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

Percentage Accurate: 89.6% → 96.3%

Time: 4.2s

Alternatives: 15

Speedup: 0.5×

• 48.2% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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: 89.6% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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: 96.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))) < +inf.0

   1. Initial program 89.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower-neg.f64 94.6

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 95.0

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 95.0

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

   3. Applied rewrites 95.0%

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

   if +inf.0 < (*.f64 #s(literal 2 binary64) (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)))

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. lift-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-fma.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

   6. Applied rewrites 69.6%

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

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(c, b, a\right), \left(-c\right) \cdot i, t \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+257}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, t \cdot z - i \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 (- INFINITY))
     (* 2.0 (fma (fma c b a) (* (- c) i) (* t z)))
     (if (<= t_1 1e+257)
       (* 2.0 (fma y x (- (* t z) (* i (* (fma c b a) c)))))
       (* (fma b c a) (* (* i c) -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 2.0 * fma(fma(c, b, a), (-c * i), (t * z));
	} else if (t_1 <= 1e+257) {
		tmp = 2.0 * fma(y, x, ((t * z) - (i * (fma(c, b, a) * c))));
	} else {
		tmp = fma(b, c, a) * ((i * c) * -2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(2.0 * fma(fma(c, b, a), Float64(Float64(-c) * i), Float64(t * z)));
	elseif (t_1 <= 1e+257)
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(t * z) - Float64(i * Float64(fma(c, b, a) * c)))));
	else
		tmp = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(2.0 * N[(N[(c * b + a), $MachinePrecision] * N[((-c) * i), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+257], N[(2.0 * N[(y * x + N[(N[(t * z), $MachinePrecision] - N[(i * N[(N[(c * b + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $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 89.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower-neg.f64 94.6

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 95.0

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 95.0

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

   3. Applied rewrites 95.0%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 73.9

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

   6. Applied rewrites 73.9%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.00000000000000003e257

   1. Initial program 89.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 91.3

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 91.3

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 91.3

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 91.3

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

   3. Applied rewrites 91.3%

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

   if 1.00000000000000003e257 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

Alternative 3: 88.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(t\_1 \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot t\_1\right)\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, \left(-i\right) \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* t_1 c) i)))
   (if (<= t_2 -1e+303)
     (* -2.0 (* c (* i t_1)))
     (if (<= t_2 -5e+137)
       (* 2.0 (fma y x (* (- i) (* (fma b c a) c))))
       (if (<= t_2 5e+157)
         (* 2.0 (- (fma t z (* x y)) (* a (* c i))))
         (* (fma b c a) (* (* i c) -2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (t_1 * c) * i;
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = -2.0 * (c * (i * t_1));
	} else if (t_2 <= -5e+137) {
		tmp = 2.0 * fma(y, x, (-i * (fma(b, c, a) * c)));
	} else if (t_2 <= 5e+157) {
		tmp = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	} else {
		tmp = fma(b, c, a) * ((i * c) * -2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(t_1 * c) * i)
	tmp = 0.0
	if (t_2 <= -1e+303)
		tmp = Float64(-2.0 * Float64(c * Float64(i * t_1)));
	elseif (t_2 <= -5e+137)
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(-i) * Float64(fma(b, c, a) * c))));
	elseif (t_2 <= 5e+157)
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+303], N[(-2.0 * N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+137], N[(2.0 * N[(y * x + N[((-i) * N[(N[(b * c + a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+157], N[(2.0 * N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1e303

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

   if -1e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000002e137

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. lift-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-fma.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

   6. Applied rewrites 69.6%

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

   if -5.0000000000000002e137 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.4

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

   4. Applied rewrites 73.4%

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

   if 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

Alternative 4: 88.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, \left(-i\right) \cdot \left(\left(b \cdot c\right) \cdot c\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* (* i c) -2.0))) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -2e+298)
     t_1
     (if (<= t_2 -5e+137)
       (* 2.0 (fma y x (* (- i) (* (* b c) c))))
       (if (<= t_2 5e+157) (* 2.0 (- (fma t z (* x y)) (* a (* c i)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * ((i * c) * -2.0);
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -2e+298) {
		tmp = t_1;
	} else if (t_2 <= -5e+137) {
		tmp = 2.0 * fma(y, x, (-i * ((b * c) * c)));
	} else if (t_2 <= 5e+157) {
		tmp = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -2e+298)
		tmp = t_1;
	elseif (t_2 <= -5e+137)
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(-i) * Float64(Float64(b * c) * c))));
	elseif (t_2 <= 5e+157)
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+298], t$95$1, If[LessEqual[t$95$2, -5e+137], N[(2.0 * N[(y * x + N[((-i) * N[(N[(b * c), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+157], N[(2.0 * N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.9999999999999999e298 or 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

   if -1.9999999999999999e298 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000002e137

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. lift-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-fma.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

   6. Applied rewrites 69.6%

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

   7. Taylor expanded in a around 0

      \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \left(-i\right) \cdot \left(\left(b \cdot c\right) \cdot c\right)\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 55.1

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

   9. Applied rewrites 55.1%

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

   if -5.0000000000000002e137 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.4

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

   4. Applied rewrites 73.4%

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

Alternative 5: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(c, b, a\right), \left(-c\right) \cdot i, t \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -4e+98)
     (* 2.0 (fma (fma c b a) (* (- c) i) (* t z)))
     (if (<= t_1 5e+157)
       (* 2.0 (- (fma t z (* x y)) (* a (* c i))))
       (* (fma b c a) (* (* i c) -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -4e+98) {
		tmp = 2.0 * fma(fma(c, b, a), (-c * i), (t * z));
	} else if (t_1 <= 5e+157) {
		tmp = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	} else {
		tmp = fma(b, c, a) * ((i * c) * -2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -4e+98)
		tmp = Float64(2.0 * fma(fma(c, b, a), Float64(Float64(-c) * i), Float64(t * z)));
	elseif (t_1 <= 5e+157)
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+98], N[(2.0 * N[(N[(c * b + a), $MachinePrecision] * N[((-c) * i), $MachinePrecision] + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+157], N[(2.0 * N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -3.99999999999999999e98

   1. Initial program 89.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lower-neg.f64 94.6

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 95.0

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 95.0

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

   3. Applied rewrites 95.0%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 73.9

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

   6. Applied rewrites 73.9%

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

   if -3.99999999999999999e98 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.4

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

   4. Applied rewrites 73.4%

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

   if 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

Alternative 6: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;\left(x \cdot y - \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right) \cdot c\right) \cdot 2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(t, z, x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+137)
     (* (- (* x y) (* (* (fma b c a) i) c)) 2.0)
     (if (<= t_1 5e+157)
       (* 2.0 (- (fma t z (* x y)) (* a (* c i))))
       (* (fma b c a) (* (* i c) -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+137) {
		tmp = ((x * y) - ((fma(b, c, a) * i) * c)) * 2.0;
	} else if (t_1 <= 5e+157) {
		tmp = 2.0 * (fma(t, z, (x * y)) - (a * (c * i)));
	} else {
		tmp = fma(b, c, a) * ((i * c) * -2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+137)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(fma(b, c, a) * i) * c)) * 2.0);
	elseif (t_1 <= 5e+157)
		tmp = Float64(2.0 * Float64(fma(t, z, Float64(x * y)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+137], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(N[(b * c + a), $MachinePrecision] * i), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+157], N[(2.0 * N[(N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000002e137

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.5

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

   6. Applied rewrites 68.5%

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

   if -5.0000000000000002e137 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.4

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

   4. Applied rewrites 73.4%

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

   if 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

Alternative 7: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, \left(-i\right) \cdot \left(\left(b \cdot c\right) \cdot c\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* (* i c) -2.0))) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -2e+298)
     t_1
     (if (<= t_2 -5e+137)
       (* 2.0 (fma y x (* (- i) (* (* b c) c))))
       (if (<= t_2 5e+157) (* 2.0 (fma t z (* x y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * ((i * c) * -2.0);
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -2e+298) {
		tmp = t_1;
	} else if (t_2 <= -5e+137) {
		tmp = 2.0 * fma(y, x, (-i * ((b * c) * c)));
	} else if (t_2 <= 5e+157) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -2e+298)
		tmp = t_1;
	elseif (t_2 <= -5e+137)
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(-i) * Float64(Float64(b * c) * c))));
	elseif (t_2 <= 5e+157)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+298], t$95$1, If[LessEqual[t$95$2, -5e+137], N[(2.0 * N[(y * x + N[((-i) * N[(N[(b * c), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+157], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.9999999999999999e298 or 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

   if -1.9999999999999999e298 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -5.0000000000000002e137

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

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

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

      11. lift-neg.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lift-fma.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-fma.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

   6. Applied rewrites 69.6%

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

   7. Taylor expanded in a around 0

      \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \left(-i\right) \cdot \left(\left(b \cdot c\right) \cdot c\right)\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 55.1

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

   9. Applied rewrites 55.1%

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

   if -5.0000000000000002e137 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

Alternative 8: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(\left(i \cdot c\right) \cdot -2\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* (* i c) -2.0))) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -4e+98)
     t_1
     (if (<= t_2 5e+157) (* 2.0 (fma t z (* x y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * ((i * c) * -2.0);
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -4e+98) {
		tmp = t_1;
	} else if (t_2 <= 5e+157) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(Float64(i * c) * -2.0))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -4e+98)
		tmp = t_1;
	elseif (t_2 <= 5e+157)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(N[(i * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+98], t$95$1, If[LessEqual[t$95$2, 5e+157], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -3.99999999999999999e98 or 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. lift-*.f64 N/A

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

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

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. lower-fma.f64 N/A

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

      21. lift-*.f64 N/A

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

      22. lift-neg.f64 N/A

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

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

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

      24. lift-*.f64 N/A

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

   6. Applied rewrites 50.3%

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

   if -3.99999999999999999e98 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

Alternative 9: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right) \cdot \left(i \cdot -2\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (fma b c a) c) (* i -2.0))) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -4e+98)
     t_1
     (if (<= t_2 5e+157) (* 2.0 (fma t z (* x y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (fma(b, c, a) * c) * (i * -2.0);
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -4e+98) {
		tmp = t_1;
	} else if (t_2 <= 5e+157) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(fma(b, c, a) * c) * Float64(i * -2.0))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -4e+98)
		tmp = t_1;
	elseif (t_2 <= 5e+157)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(b * c + a), $MachinePrecision] * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+98], t$95$1, If[LessEqual[t$95$2, 5e+157], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -3.99999999999999999e98 or 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lift-*.f64 N/A

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

      18. lower-fma.f64 N/A

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

      19. lower-*.f64 48.0

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

   6. Applied rewrites 48.0%

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

   if -3.99999999999999999e98 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

Alternative 10: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+292}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(i \cdot b\right) \cdot c\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+292)
     (* -2.0 (* c (* (* i b) c)))
     (if (<= t_1 5e+157)
       (* 2.0 (fma t z (* x y)))
       (* -2.0 (* c (* b (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+292) {
		tmp = -2.0 * (c * ((i * b) * c));
	} else if (t_1 <= 5e+157) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+292)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(i * b) * c)));
	elseif (t_1 <= 5e+157)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+292], N[(-2.0 * N[(c * N[(N[(i * b), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+157], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999996e292

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   7. Applied rewrites 34.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 33.7

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

   9. Applied rewrites 33.7%

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

   if -4.9999999999999996e292 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

   if 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   7. Applied rewrites 34.6%

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

Alternative 11: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+292}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* (+ a (* b c)) c) i)))
   (if (<= t_1 -5e+292)
     (* -2.0 (* c (* (* b c) i)))
     (if (<= t_1 5e+157)
       (* 2.0 (fma t z (* x y)))
       (* -2.0 (* c (* b (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_1 <= -5e+292) {
		tmp = -2.0 * (c * ((b * c) * i));
	} else if (t_1 <= 5e+157) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_1 <= -5e+292)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(b * c) * i)));
	elseif (t_1 <= 5e+157)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+292], N[(-2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+157], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999996e292

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   7. Applied rewrites 34.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 33.8

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

   9. Applied rewrites 33.8%

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

   if -4.9999999999999996e292 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

   if 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   7. Applied rewrites 34.6%

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

Alternative 12: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* b (* c i))))) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -5e+292)
     t_1
     (if (<= t_2 5e+157) (* 2.0 (fma t z (* x y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -5e+292) {
		tmp = t_1;
	} else if (t_2 <= 5e+157) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -5e+292)
		tmp = t_1;
	elseif (t_2 <= 5e+157)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+292], t$95$1, If[LessEqual[t$95$2, 5e+157], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999996e292 or 4.99999999999999976e157 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-*.f64 48.2

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

   4. Applied rewrites 48.2%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   7. Applied rewrites 34.6%

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

   if -4.9999999999999996e292 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999976e157

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

Alternative 13: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+254}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(t, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* a (* c i)))) (t_2 (* (* (+ a (* b c)) c) i)))
   (if (<= t_2 -2e+298)
     t_1
     (if (<= t_2 5e+254) (* 2.0 (fma t z (* x y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = ((a + (b * c)) * c) * i;
	double tmp;
	if (t_2 <= -2e+298) {
		tmp = t_1;
	} else if (t_2 <= 5e+254) {
		tmp = 2.0 * fma(t, z, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(a * Float64(c * i)))
	t_2 = Float64(Float64(Float64(a + Float64(b * c)) * c) * i)
	tmp = 0.0
	if (t_2 <= -2e+298)
		tmp = t_1;
	elseif (t_2 <= 5e+254)
		tmp = Float64(2.0 * fma(t, z, Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+298], t$95$1, If[LessEqual[t$95$2, 5e+254], N[(2.0 * N[(t * z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -1.9999999999999999e298 or 4.99999999999999994e254 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 89.6%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 26.2

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

   4. Applied rewrites 26.2%

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

   if -1.9999999999999999e298 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999994e254

   1. Initial program 89.6%

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

   2. Taylor expanded in c around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 53.8

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

   4. Applied rewrites 53.8%

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

Alternative 14: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + z\right) \cdot t\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+43}:\\ \;\;\;\;\left(y + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ z z) t)))
   (if (<= (* z t) -2e-15) t_1 (if (<= (* z t) 2e+43) (* (+ y y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z + z) * t;
	double tmp;
	if ((z * t) <= -2e-15) {
		tmp = t_1;
	} else if ((z * t) <= 2e+43) {
		tmp = (y + y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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 = (z + z) * t
    if ((z * t) <= (-2d-15)) then
        tmp = t_1
    else if ((z * t) <= 2d+43) then
        tmp = (y + y) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z + z) * t;
	double tmp;
	if ((z * t) <= -2e-15) {
		tmp = t_1;
	} else if ((z * t) <= 2e+43) {
		tmp = (y + y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z + z) * t
	tmp = 0
	if (z * t) <= -2e-15:
		tmp = t_1
	elif (z * t) <= 2e+43:
		tmp = (y + y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z + z) * t)
	tmp = 0.0
	if (Float64(z * t) <= -2e-15)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e+43)
		tmp = Float64(Float64(y + y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z + z) * t;
	tmp = 0.0;
	if ((z * t) <= -2e-15)
		tmp = t_1;
	elseif ((z * t) <= 2e+43)
		tmp = (y + y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z + z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e-15], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e+43], N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.0000000000000002e-15 or 2.00000000000000003e43 < (*.f64 z t)

   1. Initial program 89.6%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 29.5

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

   4. Applied rewrites 29.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. count-2-rev N/A

         \[\leadsto \left(z + z\right) \cdot t \]

      7. lower-+.f64 29.5

         \[\leadsto \left(z + z\right) \cdot t \]

   6. Applied rewrites 29.5%

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

   if -2.0000000000000002e-15 < (*.f64 z t) < 2.00000000000000003e43

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 27.5

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

   4. Applied rewrites 27.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. count-2-rev N/A

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

      7. lower-+.f64 27.5

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

   6. Applied rewrites 27.5%

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

Alternative 15: 27.5% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    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 + y) * x
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 + y) * x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

2. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 27.5

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

4. Applied rewrites 27.5%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-*r* N/A

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

   5. lower-*.f64 N/A

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

   6. count-2-rev N/A

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

   7. lower-+.f64 27.5

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

6. Applied rewrites 27.5%

   \[\leadsto \left(y + y\right) \cdot \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025154 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))