Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 90.4% → 95.4%

Time: 10.3s

Alternatives: 15

Speedup: 0.5×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + b \cdot c\right) \cdot c\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+205}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\left(-i\right) \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+197}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t\_1 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ a (* b c)) c)))
   (if (<= t_1 -5e+205)
     (* 2.0 (fma z t (fma (* (- i) (fma c b a)) c (* y x))))
     (if (<= t_1 1e+197)
       (* 2.0 (- (+ (* x y) (* z t)) (* t_1 i)))
       (* 2.0 (fma z t (* (- c) (* (fma b c a) i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a + (b * c)) * c;
	double tmp;
	if (t_1 <= -5e+205) {
		tmp = 2.0 * fma(z, t, fma((-i * fma(c, b, a)), c, (y * x)));
	} else if (t_1 <= 1e+197) {
		tmp = 2.0 * (((x * y) + (z * t)) - (t_1 * i));
	} else {
		tmp = 2.0 * fma(z, t, (-c * (fma(b, c, a) * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a + Float64(b * c)) * c)
	tmp = 0.0
	if (t_1 <= -5e+205)
		tmp = Float64(2.0 * fma(z, t, fma(Float64(Float64(-i) * fma(c, b, a)), c, Float64(y * x))));
	elseif (t_1 <= 1e+197)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_1 * i)));
	else
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(-c) * Float64(fma(b, c, a) * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+205], N[(2.0 * N[(z * t + N[(N[((-i) * N[(c * b + a), $MachinePrecision]), $MachinePrecision] * c + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+197], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t + N[((-c) * N[(N[(b * c + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -5.0000000000000002e205

   1. Initial program 69.3%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 93.7%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   if -5.0000000000000002e205 < (*.f64 (+.f64 a (*.f64 b c)) c) < 9.9999999999999995e196

   1. Initial program 98.6%

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

   if 9.9999999999999995e196 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 74.0%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 89.4%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      8. lower-fma.f64 96.5

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   7. Applied rewrites 96.5%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \leq -5 \cdot 10^{+205}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\left(-i\right) \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)\\ \mathbf{elif}\;\left(a + b \cdot c\right) \cdot c \leq 10^{+197}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ t_3 := 2 \cdot \mathsf{fma}\left(-i, \mathsf{fma}\left(c, b, a\right) \cdot c, t \cdot z\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+17}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+296}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* -2.0 (* (fma c b a) i)) c))
        (t_2 (* (* (+ a (* b c)) c) i))
        (t_3 (* 2.0 (fma (- i) (* (fma c b a) c) (* t z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e+26)
       t_3
       (if (<= t_2 5e+17)
         (* 2.0 (fma t z (* y x)))
         (if (<= t_2 1e+296) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (-2.0 * (fma(c, b, a) * i)) * c;
	double t_2 = ((a + (b * c)) * c) * i;
	double t_3 = 2.0 * fma(-i, (fma(c, b, a) * c), (t * z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e+26) {
		tmp = t_3;
	} else if (t_2 <= 5e+17) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else if (t_2 <= 1e+296) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c)
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	t_3 = Float64(2.0 * fma(Float64(-i), Float64(fma(c, b, a) * c), Float64(t * z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e+26)
		tmp = t_3;
	elseif (t_2 <= 5e+17)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	elseif (t_2 <= 1e+296)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[((-i) * N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e+26], t$95$3, If[LessEqual[t$95$2, 5e+17], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+296], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 9.99999999999999981e295 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \color{blue}{\left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \color{blue}{\left(a \cdot i + \left(b \cdot c\right) \cdot i\right)}\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \color{blue}{b \cdot \left(c \cdot i\right)}\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c} \]

      7. distribute-lft-out N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)} \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \color{blue}{\left(b \cdot c\right) \cdot i}\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(\color{blue}{c \cdot b} + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 91.2

          \[\leadsto \left(-2 \cdot \left(\color{blue}{\mathsf{fma}\left(c, b, a\right)} \cdot i\right)\right) \cdot c \]

   5. Applied rewrites 91.2%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -2.0000000000000001e26 or 5e17 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999981e295

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right) + t \cdot z\right)} \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} + t \cdot z\right) \]

      4. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} + t \cdot z\right) \]

      5. associate-*r* N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)}\right)\right) + t \cdot z\right) \]

      6. +-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(c \cdot i\right) \cdot \color{blue}{\left(b \cdot c + a\right)}\right)\right) + t \cdot z\right) \]

      7. distribute-lft-in N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(c \cdot i\right) \cdot \left(b \cdot c\right) + \left(c \cdot i\right) \cdot a\right)}\right)\right) + t \cdot z\right) \]

      8. associate-*l* N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(\color{blue}{\left(\left(c \cdot i\right) \cdot b\right) \cdot c} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      9. *-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(\color{blue}{\left(b \cdot \left(c \cdot i\right)\right)} \cdot c + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      10. associate-*l* N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(\color{blue}{b \cdot \left(\left(c \cdot i\right) \cdot c\right)} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      11. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \left(\color{blue}{\left(i \cdot c\right)} \cdot c\right) + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \color{blue}{\left(i \cdot \left(c \cdot c\right)\right)} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      13. unpow2 N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \left(i \cdot \color{blue}{{c}^{2}}\right) + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      14. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \color{blue}{\left({c}^{2} \cdot i\right)} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      15. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \left({c}^{2} \cdot i\right) + \color{blue}{a \cdot \left(c \cdot i\right)}\right)\right)\right) + t \cdot z\right) \]

      16. distribute-neg-in N/A

          \[\leadsto 2 \cdot \left(\color{blue}{\left(\left(\mathsf{neg}\left(b \cdot \left({c}^{2} \cdot i\right)\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(c \cdot i\right)\right)\right)\right)} + t \cdot z\right) \]

   5. Applied rewrites 80.9%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(-i, \mathsf{fma}\left(c, b, a\right) \cdot c, t \cdot z\right)} \]

   if -2.0000000000000001e26 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e17

   1. Initial program 99.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, x \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

      4. lower-*.f64 96.1

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 96.1%

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

Alternative 3: 86.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+17}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+296}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(-i, \mathsf{fma}\left(c, b, a\right) \cdot c, t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (fma z t (* (- c) (* (fma b c a) i)))))
        (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -2e+26)
     t_1
     (if (<= t_2 5e+17)
       (* 2.0 (fma t z (* y x)))
       (if (<= t_2 1e+296)
         (* 2.0 (fma (- i) (* (fma c b a) c) (* t z)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * fma(z, t, (-c * (fma(b, c, a) * i)));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -2e+26) {
		tmp = t_1;
	} else if (t_2 <= 5e+17) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else if (t_2 <= 1e+296) {
		tmp = 2.0 * fma(-i, (fma(c, b, a) * c), (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * fma(z, t, Float64(Float64(-c) * Float64(fma(b, c, a) * i))))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -2e+26)
		tmp = t_1;
	elseif (t_2 <= 5e+17)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	elseif (t_2 <= 1e+296)
		tmp = Float64(2.0 * fma(Float64(-i), Float64(fma(c, b, a) * c), Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t + N[((-c) * N[(N[(b * c + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+26], t$95$1, If[LessEqual[t$95$2, 5e+17], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+296], N[(2.0 * N[((-i) * N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -2.0000000000000001e26 or 9.99999999999999981e295 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.4%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 91.2%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      8. lower-fma.f64 90.5

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   7. Applied rewrites 90.5%

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)}\right) \]

   if -2.0000000000000001e26 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e17

   1. Initial program 99.0%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, x \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

      4. lower-*.f64 96.1

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 96.1%

      \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 5e17 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999981e295

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + \left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right) + t \cdot z\right)} \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} + t \cdot z\right) \]

      4. mul-1-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(\mathsf{neg}\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} + t \cdot z\right) \]

      5. associate-*r* N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)}\right)\right) + t \cdot z\right) \]

      6. +-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(c \cdot i\right) \cdot \color{blue}{\left(b \cdot c + a\right)}\right)\right) + t \cdot z\right) \]

      7. distribute-lft-in N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(\left(c \cdot i\right) \cdot \left(b \cdot c\right) + \left(c \cdot i\right) \cdot a\right)}\right)\right) + t \cdot z\right) \]

      8. associate-*l* N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(\color{blue}{\left(\left(c \cdot i\right) \cdot b\right) \cdot c} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      9. *-commutative N/A

         \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(\color{blue}{\left(b \cdot \left(c \cdot i\right)\right)} \cdot c + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      10. associate-*l* N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(\color{blue}{b \cdot \left(\left(c \cdot i\right) \cdot c\right)} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      11. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \left(\color{blue}{\left(i \cdot c\right)} \cdot c\right) + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \color{blue}{\left(i \cdot \left(c \cdot c\right)\right)} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      13. unpow2 N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \left(i \cdot \color{blue}{{c}^{2}}\right) + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      14. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \color{blue}{\left({c}^{2} \cdot i\right)} + \left(c \cdot i\right) \cdot a\right)\right)\right) + t \cdot z\right) \]

      15. *-commutative N/A

          \[\leadsto 2 \cdot \left(\left(\mathsf{neg}\left(\left(b \cdot \left({c}^{2} \cdot i\right) + \color{blue}{a \cdot \left(c \cdot i\right)}\right)\right)\right) + t \cdot z\right) \]

      16. distribute-neg-in N/A

          \[\leadsto 2 \cdot \left(\color{blue}{\left(\left(\mathsf{neg}\left(b \cdot \left({c}^{2} \cdot i\right)\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(c \cdot i\right)\right)\right)\right)} + t \cdot z\right) \]

   5. Applied rewrites 84.6%

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

Alternative 4: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+26} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(-a \cdot i, c, y \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -2e+26) (not (<= t_1 2e+85)))
     (* 2.0 (fma z t (* (- c) (* (fma b c a) i))))
     (* 2.0 (fma z t (fma (- (* a i)) c (* y x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if ((t_1 <= -2e+26) || !(t_1 <= 2e+85)) {
		tmp = 2.0 * fma(z, t, (-c * (fma(b, c, a) * i)));
	} else {
		tmp = 2.0 * fma(z, t, fma(-(a * i), c, (y * x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if ((t_1 <= -2e+26) || !(t_1 <= 2e+85))
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(-c) * Float64(fma(b, c, a) * i))));
	else
		tmp = Float64(2.0 * fma(z, t, fma(Float64(-Float64(a * i)), c, Float64(y * x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+26], N[Not[LessEqual[t$95$1, 2e+85]], $MachinePrecision]], N[(2.0 * N[(z * t + N[((-c) * N[(N[(b * c + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t + N[((-N[(a * i), $MachinePrecision]) * c + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -2.0000000000000001e26 or 2e85 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.1%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 88.4%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      8. lower-fma.f64 87.9

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   7. Applied rewrites 87.9%

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)}\right) \]

   if -2.0000000000000001e26 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e85

   1. Initial program 99.0%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 98.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(-\color{blue}{a \cdot i}, c, y \cdot x\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 96.2

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(-\color{blue}{a \cdot i}, c, y \cdot x\right)\right) \]

   7. Applied rewrites 96.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -2 \cdot 10^{+26} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(-a \cdot i, c, y \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(\left(-i\right) \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((x * y) + (z * t)) - (((a + (b * c)) * c) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * fma(z, t, fma((-i * fma(c, b, a)), c, (y * x)));
	} else {
		tmp = 2.0 * fma(z, t, (-c * (fma(b, c, a) * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)) <= Inf)
		tmp = Float64(2.0 * fma(z, t, fma(Float64(Float64(-i) * fma(c, b, a)), c, Float64(y * x))));
	else
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(-c) * Float64(fma(b, c, a) * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(z * t + N[(N[((-i) * N[(c * b + a), $MachinePrecision]), $MachinePrecision] * c + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t + N[((-c) * N[(N[(b * c + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.4%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 95.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

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

   1. Initial program 0.0%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 55.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(c\right)\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      8. lower-fma.f64 77.8

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(-c\right) \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   7. Applied rewrites 77.8%

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

4. Final simplification 93.9%

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

Alternative 6: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+72} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 -5e+72) (not (<= t_1 2e+184)))
     (* (* -2.0 (* (fma c b a) i)) c)
     (* 2.0 (fma t z (* y x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if ((t_1 <= -5e+72) || !(t_1 <= 2e+184)) {
		tmp = (-2.0 * (fma(c, b, a) * i)) * c;
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if ((t_1 <= -5e+72) || !(t_1 <= 2e+184))
		tmp = Float64(Float64(-2.0 * Float64(fma(c, b, a) * i)) * c);
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+72], N[Not[LessEqual[t$95$1, 2e+184]], $MachinePrecision]], N[(N[(-2.0 * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.99999999999999992e72 or 2.00000000000000003e184 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 77.6%

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

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \color{blue}{\left(\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} \]

      3. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \color{blue}{\left(a \cdot i + \left(b \cdot c\right) \cdot i\right)}\right) \cdot c \]

      4. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \color{blue}{b \cdot \left(c \cdot i\right)}\right)\right) \cdot c \]

      5. distribute-lft-out N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \cdot c \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(a \cdot i\right) + -2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c} \]

      7. distribute-lft-out N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)} \cdot c \]

      8. associate-*r* N/A

         \[\leadsto \left(-2 \cdot \left(a \cdot i + \color{blue}{\left(b \cdot c\right) \cdot i}\right)\right) \cdot c \]

      9. distribute-rgt-in N/A

         \[\leadsto \left(-2 \cdot \color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right)}\right) \cdot c \]

      10. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-2 \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \cdot c \]

      11. *-commutative N/A

          \[\leadsto \left(-2 \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \cdot c \]

      12. lower-*.f64 N/A

          \[\leadsto \left(-2 \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \cdot c \]

      13. +-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \cdot c \]

      14. *-commutative N/A

          \[\leadsto \left(-2 \cdot \left(\left(\color{blue}{c \cdot b} + a\right) \cdot i\right)\right) \cdot c \]

      15. lower-fma.f64 83.8

          \[\leadsto \left(-2 \cdot \left(\color{blue}{\mathsf{fma}\left(c, b, a\right)} \cdot i\right)\right) \cdot c \]

   5. Applied rewrites 83.8%

      \[\leadsto \color{blue}{\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c} \]

   if -4.99999999999999992e72 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.00000000000000003e184

   1. Initial program 98.3%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, x \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

      4. lower-*.f64 85.2

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 85.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -5 \cdot 10^{+72} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 2 \cdot 10^{+184}\right):\\ \;\;\;\;\left(-2 \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+275}\right):\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+275)))
     (* (* (* (* c c) i) b) -2.0)
     (* 2.0 (fma t z (* y x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+275)) {
		tmp = (((c * c) * i) * b) * -2.0;
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+275))
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * b) * -2.0);
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+275]], $MachinePrecision]], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 5.0000000000000003e275 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 71.7%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 89.6%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left({c}^{2} \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left({c}^{2} \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left({c}^{2} \cdot i\right)} \cdot b\right) \cdot -2 \]

      6. unpow2 N/A

         \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

      7. lower-*.f64 62.8

         \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   7. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2} \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000003e275

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, x \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

      4. lower-*.f64 78.3

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 78.3%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -\infty \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 5 \cdot 10^{+275}\right):\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 (- INFINITY))
     (* (* (* (* i c) b) -2.0) c)
     (if (<= t_1 5e+275)
       (* 2.0 (fma t z (* y x)))
       (* (* (* (* c c) i) b) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((i * c) * b) * -2.0) * c;
	} else if (t_1 <= 5e+275) {
		tmp = 2.0 * fma(t, z, (y * x));
	} else {
		tmp = (((c * c) * i) * b) * -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(i * c) * b) * -2.0) * c);
	elseif (t_1 <= 5e+275)
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	else
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * b) * -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(i * c), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision] * c), $MachinePrecision], If[LessEqual[t$95$1, 5e+275], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * b), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -2 \cdot \left(b \cdot \color{blue}{\left(i \cdot {c}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto -2 \cdot \left(b \cdot \left(i \cdot \color{blue}{\left(c \cdot c\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto -2 \cdot \left(b \cdot \color{blue}{\left(\left(i \cdot c\right) \cdot c\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto -2 \cdot \left(b \cdot \left(\color{blue}{\left(c \cdot i\right)} \cdot c\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto -2 \cdot \color{blue}{\left(\left(b \cdot \left(c \cdot i\right)\right) \cdot c\right)} \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \left(b \cdot \left(c \cdot i\right)\right)\right) \cdot c} \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(c \cdot i\right)\right) \cdot -2\right)} \cdot c \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(c \cdot i\right)\right) \cdot -2\right)} \cdot c \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\left(c \cdot i\right) \cdot b\right)} \cdot -2\right) \cdot c \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(\left(c \cdot i\right) \cdot b\right)} \cdot -2\right) \cdot c \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\color{blue}{\left(i \cdot c\right)} \cdot b\right) \cdot -2\right) \cdot c \]

      13. lower-*.f64 68.0

          \[\leadsto \left(\left(\color{blue}{\left(i \cdot c\right)} \cdot b\right) \cdot -2\right) \cdot c \]

   5. Applied rewrites 68.0%

      \[\leadsto \color{blue}{\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c} \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000003e275

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, x \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

      4. lower-*.f64 78.3

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 78.3%

      \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)} \]

   if 5.0000000000000003e275 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 68.2%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 88.1%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-2 \cdot \left(b \cdot \left({c}^{2} \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left({c}^{2} \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left({c}^{2} \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left({c}^{2} \cdot i\right) \cdot b\right)} \cdot -2 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left({c}^{2} \cdot i\right)} \cdot b\right) \cdot -2 \]

      6. unpow2 N/A

         \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

      7. lower-*.f64 59.7

         \[\leadsto \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot i\right) \cdot b\right) \cdot -2 \]

   7. Applied rewrites 59.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(\left(\left(i \cdot c\right) \cdot b\right) \cdot -2\right) \cdot c\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 5 \cdot 10^{+275}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot b\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+275}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+275)))
     (* (* (* i c) a) -2.0)
     (* 2.0 (fma t z (* y x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+275)) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = 2.0 * fma(t, z, (y * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+275))
		tmp = Float64(Float64(Float64(i * c) * a) * -2.0);
	else
		tmp = Float64(2.0 * fma(t, z, Float64(y * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+275]], $MachinePrecision]], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 5.0000000000000003e275 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 71.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

      6. lower-*.f64 48.0

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

   5. Applied rewrites 48.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000003e275

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(t, z, x \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

      4. lower-*.f64 78.3

         \[\leadsto 2 \cdot \mathsf{fma}\left(t, z, \color{blue}{y \cdot x}\right) \]

   5. Applied rewrites 78.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -\infty \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 5 \cdot 10^{+275}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+275}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot z\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+275)))
     (* (* (* i c) a) -2.0)
     (* (fma x y (* t z)) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+275)) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = fma(x, y, (t * z)) * 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+275))
		tmp = Float64(Float64(Float64(i * c) * a) * -2.0);
	else
		tmp = Float64(fma(x, y, Float64(t * z)) * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+275]], $MachinePrecision]], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(x * y + N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 5.0000000000000003e275 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 71.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

      6. lower-*.f64 48.0

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

   5. Applied rewrites 48.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000003e275

   1. Initial program 98.5%

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

      1. lift--.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      2. lift-+.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      3. associate--l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      5. sub-neg N/A

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)\right)} + x \cdot y\right) \]

      6. associate-+l+ N/A

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \left(\color{blue}{z \cdot t} + \left(\left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) + x \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right)\right) + x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      11. lift-*.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) + x \cdot y\right) \]

      12. associate-*r* N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \left(\mathsf{neg}\left(\color{blue}{\left(i \cdot \left(a + b \cdot c\right)\right) \cdot c}\right)\right) + x \cdot y\right) \]

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

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot c} + x \cdot y\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(i \cdot \left(a + b \cdot c\right)\right), c, x \cdot y\right)}\right) \]

   4. Applied rewrites 94.2%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(-i \cdot \mathsf{fma}\left(c, b, a\right), c, y \cdot x\right)\right)} \]

   5. Taylor expanded in c around 0

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z + x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot z + x \cdot y\right) \cdot 2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t \cdot z + x \cdot y\right) \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y + t \cdot z\right)} \cdot 2 \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, t \cdot z\right)} \cdot 2 \]

      5. lower-*.f64 78.3

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{t \cdot z}\right) \cdot 2 \]

   7. Applied rewrites 78.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -\infty \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 5 \cdot 10^{+275}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot z\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ t_2 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-319}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (* i c) a) -2.0)) (t_2 (* 2.0 (* t z))))
   (if (<= (* z t) -5e+97)
     t_2
     (if (<= (* z t) -2e-319)
       t_1
       (if (<= (* z t) 2e-44)
         (* 2.0 (* y x))
         (if (<= (* z t) 5e+142) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((i * c) * a) * -2.0;
	double t_2 = 2.0 * (t * z);
	double tmp;
	if ((z * t) <= -5e+97) {
		tmp = t_2;
	} else if ((z * t) <= -2e-319) {
		tmp = t_1;
	} else if ((z * t) <= 2e-44) {
		tmp = 2.0 * (y * x);
	} else if ((z * t) <= 5e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((i * c) * a) * (-2.0d0)
    t_2 = 2.0d0 * (t * z)
    if ((z * t) <= (-5d+97)) then
        tmp = t_2
    else if ((z * t) <= (-2d-319)) then
        tmp = t_1
    else if ((z * t) <= 2d-44) then
        tmp = 2.0d0 * (y * x)
    else if ((z * t) <= 5d+142) 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 t_1 = ((i * c) * a) * -2.0;
	double t_2 = 2.0 * (t * z);
	double tmp;
	if ((z * t) <= -5e+97) {
		tmp = t_2;
	} else if ((z * t) <= -2e-319) {
		tmp = t_1;
	} else if ((z * t) <= 2e-44) {
		tmp = 2.0 * (y * x);
	} else if ((z * t) <= 5e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((i * c) * a) * -2.0
	t_2 = 2.0 * (t * z)
	tmp = 0
	if (z * t) <= -5e+97:
		tmp = t_2
	elif (z * t) <= -2e-319:
		tmp = t_1
	elif (z * t) <= 2e-44:
		tmp = 2.0 * (y * x)
	elif (z * t) <= 5e+142:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(i * c) * a) * -2.0)
	t_2 = Float64(2.0 * Float64(t * z))
	tmp = 0.0
	if (Float64(z * t) <= -5e+97)
		tmp = t_2;
	elseif (Float64(z * t) <= -2e-319)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e-44)
		tmp = Float64(2.0 * Float64(y * x));
	elseif (Float64(z * t) <= 5e+142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((i * c) * a) * -2.0;
	t_2 = 2.0 * (t * z);
	tmp = 0.0;
	if ((z * t) <= -5e+97)
		tmp = t_2;
	elseif ((z * t) <= -2e-319)
		tmp = t_1;
	elseif ((z * t) <= 2e-44)
		tmp = 2.0 * (y * x);
	elseif ((z * t) <= 5e+142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+97], t$95$2, If[LessEqual[N[(z * t), $MachinePrecision], -2e-319], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e-44], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+142], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999999e97 or 5.0000000000000001e142 < (*.f64 z t)

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

      2. lower-*.f64 65.7

         \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   5. Applied rewrites 65.7%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

   if -4.99999999999999999e97 < (*.f64 z t) < -1.99998e-319 or 1.99999999999999991e-44 < (*.f64 z t) < 5.0000000000000001e142

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

      6. lower-*.f64 38.8

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

   5. Applied rewrites 38.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]

   if -1.99998e-319 < (*.f64 z t) < 1.99999999999999991e-44

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

      3. lower-*.f64 42.9

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   5. Applied rewrites 42.9%

      \[\leadsto \color{blue}{2 \cdot \left(y \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 41.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-319}:\\ \;\;\;\;\left(\left(a \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+142}:\\ \;\;\;\;\left(\left(a \cdot i\right) \cdot c\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* t z))))
   (if (<= (* z t) -5e+97)
     t_1
     (if (<= (* z t) -2e-319)
       (* (* (* a c) i) -2.0)
       (if (<= (* z t) 2e-44)
         (* 2.0 (* y x))
         (if (<= (* z t) 5e+142) (* (* (* a i) c) -2.0) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (t * z);
	double tmp;
	if ((z * t) <= -5e+97) {
		tmp = t_1;
	} else if ((z * t) <= -2e-319) {
		tmp = ((a * c) * i) * -2.0;
	} else if ((z * t) <= 2e-44) {
		tmp = 2.0 * (y * x);
	} else if ((z * t) <= 5e+142) {
		tmp = ((a * i) * c) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (t * z)
    if ((z * t) <= (-5d+97)) then
        tmp = t_1
    else if ((z * t) <= (-2d-319)) then
        tmp = ((a * c) * i) * (-2.0d0)
    else if ((z * t) <= 2d-44) then
        tmp = 2.0d0 * (y * x)
    else if ((z * t) <= 5d+142) then
        tmp = ((a * i) * c) * (-2.0d0)
    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 t_1 = 2.0 * (t * z);
	double tmp;
	if ((z * t) <= -5e+97) {
		tmp = t_1;
	} else if ((z * t) <= -2e-319) {
		tmp = ((a * c) * i) * -2.0;
	} else if ((z * t) <= 2e-44) {
		tmp = 2.0 * (y * x);
	} else if ((z * t) <= 5e+142) {
		tmp = ((a * i) * c) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (t * z)
	tmp = 0
	if (z * t) <= -5e+97:
		tmp = t_1
	elif (z * t) <= -2e-319:
		tmp = ((a * c) * i) * -2.0
	elif (z * t) <= 2e-44:
		tmp = 2.0 * (y * x)
	elif (z * t) <= 5e+142:
		tmp = ((a * i) * c) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(t * z))
	tmp = 0.0
	if (Float64(z * t) <= -5e+97)
		tmp = t_1;
	elseif (Float64(z * t) <= -2e-319)
		tmp = Float64(Float64(Float64(a * c) * i) * -2.0);
	elseif (Float64(z * t) <= 2e-44)
		tmp = Float64(2.0 * Float64(y * x));
	elseif (Float64(z * t) <= 5e+142)
		tmp = Float64(Float64(Float64(a * i) * c) * -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (t * z);
	tmp = 0.0;
	if ((z * t) <= -5e+97)
		tmp = t_1;
	elseif ((z * t) <= -2e-319)
		tmp = ((a * c) * i) * -2.0;
	elseif ((z * t) <= 2e-44)
		tmp = 2.0 * (y * x);
	elseif ((z * t) <= 5e+142)
		tmp = ((a * i) * c) * -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+97], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -2e-319], N[(N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-44], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+142], N[(N[(N[(a * i), $MachinePrecision] * c), $MachinePrecision] * -2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -4.99999999999999999e97 or 5.0000000000000001e142 < (*.f64 z t)

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

      2. lower-*.f64 65.7

         \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   5. Applied rewrites 65.7%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

   if -4.99999999999999999e97 < (*.f64 z t) < -1.99998e-319

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

      6. lower-*.f64 37.1

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

   5. Applied rewrites 37.1%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

      \[\leadsto \left(\left(a \cdot c\right) \cdot i\right) \cdot -2 \]

   if -1.99998e-319 < (*.f64 z t) < 1.99999999999999991e-44

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

      3. lower-*.f64 42.9

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   5. Applied rewrites 42.9%

      \[\leadsto \color{blue}{2 \cdot \left(y \cdot x\right)} \]

   if 1.99999999999999991e-44 < (*.f64 z t) < 5.0000000000000001e142

   1. Initial program 82.4%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

      6. lower-*.f64 41.2

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

   5. Applied rewrites 41.2%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

      \[\leadsto \left(\left(a \cdot i\right) \cdot c\right) \cdot -2 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 42.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-319}:\\ \;\;\;\;\left(\left(a \cdot c\right) \cdot i\right) \cdot -2\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* t z))))
   (if (<= (* z t) -5e+97)
     t_1
     (if (<= (* z t) -2e-319)
       (* (* (* a c) i) -2.0)
       (if (<= (* z t) 4e+129) (* 2.0 (* y x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (t * z);
	double tmp;
	if ((z * t) <= -5e+97) {
		tmp = t_1;
	} else if ((z * t) <= -2e-319) {
		tmp = ((a * c) * i) * -2.0;
	} else if ((z * t) <= 4e+129) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (t * z)
    if ((z * t) <= (-5d+97)) then
        tmp = t_1
    else if ((z * t) <= (-2d-319)) then
        tmp = ((a * c) * i) * (-2.0d0)
    else if ((z * t) <= 4d+129) then
        tmp = 2.0d0 * (y * x)
    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 t_1 = 2.0 * (t * z);
	double tmp;
	if ((z * t) <= -5e+97) {
		tmp = t_1;
	} else if ((z * t) <= -2e-319) {
		tmp = ((a * c) * i) * -2.0;
	} else if ((z * t) <= 4e+129) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (t * z)
	tmp = 0
	if (z * t) <= -5e+97:
		tmp = t_1
	elif (z * t) <= -2e-319:
		tmp = ((a * c) * i) * -2.0
	elif (z * t) <= 4e+129:
		tmp = 2.0 * (y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(t * z))
	tmp = 0.0
	if (Float64(z * t) <= -5e+97)
		tmp = t_1;
	elseif (Float64(z * t) <= -2e-319)
		tmp = Float64(Float64(Float64(a * c) * i) * -2.0);
	elseif (Float64(z * t) <= 4e+129)
		tmp = Float64(2.0 * Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (t * z);
	tmp = 0.0;
	if ((z * t) <= -5e+97)
		tmp = t_1;
	elseif ((z * t) <= -2e-319)
		tmp = ((a * c) * i) * -2.0;
	elseif ((z * t) <= 4e+129)
		tmp = 2.0 * (y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+97], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -2e-319], N[(N[(N[(a * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+129], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999999e97 or 4e129 < (*.f64 z t)

   1. Initial program 85.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

      2. lower-*.f64 63.6

         \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   5. Applied rewrites 63.6%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

   if -4.99999999999999999e97 < (*.f64 z t) < -1.99998e-319

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      5. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

      6. lower-*.f64 37.1

         \[\leadsto \left(\color{blue}{\left(i \cdot c\right)} \cdot a\right) \cdot -2 \]

   5. Applied rewrites 37.1%

      \[\leadsto \color{blue}{\left(\left(i \cdot c\right) \cdot a\right) \cdot -2} \]
   6. Step-by-step derivation

   7. Applied rewrites 35.8%

      \[\leadsto \left(\left(a \cdot c\right) \cdot i\right) \cdot -2 \]

   if -1.99998e-319 < (*.f64 z t) < 4e129

   1. Initial program 87.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

      3. lower-*.f64 38.7

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   5. Applied rewrites 38.7%

      \[\leadsto \color{blue}{2 \cdot \left(y \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 45.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+74} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -5e+74) (not (<= (* z t) 4e+129)))
   (* 2.0 (* t z))
   (* 2.0 (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -5e+74) || !((z * t) <= 4e+129)) {
		tmp = 2.0 * (t * z);
	} else {
		tmp = 2.0 * (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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) :: tmp
    if (((z * t) <= (-5d+74)) .or. (.not. ((z * t) <= 4d+129))) then
        tmp = 2.0d0 * (t * z)
    else
        tmp = 2.0d0 * (y * 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 tmp;
	if (((z * t) <= -5e+74) || !((z * t) <= 4e+129)) {
		tmp = 2.0 * (t * z);
	} else {
		tmp = 2.0 * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -5e+74) or not ((z * t) <= 4e+129):
		tmp = 2.0 * (t * z)
	else:
		tmp = 2.0 * (y * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+74) || !(Float64(z * t) <= 4e+129))
		tmp = Float64(2.0 * Float64(t * z));
	else
		tmp = Float64(2.0 * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((z * t) <= -5e+74) || ~(((z * t) <= 4e+129)))
		tmp = 2.0 * (t * z);
	else
		tmp = 2.0 * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+74], N[Not[LessEqual[N[(z * t), $MachinePrecision], 4e+129]], $MachinePrecision]], N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999963e74 or 4e129 < (*.f64 z t)

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

      2. lower-*.f64 62.4

         \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   5. Applied rewrites 62.4%

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

   if -4.99999999999999963e74 < (*.f64 z t) < 4e129

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]

      2. *-commutative N/A

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

      3. lower-*.f64 33.2

         \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   5. Applied rewrites 33.2%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+74} \lor \neg \left(z \cdot t \leq 4 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(t \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* 2.0 (* t z)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (t * z);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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
    code = 2.0d0 * (t * z)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (t * z);
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (t * z)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(t * z))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (t * z);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.7%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]

   2. lower-*.f64 29.4

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

5. Applied rewrites 29.4%

   \[\leadsto \color{blue}{2 \cdot \left(t \cdot z\right)} \]
6. Add Preprocessing

Developer Target 1: 94.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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
    code = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024318 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))