MachinePrecision] * a), $MachinePrecision], N[(N[(t * c), $MachinePrecision] * j), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.0999999999999998e88 or 2.89999999999999984e113 < a

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(a \cdot b\right)\right)} \cdot i \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \cdot i \]

      5. *-lft-identity N/A

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \cdot i \]

      6. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot j\right)} + a \cdot b\right) \cdot i \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot j} + a \cdot b\right) \cdot i \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, j, a \cdot b\right)} \cdot i \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, j, a \cdot b\right) \cdot i \]

      10. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, j, a \cdot b\right) \cdot i \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

      12. lower-*.f64 58.1

          \[\leadsto \mathsf{fma}\left(-y, j, \color{blue}{b \cdot a}\right) \cdot i \]

   5. Applied rewrites 58.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot a\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.6%

      \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{a} \]

   if -6.0999999999999998e88 < a < 2.89999999999999984e113

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

      6. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

      8. lower-*.f64 42.5

         \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

   6. Taylor expanded in x around 0

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.7%

      \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
   9. Step-by-step derivation

   10. Applied rewrites 36.3%

       \[\leadsto \left(t \cdot c\right) \cdot j \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{+88} \lor \neg \left(a \leq 2.9 \cdot 10^{+113}\right):\\ \;\;\;\;\left(i \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(t \cdot c\right) \cdot j \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* t c) j))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (t * c) * j;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = (t * c) * j
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (t * c) * j;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (t * c) * j

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(t * c) * j)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (t * c) * j;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(t * c), $MachinePrecision] * j), $MachinePrecision]

Derivation

1. Initial program 75.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   3. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

   6. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

   7. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   8. lower-*.f64 43.4

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

5. Applied rewrites 43.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 25.7%

   \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
9. Step-by-step derivation

10. Applied rewrites 28.0%

    \[\leadsto \left(t \cdot c\right) \cdot j \]
11. Add Preprocessing

Alternative 17: 22.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(j \cdot t\right) \cdot c \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* j t) c))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (j * t) * 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 = (j * t) * 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 (j * t) * c;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (j * t) * c

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(j * t) * c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (j * t) * c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(j * t), $MachinePrecision] * c), $MachinePrecision]

Derivation

1. Initial program 75.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right) \cdot t} \]

   3. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} + c \cdot j\right) \cdot t \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot x + c \cdot j\right) \cdot t \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(a\right), x, c \cdot j\right)} \cdot t \]

   6. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-a}, x, c \cdot j\right) \cdot t \]

   7. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

   8. lower-*.f64 43.4

      \[\leadsto \mathsf{fma}\left(-a, x, \color{blue}{j \cdot c}\right) \cdot t \]

5. Applied rewrites 43.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-a, x, j \cdot c\right) \cdot t} \]

6. Taylor expanded in x around 0

   \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 25.7%

   \[\leadsto \left(j \cdot t\right) \cdot \color{blue}{c} \]
9. Add Preprocessing

Developer Target 1: 68.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))