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

Percentage Accurate: 90.4% → 95.5%

Time: 13.7s

Alternatives: 15

Speedup: 0.5×

• 47.8% 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: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z + y \cdot x\right) - i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \mathsf{fma}\left(t, z, \left(-c\right) \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ (* t z) (* y x)) (* i (* (+ (* c b) a) c)))))
   (if (<= t_1 4e+303)
     (* 2.0 t_1)
     (fma (* 2.0 y) x (* (fma t z (* (- c) (* (fma c b a) i))) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((t * z) + (y * x)) - (i * (((c * b) + a) * c));
	double tmp;
	if (t_1 <= 4e+303) {
		tmp = 2.0 * t_1;
	} else {
		tmp = fma((2.0 * y), x, (fma(t, z, (-c * (fma(c, b, a) * i))) * 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(t * z) + Float64(y * x)) - Float64(i * Float64(Float64(Float64(c * b) + a) * c)))
	tmp = 0.0
	if (t_1 <= 4e+303)
		tmp = Float64(2.0 * t_1);
	else
		tmp = fma(Float64(2.0 * y), x, Float64(fma(t, z, Float64(Float64(-c) * Float64(fma(c, b, a) * i))) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(t * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+303], N[(2.0 * t$95$1), $MachinePrecision], N[(N[(2.0 * y), $MachinePrecision] * x + N[(N[(t * z + N[((-c) * N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0), $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)) < 4e303

   1. Initial program 96.7%

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

   if 4e303 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 79.0%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 96.2%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t \cdot z + y \cdot x\right) - i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 4 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + y \cdot x\right) - i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \mathsf{fma}\left(t, z, \left(-c\right) \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot i\right)\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+40} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, \mathsf{fma}\left(c, b, a\right) \cdot c, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \left(t \cdot z\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 (- INFINITY))
     (* -2.0 (* (* (fma c b a) i) c))
     (if (or (<= t_1 -2e+40) (not (<= t_1 2e+70)))
       (* (fma (- i) (* (fma c b a) c) (* y x)) 2.0)
       (fma (* 2.0 y) x (* (* 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 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -2.0 * ((fma(c, b, a) * i) * c);
	} else if ((t_1 <= -2e+40) || !(t_1 <= 2e+70)) {
		tmp = fma(-i, (fma(c, b, a) * c), (y * x)) * 2.0;
	} else {
		tmp = fma((2.0 * y), x, ((t * z) * 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-2.0 * Float64(Float64(fma(c, b, a) * i) * c));
	elseif ((t_1 <= -2e+40) || !(t_1 <= 2e+70))
		tmp = Float64(fma(Float64(-i), Float64(fma(c, b, a) * c), Float64(y * x)) * 2.0);
	else
		tmp = fma(Float64(2.0 * y), x, Float64(Float64(t * z) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-2.0 * N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e+40], N[Not[LessEqual[t$95$1, 2e+70]], $MachinePrecision]], N[(N[((-i) * N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(2.0 * y), $MachinePrecision] * x + N[(N[(t * z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.2%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -2.00000000000000006e40 or 2.00000000000000015e70 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 88.2%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. unpow2 N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. distribute-neg-in N/A

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

   5. Applied rewrites 82.4%

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

   if -2.00000000000000006e40 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.00000000000000015e70

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 89.5

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

   7. Applied rewrites 89.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -\infty:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -2 \cdot 10^{+40} \lor \neg \left(i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, \mathsf{fma}\left(c, b, a\right) \cdot c, y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \left(t \cdot z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, a\right) \cdot i\\ t_2 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(t\_1 \cdot c\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + y \cdot x\right) - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -c, \mathsf{fma}\left(t, z, y \cdot x\right)\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma c b a) i)) (t_2 (* i (* (+ (* c b) a) c))))
   (if (<= t_2 (- INFINITY))
     (* -2.0 (* t_1 c))
     (if (<= t_2 2e+288)
       (* 2.0 (- (+ (* t z) (* y x)) t_2))
       (* (fma t_1 (- c) (fma t z (* y x))) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(c, b, a) * i;
	double t_2 = i * (((c * b) + a) * c);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = -2.0 * (t_1 * c);
	} else if (t_2 <= 2e+288) {
		tmp = 2.0 * (((t * z) + (y * x)) - t_2);
	} else {
		tmp = fma(t_1, -c, fma(t, z, (y * x))) * 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(c, b, a) * i)
	t_2 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(-2.0 * Float64(t_1 * c));
	elseif (t_2 <= 2e+288)
		tmp = Float64(2.0 * Float64(Float64(Float64(t * z) + Float64(y * x)) - t_2));
	else
		tmp = Float64(fma(t_1, Float64(-c), fma(t, z, Float64(y * x))) * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(-2.0 * N[(t$95$1 * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+288], N[(2.0 * N[(N[(N[(t * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * (-c) + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $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 79.2%

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

   3. Taylor expanded in 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

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2e288

   1. Initial program 99.8%

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

   if 2e288 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 77.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 77.8

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

   4. Applied rewrites 88.7%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -\infty:\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 2 \cdot 10^{+288}:\\ \;\;\;\;2 \cdot \left(\left(t \cdot z + y \cdot x\right) - i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(c, b, a\right) \cdot i, -c, \mathsf{fma}\left(t, z, y \cdot x\right)\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(t * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * (-c) + N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(-2.0 * i), $MachinePrecision] * N[(N[(c * c), $MachinePrecision] * b), $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 96.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 96.0

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

   4. Applied rewrites 94.1%

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

   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. Taylor expanded in c 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 69.5

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

   5. Applied rewrites 69.5%

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

   7. Applied rewrites 69.5%

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

4. Final simplification 92.8%

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

Alternative 5: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+159}\right):\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot c\right) \cdot \left(-i\right)\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \left(t \cdot z\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (or (<= t_1 -4e+84) (not (<= t_1 5e+159)))
     (* (* (* (fma c b a) c) (- i)) 2.0)
     (fma (* 2.0 y) x (* (* 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 = i * (((c * b) + a) * c);
	double tmp;
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+159)) {
		tmp = ((fma(c, b, a) * c) * -i) * 2.0;
	} else {
		tmp = fma((2.0 * y), x, ((t * z) * 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+159))
		tmp = Float64(Float64(Float64(fma(c, b, a) * c) * Float64(-i)) * 2.0);
	else
		tmp = fma(Float64(2.0 * y), x, Float64(Float64(t * z) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+84], N[Not[LessEqual[t$95$1, 5e+159]], $MachinePrecision]], N[(N[(N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision] * (-i)), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(2.0 * y), $MachinePrecision] * x + N[(N[(t * z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.00000000000000023e84 or 5.00000000000000003e159 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.8%

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

   3. Taylor expanded in i around inf

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 83.8

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

   5. Applied rewrites 83.8%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.00000000000000003e159

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 98.4%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.2

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

   7. Applied rewrites 84.2%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84} \lor \neg \left(i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+159}\right):\\ \;\;\;\;\left(\left(\mathsf{fma}\left(c, b, a\right) \cdot c\right) \cdot \left(-i\right)\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \left(t \cdot z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+168}\right):\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \left(t \cdot z\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (or (<= t_1 -4e+84) (not (<= t_1 5e+168)))
     (* -2.0 (* (* (fma c b a) i) c))
     (fma (* 2.0 y) x (* (* 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 = i * (((c * b) + a) * c);
	double tmp;
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+168)) {
		tmp = -2.0 * ((fma(c, b, a) * i) * c);
	} else {
		tmp = fma((2.0 * y), x, ((t * z) * 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+168))
		tmp = Float64(-2.0 * Float64(Float64(fma(c, b, a) * i) * c));
	else
		tmp = fma(Float64(2.0 * y), x, Float64(Float64(t * z) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+84], N[Not[LessEqual[t$95$1, 5e+168]], $MachinePrecision]], N[(-2.0 * N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * y), $MachinePrecision] * x + N[(N[(t * z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.00000000000000023e84 or 4.99999999999999967e168 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.6%

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

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999967e168

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in c around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 83.7

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

   7. Applied rewrites 83.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84} \lor \neg \left(i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+168}\right):\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot y, x, \left(t \cdot z\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+168}\right):\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (or (<= t_1 -4e+84) (not (<= t_1 5e+168)))
     (* -2.0 (* (* (fma c b a) i) c))
     (* (fma y x (* 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 = i * (((c * b) + a) * c);
	double tmp;
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+168)) {
		tmp = -2.0 * ((fma(c, b, a) * i) * c);
	} else {
		tmp = fma(y, x, (t * z)) * 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+168))
		tmp = Float64(-2.0 * Float64(Float64(fma(c, b, a) * i) * c));
	else
		tmp = Float64(fma(y, x, Float64(t * z)) * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+84], N[Not[LessEqual[t$95$1, 5e+168]], $MachinePrecision]], N[(-2.0 * N[(N[(N[(c * b + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * x + 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) < -4.00000000000000023e84 or 4.99999999999999967e168 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.6%

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

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999967e168

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84} \lor \neg \left(i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+168}\right):\\ \;\;\;\;-2 \cdot \left(\left(\mathsf{fma}\left(c, b, a\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+168}\right):\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (or (<= t_1 -4e+84) (not (<= t_1 5e+168)))
     (* (* (* -2.0 b) (* i c)) c)
     (* (fma y x (* 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 = i * (((c * b) + a) * c);
	double tmp;
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+168)) {
		tmp = ((-2.0 * b) * (i * c)) * c;
	} else {
		tmp = fma(y, x, (t * z)) * 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if ((t_1 <= -4e+84) || !(t_1 <= 5e+168))
		tmp = Float64(Float64(Float64(-2.0 * b) * Float64(i * c)) * c);
	else
		tmp = Float64(fma(y, x, Float64(t * z)) * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+84], N[Not[LessEqual[t$95$1, 5e+168]], $MachinePrecision]], N[(N[(N[(-2.0 * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision], N[(N[(y * x + 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) < -4.00000000000000023e84 or 4.99999999999999967e168 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.6%

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

   3. Taylor expanded in c 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 67.2

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

   5. Applied rewrites 67.2%

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

   7. Applied rewrites 66.5%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999967e168

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84} \lor \neg \left(i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+168}\right):\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(-2 \cdot i\right) \cdot c\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot -2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -4e+84)
     (* (* (* -2.0 i) c) (* c b))
     (if (<= t_1 5e+168)
       (* (fma y x (* t z)) 2.0)
       (* (* (* (* c c) i) -2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -4e+84) {
		tmp = ((-2.0 * i) * c) * (c * b);
	} else if (t_1 <= 5e+168) {
		tmp = fma(y, x, (t * z)) * 2.0;
	} else {
		tmp = (((c * c) * i) * -2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -4e+84)
		tmp = Float64(Float64(Float64(-2.0 * i) * c) * Float64(c * b));
	elseif (t_1 <= 5e+168)
		tmp = Float64(fma(y, x, Float64(t * z)) * 2.0);
	else
		tmp = Float64(Float64(Float64(Float64(c * c) * i) * -2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+84], N[(N[(N[(-2.0 * i), $MachinePrecision] * c), $MachinePrecision] * N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+168], N[(N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(N[(c * c), $MachinePrecision] * i), $MachinePrecision] * -2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.00000000000000023e84

   1. Initial program 84.4%

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

   3. Taylor expanded in c 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

   7. Applied rewrites 67.8%

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

   9. Applied rewrites 71.9%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999967e168

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

   if 4.99999999999999967e168 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   3. Taylor expanded in c around 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(-2 \cdot i\right) \cdot c\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(c \cdot c\right) \cdot i\right) \cdot -2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(-2 \cdot i\right) \cdot c\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot i\right) \cdot \left(\left(c \cdot c\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -4e+84)
     (* (* (* -2.0 i) c) (* c b))
     (if (<= t_1 5e+168)
       (* (fma y x (* t z)) 2.0)
       (* (* -2.0 i) (* (* c c) b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -4e+84) {
		tmp = ((-2.0 * i) * c) * (c * b);
	} else if (t_1 <= 5e+168) {
		tmp = fma(y, x, (t * z)) * 2.0;
	} else {
		tmp = (-2.0 * i) * ((c * c) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -4e+84)
		tmp = Float64(Float64(Float64(-2.0 * i) * c) * Float64(c * b));
	elseif (t_1 <= 5e+168)
		tmp = Float64(fma(y, x, Float64(t * z)) * 2.0);
	else
		tmp = Float64(Float64(-2.0 * i) * Float64(Float64(c * c) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+84], N[(N[(N[(-2.0 * i), $MachinePrecision] * c), $MachinePrecision] * N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+168], N[(N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(-2.0 * i), $MachinePrecision] * N[(N[(c * c), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.00000000000000023e84

   1. Initial program 84.4%

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

   3. Taylor expanded in c 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

   7. Applied rewrites 67.8%

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

   9. Applied rewrites 71.9%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999967e168

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

   if 4.99999999999999967e168 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   3. Taylor expanded in c around 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

   7. Applied rewrites 62.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(-2 \cdot i\right) \cdot c\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(-2 \cdot i\right) \cdot \left(\left(c \cdot c\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(-2 \cdot i\right) \cdot c\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (<= t_1 -4e+84)
     (* (* (* -2.0 i) c) (* c b))
     (if (<= t_1 5e+168)
       (* (fma y x (* t z)) 2.0)
       (* (* (* -2.0 b) (* i c)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (((c * b) + a) * c);
	double tmp;
	if (t_1 <= -4e+84) {
		tmp = ((-2.0 * i) * c) * (c * b);
	} else if (t_1 <= 5e+168) {
		tmp = fma(y, x, (t * z)) * 2.0;
	} else {
		tmp = ((-2.0 * b) * (i * c)) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if (t_1 <= -4e+84)
		tmp = Float64(Float64(Float64(-2.0 * i) * c) * Float64(c * b));
	elseif (t_1 <= 5e+168)
		tmp = Float64(fma(y, x, Float64(t * z)) * 2.0);
	else
		tmp = Float64(Float64(Float64(-2.0 * b) * Float64(i * c)) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+84], N[(N[(N[(-2.0 * i), $MachinePrecision] * c), $MachinePrecision] * N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+168], N[(N[(y * x + N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(-2.0 * b), $MachinePrecision] * N[(i * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.00000000000000023e84

   1. Initial program 84.4%

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

   3. Taylor expanded in c 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

   7. Applied rewrites 67.8%

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

   9. Applied rewrites 71.9%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999967e168

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

   if 4.99999999999999967e168 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   3. Taylor expanded in c around 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

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

   7. Applied rewrites 61.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(-2 \cdot i\right) \cdot c\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot b\right) \cdot \left(i \cdot c\right)\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(\left(c \cdot b + a\right) \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+84} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+293}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* (+ (* c b) a) c))))
   (if (or (<= t_1 -4e+84) (not (<= t_1 2e+293)))
     (* (* (* i c) a) -2.0)
     (* (fma y x (* 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 = i * (((c * b) + a) * c);
	double tmp;
	if ((t_1 <= -4e+84) || !(t_1 <= 2e+293)) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = fma(y, x, (t * z)) * 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(Float64(Float64(c * b) + a) * c))
	tmp = 0.0
	if ((t_1 <= -4e+84) || !(t_1 <= 2e+293))
		tmp = Float64(Float64(Float64(i * c) * a) * -2.0);
	else
		tmp = Float64(fma(y, x, Float64(t * z)) * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(N[(N[(c * b), $MachinePrecision] + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+84], N[Not[LessEqual[t$95$1, 2e+293]], $MachinePrecision]], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(y * x + 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) < -4.00000000000000023e84 or 1.9999999999999998e293 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 81.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   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 43.8

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

   5. Applied rewrites 43.8%

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

   if -4.00000000000000023e84 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999998e293

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq -4 \cdot 10^{+84} \lor \neg \left(i \cdot \left(\left(c \cdot b + a\right) \cdot c\right) \leq 2 \cdot 10^{+293}\right):\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t \cdot z\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot x\right) \cdot 2\\ \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+59}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 2\\ \mathbf{elif}\;y \cdot x \leq 4 \cdot 10^{+109}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* y x) 2.0)))
   (if (<= (* y x) -5e+116)
     t_1
     (if (<= (* y x) 2e+59)
       (* (* t z) 2.0)
       (if (<= (* y x) 4e+109) (* (* (* i c) a) -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 = (y * x) * 2.0;
	double tmp;
	if ((y * x) <= -5e+116) {
		tmp = t_1;
	} else if ((y * x) <= 2e+59) {
		tmp = (t * z) * 2.0;
	} else if ((y * x) <= 4e+109) {
		tmp = ((i * c) * a) * -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 = (y * x) * 2.0d0
    if ((y * x) <= (-5d+116)) then
        tmp = t_1
    else if ((y * x) <= 2d+59) then
        tmp = (t * z) * 2.0d0
    else if ((y * x) <= 4d+109) then
        tmp = ((i * c) * a) * (-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 = (y * x) * 2.0;
	double tmp;
	if ((y * x) <= -5e+116) {
		tmp = t_1;
	} else if ((y * x) <= 2e+59) {
		tmp = (t * z) * 2.0;
	} else if ((y * x) <= 4e+109) {
		tmp = ((i * c) * a) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * x) * 2.0
	tmp = 0
	if (y * x) <= -5e+116:
		tmp = t_1
	elif (y * x) <= 2e+59:
		tmp = (t * z) * 2.0
	elif (y * x) <= 4e+109:
		tmp = ((i * c) * a) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * x) * 2.0)
	tmp = 0.0
	if (Float64(y * x) <= -5e+116)
		tmp = t_1;
	elseif (Float64(y * x) <= 2e+59)
		tmp = Float64(Float64(t * z) * 2.0);
	elseif (Float64(y * x) <= 4e+109)
		tmp = Float64(Float64(Float64(i * c) * a) * -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 = (y * x) * 2.0;
	tmp = 0.0;
	if ((y * x) <= -5e+116)
		tmp = t_1;
	elseif ((y * x) <= 2e+59)
		tmp = (t * z) * 2.0;
	elseif ((y * x) <= 4e+109)
		tmp = ((i * c) * a) * -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[(N[(y * x), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(y * x), $MachinePrecision], -5e+116], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 2e+59], N[(N[(t * z), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 4e+109], N[(N[(N[(i * c), $MachinePrecision] * a), $MachinePrecision] * -2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000025e116 or 3.99999999999999993e109 < (*.f64 x y)

   1. Initial program 87.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.1

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

   5. Applied rewrites 60.1%

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

   if -5.00000000000000025e116 < (*.f64 x y) < 1.99999999999999994e59

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 39.7

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

   5. Applied rewrites 39.7%

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

   if 1.99999999999999994e59 < (*.f64 x y) < 3.99999999999999993e109

   1. Initial program 93.2%

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

   3. Taylor expanded in 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 60.4

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

   5. Applied rewrites 60.4%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+116}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+59}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 2\\ \mathbf{elif}\;y \cdot x \leq 4 \cdot 10^{+109}:\\ \;\;\;\;\left(\left(i \cdot c\right) \cdot a\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+116} \lor \neg \left(y \cdot x \leq 10^{+60}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* y x) -5e+116) (not (<= (* y x) 1e+60)))
   (* (* y x) 2.0)
   (* (* t z) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((y * x) <= -5e+116) || !((y * x) <= 1e+60)) {
		tmp = (y * x) * 2.0;
	} else {
		tmp = (t * z) * 2.0;
	}
	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 (((y * x) <= (-5d+116)) .or. (.not. ((y * x) <= 1d+60))) then
        tmp = (y * x) * 2.0d0
    else
        tmp = (t * z) * 2.0d0
    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 (((y * x) <= -5e+116) || !((y * x) <= 1e+60)) {
		tmp = (y * x) * 2.0;
	} else {
		tmp = (t * z) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((y * x) <= -5e+116) or not ((y * x) <= 1e+60):
		tmp = (y * x) * 2.0
	else:
		tmp = (t * z) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(y * x) <= -5e+116) || !(Float64(y * x) <= 1e+60))
		tmp = Float64(Float64(y * x) * 2.0);
	else
		tmp = Float64(Float64(t * z) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((y * x) <= -5e+116) || ~(((y * x) <= 1e+60)))
		tmp = (y * x) * 2.0;
	else
		tmp = (t * z) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(y * x), $MachinePrecision], -5e+116], N[Not[LessEqual[N[(y * x), $MachinePrecision], 1e+60]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.00000000000000025e116 or 9.9999999999999995e59 < (*.f64 x y)

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.6

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

   5. Applied rewrites 55.6%

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

   if -5.00000000000000025e116 < (*.f64 x y) < 9.9999999999999995e59

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 39.4

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

   5. Applied rewrites 39.4%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+116} \lor \neg \left(y \cdot x \leq 10^{+60}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \left(y \cdot x\right) \cdot 2 \end{array} \]

FPCore

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

C

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

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 = (y * x) * 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 25.2

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

5. Applied rewrites 25.2%

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

6. Final simplification 25.2%

   \[\leadsto \left(y \cdot x\right) \cdot 2 \]
7. Add Preprocessing

Developer Target 1: 94.3% 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 2024271 
(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))))